Journal papers by Gawthrop for all years

The implementation of a class of self-tuning controllers using a portable microcomputer system is described. The self-tuning control theory is shown to provide a variety of control objectives such as model-reference, optimal Smith prediction and the minimization of a general k-step-ahead cost-function. Hardware and software details of the portable computer, SESAME, are presented with particular reference to the use of a new high-level language, Control Basic. Studies of the application of self-tuning to the control of room-temperature, acid neutralization, and batch chemical reactors in industry are outlined.

The paper shows how a certain self-tuning algorithm can be interpreted as a self-tuning PI controller, and this algorithm has been successfully tested on a full-scale pH neutralisation process. Extended trials showed that although this process could be well controlled by a fixed parameter PI controller, the self-tuning algorithm could easily find suitable fixed parameter values for the controller, whereas human operators found the tuning difficult, if not impossible.

Keywords: PI control;pH neutralisation process;self-tuning;pH control;self-adjusting systems;two-term control;

A `linear-in-the-parameters¿ representation is derived for a data set formed by concatenating a number of input-output data records which, although arising from the same system, are not contiguous in time. As well as parameters describing the system, further `splicing parameters¿ arise from the discontinuities in the concatenated data records at the joins. This representation gives rise to a method of `data splicing¿ which enables system parameters to be recursively identified from the concatenated data records. The method is particularly useful when each individual data record is not, by itself, sufficient to identify the system parameters. The method is developed for noise-free differential equation models, but the basic principles are more widely applicable. An illustrative example is given.

Keywords: parameter estimation;discontinuities;input-output data records;noise-free differential equation models;parameter estimation;splicing parameters

The state-variable filter method of continuous-time parameter identification using a discrete-time identifier is extended to be applicable to signals composed of a transient response generated by a class of unforced nonlinear systems to which has been added a constant offset. The results are illustrated by estimating some hydrodynamic coefficients of a ship from free decay data; and some implications for self-tuning control are discussed.

An algorithm for the exact least-squares identification of an approximate continuous-time time-delay system is derived and its operation verified by simulation.

Keywords: Time-delay, Continuous-time identification, Non-linear identification

A continuous-time self-tuning controller, based on the well-known discrete-time generalized minimum-variance self-tuning controller, is introduced. Using input—output stability methods, frequency domain conditions are derived which ensure L∞ stability in the face of multiplicative process perturbations. The analysis is illustrated using an example of Rohrs et al.

Keywords: Self-tuning, Adaptive, Stability, Robustness

In the paper the authors describe two tools for use in an intelligent fault-detection system. The first tool is a method for fault localisation, called constraint suspension, which helps us find and identify the parts suspension, which helps us find and identify the parts of the process which are responsible for any inconsistencies in the measurements. The second tool gives us a flexible framework in which we can build a software model of the process in terms of hierarchies of component parts or objects, it is called object orientation. We use these tools to describe algorithms for automatic fault detection in a physical process plant. The algorithms are tested on a simulation of a liquid level control system.

Keywords: constraint suspension;fault detection;intelligent fault-detection system;liquid level control system;object orientation;parts suspension;process control;software model;control system analysis;fault location;level control;process computer control;

The results of an earlier paper concerning global robustness of single-loop self-tuning controllers are extended to include multiple self-tuning controllers operating in a multiple-interacting-loop environment. The robust stability is shown to depend on the singular value loci of a certain transfer function matrix. The need for control weighting to ensure global robust stability is emphasized.

Keywords: Adaptive control, Robust stability, Multivariable control

A standard general algorithm, the stochastic approximation algorithm of Albert and Gardner [1], is applied in a new context to compute the weights of a multilayer perceptron network. This leads to a new algorithm, the gain backpropagation algorithm, which is related to, but significantly different from, the standard backpropagation algorithm [2]. Some simulation examples show the potential and limitations of the proposed approach and provide comparisons with the conventional backpropagation algorithm.

A tutorial introduction to the use of bond graphs in modelling mechatronic systems is given. Four illustrative examples of increasing complexity are given, culminating in a two link robotic arm with flexible drives. The role of symbolic algebra techniques in this context is emphasized and it is suggested that the marriage of bond graphs and symbolic techniques provides the basis of computer-based support tools for the analysis and design of mechatronic systems.

A systematic approach to constructing dynamic models involving phase equilibrium is presented.

The view appears to be widely held that the dynamic modelling of VLE systems invariably leads to an "index problem". We show that this in general is not the case if an appropriate model formulation is used. This is provided by our systematic procedure.

Index problems do in general occur when a state variable is constrained by an implied control system. Some properties of such systems are discussed and it is shown that it may not in practice be useful to attempt the solution of intractable index problems, as these may differ substantially from the behaviour of an achievable control system.

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The concepts of partially-known system identification are introduced and the advantages of a method whereby process information can be utilized in a linear transfer function representation of the system are highlighted and discussed. In particular, an algorithm for identifying a single unknown physical system parameter associated with a linear system is given. It is assumed that the system is polynomial (as opposed to linear) in the physical parameter. The Bond graph representation is used as the basis for deriving a system-dependent algorithm for each partially-known system. The method is illustrated by simulated examples.

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An algorithm for the causal augmentation of bond graphs with algebraic loops is given. Unlike previous algorithms, this involves bond graph rather than equation manipulation. A number of illustrative examples are given.

Keywords: 11

This paper focuses on the promise of artificial neural networks in the realm of modelling, identification and control of nonlinear systems. The basic ideas and techniques of artificial neural networks are presented in language and notation familiar to control engineers. Applications of a variety of neural network architectures in control are surveyed. We explore the links between the fields of control science and neural networks in a unified presentation and identify key areas for future research.

Keywords:

A bond graph representation of model-based observer control is introduced and shown to provide a convenient framework for the design of controllers in the physical domain. The approach is illustrated by a series of examples and the robustness of the method is investigated by simulation.

In robotics, high-precision measurements of link positions are available for feedback control but tachometer measurements of link velocities are often severely contaminated by noise. This paper presents the use of a bond-graph model-based nonlinear observer to estimate the velocities in the control of an experimental two-link manipulator. A significant advantage of this approach is that the observer software may be written automatically from the bond-graph observer representation. Results are presented in simulation form, and for practical implementation on the experimental arm.

Keywords: Robots, modelling, bond graphs, state estimation, position control

Two alternative approaches to controller design, the internal model control (IMC) of Morari and Zafiriou [Morari, M. and E. Zafiriou (1989). Robust Process Control. Prentice Hall, Englewood Cliffs, NJ] and the emulator-based control (EBC) of Gawthrop [Gawthrop, P. J. (1987). Continuous-time Self-tuning Control. Vol. 1: Design, Engineering Control Series. Research Studies Press, Lechworth, U.K.] (based on the generalized minimum variance control of Clarke and Gawthrop [Clarke, D. W. and P. J. Gawthrop (1975). Self-tuning controller. Proc. IEE, 122(9), 929–934. Clarke, D. W. and P. J. Gawthrop (1979). Self-tuning control. Proc. IEE, 126(6), 640–6333. Gawthrop, P. J. (1977). Some interpretations of the self-tuning controller. Proc. IEE, 124(10), 889–894]) are shown to differ only superficially in approach and notation. This result provides a link between robust control based on IMC and adaptive control based on EBC.

Keywords: Control system analysis, internal model control

In the pursuit of generic methods, control theory has become separated from its prime objective: the control of physical systems. These generic techniques have a wide range of applications yet do not easily allow inclusion of system specific information into the control design. There are two important categories for which the inclusion of system-specific information is important: partially-known systems and non-linear systems. Physical-Model Based Control (PMBC) is a novel approach to using such system-specific information. The objective of this paper is to demonstrate the experimental application of PMBC to a partiallyknown nonlinear system. In so doing, the performance of the PMBC method is evaluated, and it is demonstrated how process and control engineering insights can be combined within this PMBC framework to yield a novel system-specific control algorithm.

Keywords: state estimation, model-based control, partially-known systems

In order to achieve the best possible control of a particular system, it is clear that as much information about the system as possible should be used when designing the controller. This leads to a controller specifically tailored to the system being controlled. Unfortunately, this is expensive in terms of design time and expertise, and a number of approaches have been suggested to overcome this problem. The approach taken by physical-model-based control is to model the system in a generic manner and then automatically design the controller based on this model. This process requires symbolic algebra to enable the controller to be designed

The multivariable continuous-time generalised predictive controller (CGPC) is recast in a state-space form and shown to include generalised minimum variance (GMV) and a new algorithm, predictive GMV (PGMV) as special cases. Comparisons are drawn with the exact linearisation methods of nonlinear control, and it is noted that, unlike the transfer function approach, the state-space approach extends readily to the nonlinear case. The resulting state space design algorithms are conceptually and algorithmically simpler than the corresponding transfer function based versions and have been realised as a freely available Matlab tool-box

Keywords: CGPC;Matlab tool-box;PGMV;exact linearisation methods;generalised minimum variance;linear systems;multivariable continuous-time generalised predictive control ;nonlinear control;nonlinear systems;predictive GMV;state space design algorithms;state-space approach;transfer function based versions;multivariable control systems;nonlinear control systems;predictive control;state-space methods;

In conventional gain-scheduled control design, linearisation of a time-invariant nonlinear system and local control design for the resulting set of linear time-invariant systems is performed at a set of equilibrium points. Due to its validity only near equilibrium, such a design may result in poor transient performance. To resolve this problem, one can base the control design on a dynamic linearisation about some nominal trajectory. However, a drawback with this approach is that control design for the resulting linear time-varying system is in general a difficult problem. In this paper it is suggested that linearisation and local controller design should be carried out not only at equilibrium states, but also in transient operating regimes. It is shown that this results in a set of time-invariant linearisations which, when they are interpolated, form a close approximation to the time-varying system resulting from dynamic linearisation. Consequently, the transient performance can be improved by increasing the number of linear time-invariant controllers. The feasibility of this approach, and possible improvements in transient performance, are illustrated with results from an experimental vehicle speed-control application.

A new class of nonlinear PID controllers are derived for nonlinear systems using a nonlinear generalised predictive control (NGPC) approach. First, the disturbance decoupling ability of the NGPC is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable. It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system

Pseudo and true Bond Graphs have been seen as competing approaches to modelling thermodynamic systems. This paper provides a simple mechanism for mixing the two approaches to obtain the best features of each. In so doing, an alternative and more accessible approach to thermodynamic modelling than that provided by classical texts is given.

Analysis and simulation of non-linear inverse systems are sometimes necessary in the design of control systems particularly when trying to determine an input control required to achieve some predefined output specifications. But unlike physical systems which are proper, the inverse systems are very often improper leading to numerical problems in simulation as their models sometimes have a high index when written in the form of differential-algebraic equations (DAE). This paper provides an alternative approach whereby performance specifications and the physical system are combined within a single bond graph leading to a greatly simplified simulation problem.

A conceptual, and practical difficulty with the continuous-time generalised predictive controller is solved by replacing the continuously moving horizon by an intermittently moving horizon. This allows slow optimisation to occur concurrently with a fast control action. Some nonlinear simulations illustrate the potential of this approach.

An `incremental polynomial model-controller network' (IPMCN) is introduced. Smooth control switching is obtained from the use of odd polynomial controllers. The decomposition of the operating space, together with the construction of the network, is achieved on-line while controlling the system. The performance and robustness of this scheme are illustrated through various simulations.

A new nonlinear disturbance observer (NDO) for robotic manipulators is derived in this paper. The global exponential stability of the proposed disturbance observer (DO) is guaranteed by selecting design parameters, which depend on the maximum velocity and physical parameters of robotic manipulators. This new observer overcomes the disadvantages of existing DOs, which are designed or analyzed by linear system techniques. It can be applied in robotic manipulators for various purposes such as friction compensation, independent joint control, sensorless torque control and fault diagnosis. The performance of the proposed observer is demonstrated by the friction estimation and compensation for a two-link robotic manipulator. Both simulation and experimental results show the NDO works well

A sensitivity bond graph, of the same structure as the system bond graph, is shown to provide a simple and effective method of generating sensitivity functions of use in optimisation. The approach is illustrated in the context of partially-known system parameter and state estimation.

A physical interpretation of the inverse dynamics of linear and nonlinear systems is given in terms of the bond graph of the inverse system. It is argued that this interpretation yields physical insight to guide the control engineer. Examples are drawn from both robotic and process systems.

A new bond graph framework for sensitivity theory is applied to model-based predictive control, state estimation, and parameter estimation in the context of physical systems. The approach is illustrated using a nonlinear mechatronic system.

This paper proposes a state variable filter approach to continuous time system identification. Two topics are studied in the paper. The first topic is related to the choice of state variable filters. The strategy we adopt is to adjust the time constants of the state variable filters so that a prediction error criterion is minimized. As a result, the estimated model reaches a balance between bias and variances shown by a simulation example. The second topic is related to the choice of model structure. We extend a multiple model estimation algorithm, developed using UD factorization, to continuous time sysem identification. The estimation algorithm generates a set of candidate models, among which the 'best' model structure is found. A simulation example is used to demonstrate the efficacy of the proposed procedure, and an industrial case study on a food cooking extrusion process is given to illustrate the applicability of the algorithm.

The predictive pole-placement control method introduced in this paper embeds the classical pole-placement state feedback design into a quadratic optimisation based model-predictive formulation. This provides an alternative to model-predictive controllers which are based on linear-quadratic control. The theoretical properties of the controller in a linear continuous-time setting are presented and a number of illustrative examples are given. These results provide the foundation for novel linear and nonlinear constrained predictive control methods based on continuous-time models.

Good quality control of dynamical systems relies on good models of the controlled system; it follows that the control engineer must also be a good system modeller and have effective paradigms for supporting system modelling. Much control engineering is based on the block diagram paradigm. It will be argued in this Editorial that such use of the block diagram paradigm is unfortunate and that the bond graph paradigm is preferable for a number of reasons.

A resonant filter approach is proposed for direct identification of continuous-time transfer functions from input-output data when the input contains significant periodic components. The asymptotic properties of the method are analysed; in particular, the noise reduction properties are emphasized. A simulation example is given to demonstrate the properties of the algorithm. By using a set of experimental data collected from a food cooking extruder, the proposed method has been compared with a well-known frequency response method.

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile.

The virtual earth concept, well known to designers of active electronic circuits with operational amplifier components, is shown to have a novel bicausal bond graph interpretation. This leads to simplified bond graph modelling of such circuits. Some simple operational amplifier circuits, together with a more complex active filter are used to illustrate the approach. A complex electro-mechanical system shows that the method is useful in creating a unified bond graph model of systems involving both analogue electronic and mechanical systems.

A bond-graph based approach to design in the physical domain is described which uses the concept of virtual actuators and virtual sensors.

The approach is illustrated by, and implemented on, an experimental ball and beam system

A nice feature of the LEGO system is that, although the mechanical, electrical, and structural construction is good enough for successful results, there are enough discrepancies between theory and practice to introduce the student to real-world problems of controller. This article concentrates on implementing the feedback controller within the RCX, with the host computer used for compiling, downloading, and data display. However, an interesting research project is to implement part of the controller on the host computer and communicate by means of the IR channel. The bandwidth restriction that this approach imposes can provide the basis for a research project on control through a restricted bandwidth channel.

A three-stage approach to system identification in the continuous time is presented which is appropriate for day-to-day application by plant engineers in the process industry. The three stages are: data acquisition using relay feedback; non-parametric identification of the system step response; and parametric model fitting of the identified step response. The method is evaluated on a pilot-scale food-cooking extruder.

The virtual actuator approach to bond graph based control is extended to use virtual sensor inputs. This allows relative degree conditions on the controller to be relaxed. Furthermore, the effect of the transfer system can be eliminated from the closed loop system. Illustrative examples are given.

A bond graph approach to hybrid simulation of dynamical systems using numerical-experimental real-time substructuring is presented. The bond graph concepts of a virtual junction and a virtual actuator, hitherto used in the context of physical-model based control, are used to perform the substructuring in an intuitively appealing way. The approach is illustrated by the reworking of a previously-published example.

The approach is verified experimentally using a bench-top multiple mass-spring system for the physical substructure and automatically generated real-time code is used to implement the numerical substructure.

A two-stage method for the identification of physical system parameters from experimental data is presented. The first stage compresses the data as an empirical model which encapsulates the data content at frequencies of interest. The second stage then uses data extracted from the empirical model of the first stage within a non-linear estimation scheme to estimate the unknown physical parameters. Furthermore, the paper proposes use of exponential data weighting in the identification of partially unknown, unstable systems so that they can be treated in the same framework of a stable system. Experimental data are used to demonstrate the efficacy of the proposed approach.

Predictive pole-placement (PPP) control is a continuous-time MPC using a particular set of basis functions leading to pole-placement behaviour in the unconstrained case. This paper presents two modified versions of the PPP controller which are each shown to have desirable stability properties when controlling systems with input, output and state constraints.

This paper considers the hybrid simulation of under-damped dynamical systems using numerical-experimental real-time substructuring. Substructuring joins together a physical plant with a numerical model using real-time control techniques, such that the combined model emulates the behaviour of the entire system. Due to the low damping, the control of substructured systems can be highly sensitive to delay and uncertainty. We present a technique for calculating the critical delay of the substructured system using a phase margin approach. In addition, it is shown that robustness techniques, drawn from feedback control theory, can be used to reduce the destabilising effect of uncertainty. To demonstrate this, a comparison of three different robustness compensators is presented, using a well-known linear system. The level of uncertainty is deliberately increased to compare their performances and a discussion is made on when each may be most useful.

Intermittent predictive pole-placement control is successfully applied to the constrained-state control of a prestabilised experimental inverted pendulum.

While standing naturally and when manually or pedally balancing an equivalent inverted pendulum, the load sways slowly (characteristic unidirectional duration  1s) and the controller, calf muscles or hand, makes more frequent adjustments (characteristic unidirectional duration 400ms). Here we test the hypothesis that these durations reflect load properties rather than some intrinsic property of the human neuromuscular system. Using a specialised setup mechanically analogous to real standing, subjects manually balanced inverted pendulums with different moments of inertia through a compliant spring representing the Achilles tendon. The spring bias was controlled by a sensitive joystick via a servo motor and accurate visual feedback was provided on an oscilloscope. As moment of inertia decreased inverted pendulum sway size increased and it became difficult to sustain successful balance. The mean duration of unidirectional balance adjustments did not change. Moreover, the mean duration of unidirectional inverted pendulum sway reduced only slightly remaining around 1 s. The simplest explanation is that balance was maintained by a process of manual adjustments intrinsically limited to a mean frequency of 2 to 3 unidirectional adjustments per second corresponding to intermittent control observed in manual tracking experiments. Consequently the inverted pendulum sway duration, mechanically related to the bias duration, reflects an intrinsic constraint of the neuromuscular control system. Given the similar durations of sway and muscle adjustments observed in real standing, we postulate that the characteristic duration of unidirectional standing sway reflects intrinsic intermittent control rather than the inertial properties of the body.

Bond graphs are primarily used in the network modeling of lumped parameter physical systems, but controller design with this graphical technique is relatively unexplored. It is shown that bond graphs can be used as a tool for certain model matching control designs. Some basic facts on the nonlinear model matching problem are recalled. The model matching problem is then associated with a particular disturbance decoupling problem, and it is demonstrated that bicausal assignment methods for bond graphs can be applied to solve the disturbance decoupling problem as to meet the model matching objective. The adopted bond graph approach is presented through a detailed example, which shows that the obtained controller induces port-Hamiltonian error dynamics. As a result, the closed loop system has an associated standard bond graph representation, thereby rendering energy shaping and damping injection possible from within a graphical context.

Hardware-in-the-loop (HWiL) is a form of component testing where hardware components are linked with software models. In order to test mechanical components an additional transfer system is required to link the software and hardware subsystems. The transfer system typically comprises sensors and actuators and the dynamic effects of these components need to be eliminated to give accurate results. In this paper an emulator-based control strategy is presented for actuator-based HWiL. Emulator-based control can solve the twin problems of stability and fidelity caused by the unwanted transfer system (actuator) dynamics. Significantly EBC can emulate the inverse of a transfer system which is not causally invertible, allowing a wider range of more complex transfer systems to be controlled. A robustness analysis is given and experimental results presented.

A bond graph framework giving a unified treatment of both physical model based control and hybrid experimental-numerical simulation (also known as real-time dynamic substructuring) is presented. The framework consists of two subsystems, one physical and one numerical, connected by a mphtransfer system representing non-ideal actuators and sensors. Within this context, a two-stage design procedure is proposed: firstly, design and/or analysis of the numerical and physical subsystem interconnection as if the transfer system were not present; and secondly removal of as much as possible of the transfer system dynamics while having regard for the stability margins established in the first stage. The approach allows the use of engineering insight backed up by well-established control theory; a number of possibilities for each stage are given. The approach is illustrated using two laboratory systems: an experimental mass-spring-damper substructured system and swing up and hold control of an inverted pendulum. Experimental results are provided in the latter case.

Intermittent control, where a sequence of open-loop trajectories are punctuated by intermittent feedback, is described and a number of design methods presented. A generalised hold representation is derived and shown to be useful for both implementation and analysis. The relationship between predictive control of a time delay system and intermittent control is examined and it is shown that a simplified predictor can be used in the latter case.

The applicability of intermittent control to the implementation of MPC is discussed and illustrated by the control of a difficult mechanical system -- a self-balancing seesaw.

A continuous time non-minimal state-space (NMSS) representation is shown to be explicitly related to the underlying minimal state-space observer/state feedback design method and, moreover, the corresponding state feedback gains are explicitly related. This result provides a starting point for NMSS methods in the continuous-time domain. Numerical examples are given which illustrate the underlying relationship.

Fitts' law is a well established empirical formula, known for encapsulating the “speed-accuracy trade-off”. For discrete, manual movements from a starting location to a target, Fitts' law relates movement duration to the distance moved and target size. The widespread empirical success of the formula is suggestive of underlying principles of human movement control. There have been previous attempts to relate Fitts' law to engineering-type control hypotheses and it has been shown that the law is exactly consistent with the closed-loop step-response of a time-delayed, first-order system. Assuming only the operation of closed-loop feedback, either continuous or intermittent, this paper asks whether such feedback should be predictive or not predictive to be consistent with Fitts law. Since Fitts' law is equivalent to a time delay separated from a first-order system, known control theory implies that the controller must be predictive. A predictive controller moves the time-delay outside the feedback loop such that the closed- loop response can be separated into a time delay and rational function whereas a non- predictive controller retains a state delay within feedback loop which is not consistent with Fitts' law. Using sufficient parameters, a high-order non-predictive controller could approximately reproduce Fitts' law. However, such high-order, “non-parametric” controllers are essentially empirical in nature, without physical meaning, and therefore are conceptually inferior to the predictive controller. It is a new insight that using closed-loop feedback, prediction is required to physically explain Fitts' law. The implication is that prediction is an inherent part of the “speed-accuracy trade-off”.

Causality, in the bond graph sense, is shown to provide a conceptual framework for the design of real-time dynamic substructure testing experiments. In particular, known stability problems with split-inertia substructured systems are reinterpreted as causality issues within the new conceptual framework. As an example, causality analysis is used to provide a practical solution to a split-inertia substructuring problem and the solution is experimentally verified.

Intermittent control is a feedback control design method that combines both continuous-time and discrete-time domains; a recent result shows that this form of intermittent control can be rewritten as a sampled-data feedback system with a particular vector generalised hold. This paper builds on this result to give, for the first time, a frequency domain analysis of the closed-loop system containing an intermittent controller.

This analysis is illustrated using two examples. The first example is related to the human balance control system and us thus physiologically relevant. The second example gives a theoretical explanation of the phenomenon of self-induced oscillations in intermittent control systems.

The act-and-wait control introduced by Insperger is shown to be related to a form of intermittent control. Theoretical and practical similarities and differences between the two methods are explored.

Piezoelectric tubes exhibit a highly resonant mode of vibration which, if uncontrolled, limits the maximum scan rate in nano-scale positioning applications. Highly resonant systems with collocated sensor/actuator are often controlled using resonant shunt dampers. Unfortunately, in the configuration used here, this approach is not possible due the non-minimum phase property arising from the presence of a right-half plane zero. This problem is solved by: (i) interpreting the resonant shunt damper in the context of physical-model-based control (PMBC) and (ii) extending the PMBC approach to handle non-minimum phase systems. The resultant controller combines the physical insight of the resonant shunt damper with the ability to control the non-minimum phase piezoelectric tube. A digital implementation of the controller was experimentally evaluated and found to successfully eliminate the resonant mode of vibration during an accurate and fast scan using a piezoelectric tube actuator.

Keywords: Flexible structures

In studies of human balance, it is common to fit stimulus-response data by tuning the time-delay and gain parameters of a simple delayed feedback model. Many interpret this fitted model, a simple delayed feedback model, as evidence that predictive processes are not required to explain existing data on standing balance. However, two questions lead us to doubt this approach. First, does fitting a delayed feedback model lead to reliable estimates of the time-delay? Second, can a non-predictive controller provide an explanation compatible with the independently estimated time delay?

For methodological and experimental clarity, we study human balancing of a simulated inverted pendulum via joystick and screen. A two-step approach to data analysis is used: firstly a non-parametric model -­ the closed-loop impulse response -­ is estimated from the experimental data; secondly, a parametric model is fitted to the non-parametric impulse-response by adjusting time-delay and controller parameters. To support the second step, a new explicit formula relating controller parameters to closed-loop impulse response is derived. Two classes of controller are investigated within a common state-space context: non-predictive and predictive.

It is found that the time-delay estimate arising from the second step is strongly dependent on which controller class is assumed; in particular, the non-predictive control assumption leads to time-delay estimates that are smaller than those arising from the predictive assumption. Moreover, the time-delays estimated using the non-predictive control assumption are not consistent with a lower-bound on the time-delay of the non-parametric model whereas the corresponding predictive result is consistent. Thus while the goodness of fit only marginally favoured predictive over non-predictive control, if we add the additional constraint that the model must reproduce the non-parametric time delay, then the non-predictive control model fails. We conclude (i) the time-delay should be estimated independently of fitting a low order parametric model, (ii) that balance of the simulated inverted pendulum could not be explained by the non-predictive control model and (iii) that predictive control provided a better explanation than non-predictive control.

The generalised hold formulation of intermittent control is re-examined and shown to have some useful theoretical and practical properties. It is shown that this provides a foundation for constrained model predictive control in an intermittent context. The method is illustrated using an example and verified with experimental results.

An intermittent controller with fixed sampling interval is recast as an event-driven controller. The key aspect of intermittent control that makes this possible is the use of basis functions, or, equivalently, a generalised hold, to generate the intersample open-loop control signal. The controller incorporates both feedforward events in response to known signals and feedback events in response to detected disturbances. The latter feature makes use of an extended basis-function generator to generate open-loop predictions of states to be compared with measured or observed states. Intermittent control is based on an underlying continuous-time controller; it is emphasised that the design of this continuous-time controller is important, particularly in the presence of input disturbances. Illustrative simulation examples are given.

Human balance is commonly described using linear-time-invariant (LTI) models. The feedback time delay determines the position of balance in the motor-control hierarchy. The extent of LTI control illuminates the automaticity of the control process. Using non-parametric analysis, we measured the feedback delay, extent of LTI control and visuo-motor transfer function in six randomly disturbed, visuo-manual compensatory tracking tasks analogous to standing with small mechanical perturbations and purely visual information. The delay depended primarily on load order (2nd: 220 +/- 30 ms, 1st: 124 +/- 20 ms), and secondarily on visual magnification (extent 2nd: 34 ms, 1st: 8 ms) and was unaffected by load stability. LTI control explained 1st order and stable loads relatively well. For unstable (85 passive stabilisation) 2nd order loads, LTI control accounted for 40 of manual output at 0.1 Hz decreasing below 10 as frequency increased through the important 1-3 Hz region where manual power and visuo-motor gain are high. Visual control of unstable 2nd order loads incurs substantial feedback delays and the control process will not be LTI. These features do not result from exclusive use of visual inputs because we found much shorter delays and a greater degree of LTI control when subjects visually controlled a 1st order load. Rather, these results suggest that delay and variability are inevitable when more flexible, intentional mechanisms are required to control 2nd order unstable loads. The high variability of quiet standing, and movement generally, may be indicative of flexible, variable delay, intentional mechanisms rather than the automatic LTI responses usually reported in response to large perturbations.

This article proposes a model predictive control scheme based on a non-minimal state-space (NMSS) structure. Such a combination yields a continuous-time state-space model predictive control system that permits hard constraints to be imposed on both plant input and output variables, whilst using NMSS output-feedback without the need for an observer. A comparison between the NMSS and observer-based approaches using Monte Carlo uncertainty analysis shows that the former design is considerably less sensitive to plant-model mismatch than the latter. Through simulation studies, the article also investigates the role of the implementation filter in noise attenuation, disturbance rejection and robustness of the closed-loop predictive control system. The results show that the filter poles become a subset of the closed-loop poles and this provides a straightforward method of tuning the closed-loop performance to achieve a reasonable balance between speed of response, disturbance rejection, measurement noise attenuation and robustness.

The reverse-engineering idea developed by Maciejowski in the context of model-based predictive control is applied to the redesign of continuous-time compensators as intermittent controllers. Not only does this give a way of designing constrained input and state versions of continuous-time compensators but also provides a method for turning continuous-time compensators into event-driven versions. The procedure is illustrated by three examples: an event-driven PID controller relevant to the human balance control problem, a constrained version of the classical mechanical vibration absorber of den Hartog and an event driven and constrained vibration absorber.

Human motor control is often explained in terms of engineering ″servo″ theory. Recently, continuous, optimal control using internal models has emerged as a leading paradigm for voluntary movement. However, these engineering paradigms are designed for high bandwidth, inflexible, consistent systems whereas human control is low bandwidth and flexible using noisy sensors and actuators. By contrast, engineering intermittent control was designed for bandwidth-limited applications. Our general interest is whether intermittent rather than continuous control is generic to human motor control. Currently, it would be assumed that continuous control is the superior and physiologically natural choice for controlling unstable loads, for example as required for maintaining human balance. Using visual manual tracking of an unstable load, we show that control using gentle, intermittent taps is entirely natural and effective. The gentle tapping method resulted in slightly superior position control and velocity minimisation, a reduced feedback time delay, greater robustness to changing actuator gain and equal or greater linearity with respect to the external disturbance. Control was possible with a median contact rate of 0.8±0.3 s-1. However, when optimising position or velocity regulation, a modal contact rate of 2s-1 was observed. This modal rate was consistent with insignificant disturbance-joystick coherence beyond 1-2 Hz in both tapping and continuous contact methods. For this load, these results demonstrate a motor control process of serial ballistic trajectories limited to an optimum rate of 2 s-1. Consistent with theoretical reasoning, our results suggest that intermittent open loop action is a natural consequence of human physiology.

This article develops switched linear controllers for periodic exogenous signals using the framework of a continuous-time model predictive control. In this framework, the control signal is generated by an algorithm that uses receding horizon control principle with an on-line optimisation scheme that permits inclusion of operational constraints. Unlike traditional repetitive controllers, applying this method in the form of switched linear controllers ensures bumpless transfer from one controller to another. Simulation studies are included to demonstrate the efficacy of the design with or without hard constraints.

Human motor control is often explained in terms of engineering ″servo″ theory. Recently, continuous, optimal control using internal models has emerged as a leading paradigm for voluntary movement. However, these engineering paradigms are designed for high bandwidth, inflexible, consistent systems whereas human control is low bandwidth and flexible using noisy sensors and actuators. By contrast, engineering intermittent control was designed for bandwidth-limited applications. Our general interest is whether intermittent rather than continuous control is generic to human motor control. Currently, it would be assumed that continuous control is the superior and physiologically natural choice for controlling unstable loads, for example as required for maintaining human balance. Using visual manual tracking of an unstable load, we show that control using gentle, intermittent taps is entirely natural and effective. The gentle tapping method resulted in slightly superior position control and velocity minimisation, a reduced feedback time delay, greater robustness to changing actuator gain and equal or greater linearity with respect to the external disturbance. Control was possible with a median contact rate of 0.8±0.3 s-1. However, when optimising position or velocity regulation, a modal contact rate of 2s-1 was observed. This modal rate was consistent with insignificant disturbance-joystick coherence beyond 1-2 Hz in both tapping and continuous contact methods. For this load, these results demonstrate a motor control process of serial ballistic trajectories limited to an optimum rate of 2 s-1. Consistent with theoretical reasoning, our results suggest that intermittent open loop action is a natural consequence of human physiology.

An intermittent controller is a form of hybrid controller which adds a generalised sample and hold mechanism to an underlying continuous-time feedback control system. The sampling may be non-uniform or event driven. One particular form of the hold, termed the system-matched hold (SMH) mimics the behaviour of the closed-loop feedback control signal during the intermittent intervals. It is shown in this article that this choice of hold leads to an intermittent separation principle. In particular, this simple analytical result ensures that when using the SMH, the separation properties of the underlying state-estimate feedback control system carry over to the intermittent control system. This separation principle for the SMH has the important consequence that, unlike the zero-order hold case, the stability of the closed-loop system in the fixed sampling case is not dependent on sample interval. It is therefore suggested that the SMH should replace the conventional zero-order hold in circumstances where the sample interval is unknown, time-varying or determined by events.

Control using a sequence of ‘taps’, in contrast to the usual smooth control, is shown to fit within the established intermittent control framework. In particular, a specially designed generalised hold gives rise to tapping behaviour optimised according to the underlying linear-quadratic design. Both fixed-interval and event-driven tapping are included in this approach and some basic stability analysis is given. Illustrative examples are presented and the advantages of tapping in the context of electromechanical servo systems with friction are explored using a laboratory experiment.

In this article, a hybrid control framework is used to design semi-active controllers for vibration reduction. It is shown that the semi-active skyhook damper, typically used for vibration reduction, can be recast in the framework of an event-driven intermittent controller. By doing this, we can then exploit the well-developed techniques associated with hybrid control theory to design the semi-active control system. Illustrative simulation examples are based on a 2 degree-of-freedom system, often used to model the dynamics of a quarter car body model. The simulation results demonstrate how hybrid control design techniques can improve the overall performance of the semi-active control system.

In this article, input power, as opposed to the usual input amplitude, constraints are introduced in the context of intermittent control. They are shown to result in a combination of quadratic optimisation and quadratic constraints. The main motivation for considering input power constraints is its similarity with semi-active control. Such methods are commonly used to provide damping in mechanical systems and structures. It is shown that semi-active control can be re-expressed and generalised as control with power constraints and can thus be implemented as power-constrained intermittent control. The method is illustrated using simulations of resonant mechanical systems and the constrained nature of the power flow is represented using power-phase-plane plots. We believe the approach we present will be useful for the control design of both semi-active and low-power vibration suppression systems.

System identification techniques applied to experimental human-in-the-loop data provide an objective test of three alternative control–theoretical models of the human control system: non-predictive control, predictive control, and intermittent predictive control. A two-stage approach to the identification of a single-input single-output control system is used: first, the closed-loop frequency response is derived using the periodic property of the experimental data, followed by the fitting of a parametric model. While this approach is well-established for non-predictive and predictive control, it is here used for the first time with intermittent predictive control. This technique is applied to data from experiments with human volunteers who use one of two control strategies, focusing either on position or on velocity, to manually control a virtual, unstable load which requires sustained feedback to maintain position or low velocity. The results show firstly that the non-predictive controller does not fit the data as well as the other two models, and secondly that the predictive and intermittent predictive controllers provide equally good models which cannot be distinguished using this approach. Importantly, the second observation implies that sustained visual manual control is compatible with intermittent control, and that previous results suggesting a continuous control model for the human control system do not rule out intermittent control as an alternative hypothesis. Thirdly, the parameters identified reflect the control strategy adopted by the human controller.

Regulation by negative feedback is fundamental to engineering and biological processes. Biological regulation is usually explained using continuous feedback models from both classical and modern control theory. An alternative control paradigm, intermittent control, has also been suggested as a model for biological control systems, particularly those involving the central nervous system. However, at present, there is no identification method explicitly formulated to distinguish intermittent from continuous control; here, we present such a method. The identification experiment uses a special paired-step set-point sequence. The corresponding data analysis use a conventional ARMA model to relate a theoretically derived equivalent set-point to control signal; the novelty lies in sequentially and iteratively adjusting the timing of the steps of this equivalent set-point to optimize the linear time-invariant fit. The method was verified using realistic simulation data and was found to robustly distinguish not only between continuous and intermittent control but also between event-driven intermittent and clock-driven intermittent control. When applied to human pursuit tracking, event-driven intermittent control was identified, with an intermittent interval of 260–310 ms (n = 6, p < 0.05). This new identification method is applicable for machine and biological applications.

There are two issues in balancing a stick pivoting on a finger tip (or mechanically on a moving cart): maintaining the stick angle near to vertical and maintaining the horizontal position within the bounds of reach or cart track. The (linearised) dynamics of the angle are second order (although driven by pivot acceleration), and so, as in human standing, control of the angle is not, by itself very difficult. However, once the angle is under control, the position dynamics are, in general, fourth order. This makes control quite difficult for humans (and even an engineering control system requires careful design). Recently, three of the authors have experimentally demonstrated that humans control the stick angle in a special way: the closed-loop inverted pendulum behaves as a non-inverted pendulum with a virtual pivot somewhere between the stick centre and tip and with increased gravity. Moreover, they suggest that the virtual pivot lies at the radius of gyration (about the mass centre) above the mass centre. This paper gives a continuous-time control-theoretical interpretation of the virtual-pendulum approach. In particular, by using a novel cascade control structure, it is shown that the horizontal control of the virtual pivot becomes a second-order problem which is much easier to solve than the generic fourth-order problem. Hence, the use of the virtual pivot approach allows the control problem to be perceived by the subject as two separate second-order problems rather than a single fourth-order problem, and the control problem is therefore simplified. The theoretical predictions are verified using the data previously presented by three of the authors and analysed using a standard parameter estimation method. The experimental data indicate that although all subjects adopt the virtual pivot approach, the less expert subjects exhibit larger amplitude angular motion and poorly controlled translational motion. It is known that human control systems are delayed and intermittent, and therefore, the continuous-time strategy cannot be correct. However, the model of intermittent control used in this paper is based on the virtual pivot continuous-time control scheme, handles time delays and moreover masquerades as the underlying continuous-time controller. In addition, the event-driven properties of intermittent control can explain experimentally observed variability.

Modular organisation in control architecture may underlie the versatility of human motor control; but the nature of the interface relating sensory input through task-selection in the space of performance variables to control actions in the space of the elemental variables is currently unknown. Our central question is whether the control architecture converges to a serial process along a single channel? In discrete reaction time experiments, psychologists have firmly associated a serial single channel hypothesis with refractoriness and response selection (psychological refractory period). Recently, we developed a methodology and evidence identifying refractoriness in sustained control of an external single degree-of-freedom system. We hypothesise that multi-segmental whole-body control also shows refractoriness. Eight participants controlled their whole body to ensure a head marker tracked a target as fast and accurately as possible. Analysis showed enhanced delays in response to stimuli with close temporal proximity to the preceding stimulus. Consistent with our preceding work, this evidence is incompatible with control as a linear time invariant process. This evidence is consistent with a single-channel serial ballistic process within the intermittent control paradigm with an intermittent interval of around 0.5 s. A control architecture reproducing intentional human movement control must reproduce refractoriness. Intermittent control is designed to provide computational time for an online optimisation process and is appropriate for flexible adaptive control. For human motor control we suggest that parallel sensory input converges to a serial, single channel process involving planning, selection and temporal inhibition of alternative responses prior to low dimensional motor output. Such design could aid robots to reproduce the flexibility of human control.

In biology, the control of physiological variables such as body position, blood pressure and body temperature is founded on negative feedback mechanisms governing homeostasic input-output relations. The conceptual models capturing the underlying control principles are often drawn from engineering control theory. The visuo-manual control of external systems (like balancing a stick on the palm of one's hand) has traditionally been interpreted using continuous paradigms such as the servo controller or the continuous optimal controller. These engineering controllers were designed for machine systems with precise sensors, consistent actuators, short time delays and fast computers. Quite the opposite is true for the human movement system that is characterized by long neuromuscular delays, variability, history dependence and fatigue. Serial ballistic control offers an alternative control paradigm in which smooth control proceeds as a sequence of sub-movements each planned using current sensory information but then intermittently executed “open loop”. In the current study we are the first to formally identify refractoriness, a behavioural characteristic that discriminates intermittent (serial ballistic) from continuous control, in the domain of sustained (non-discrete) control of first and second order systems providing definite evidence for the validity of intermittent open-loop control as a paradigm for sustained human control.

Thermodynamic aspects of chemical reactions have a long history in the physical chemistry literature. In particular, biochemical cycles require a source of energy to function. However, although fundamental, the role of chemical potential and Gibb's free energy in the analysis of biochemical systems is often overlooked leading to models which are physically impossible. The bond graph approach was developed for modelling engineering systems, where energy generation, storage and transmission are fundamental. The method focuses on how power flows between components and how energy is stored, transmitted or dissipated within components. Based on the early ideas of network thermodynamics, we have applied this approach to biochemical systems to generate models which automatically obey the laws of thermodynamics. We illustrate the method with examples of biochemical cycles. We have found that thermodynamically compliant models of simple biochemical cycles can easily be developed using this approach. In particular, both stoichiometric information and simulation models can be developed directly from the bond graph. Furthermore, model reduction and approximation while retaining structural and thermodynamic properties is facilitated. Because the bond graph approach is also modular and scaleable, we believe that it provides a secure foundation for building thermodynamically compliant models of large biochemical networks.

Two architectures of intermittent control are compared and contrasted in the context of the single inverted pendulum model often used for describing standing in humans. The architectures are similar insofar as they use periods of open-loop control punctuated by switching events when crossing a switching surface to keep the system state trajectories close to trajectories leading to equilibrium. The architectures differ in two significant ways. Firstly, in one case, the open-loop control trajectory is generated by a system-matched hold, and in the other case, the open-loop control signal is zero. Secondly, prediction is used in one case but not the other. The former difference is examined in this paper. The zero control alternative leads to periodic oscillations associated with limit cycles; whereas the system-matched control alternative gives trajectories (including homoclinic orbits) which contain the equilibrium point and do not have oscillatory behaviour. Despite this difference in behaviour, it is further shown that behaviour can appear similar when either the system is perturbed by additive noise or the system-matched trajectory generation is perturbed. The purpose of the research is to come to a common approach for understanding the theoretical properties of the two alternatives with the twin aims of choosing which provides the best explanation of current experimental data (which may not, by itself, distinguish beween the two alternatives) and suggesting future experiments to distinguish beween the two alternatives.

Keywords: Intermittent control; Predictive control; Human balancing; Quiet standing

Explanation of motor control is dominated by continuous neurophysiological pathways (e.g. trans-cortical, spinal) and the continuous control paradigm. Using new theoretical development, methodology and evidence, we propose intermittent control, which incorporates a serial ballistic process within the main feedback loop, provides a more general and more accurate paradigm necessary to explain attributes highly advantageous for competitive survival and performance.

The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open systems exchanging mass and energy via ports. A key feature of this approach is that the resultant models are robustly thermodynamically compliant: the thermodynamic compliance is not dependent on precise numerical values of parameters. Moreover, the models are reusable owing to the well-defined interface provided by the energy ports. To extract bond graph model parameters from parameters found in the literature, general and compact formulae are developed to relate free-energy constants and equilibrium constants. The existence and uniqueness of solutions is considered in terms of fundamental properties of stoichiometric matrices. The approach is illustrated by building a hierarchical bond graph model of glycogenolysis in skeletal muscle.

This paper investigates the use of an actuator and sensor pair coupled via a control system to damp out oscillations in resonant mechanical systems. Specifically the designs emulate passive control strategies, resulting in controller dynamics that resemble a physical system. Here, the use of the novel dynamically dual approach is proposed to design the vibration absorbers to be implemented as the controller dynamics; this gives rise to the dynamically dual vibration absorber (DDVA). It is shown that the method is a natural generalisation of the classical single-degree of freedom mass–spring–damper vibration absorber and also of the popular acceleration feedback controller. This generalisation is applicable to the vibration control of arbitrarily complex resonant dynamical systems. It is further shown that the DDVA approach is analogous to the hybrid numerical-experimental testing technique known as substructuring. This analogy enables methods and results, such as robustness to sensor/actuator dynamics, to be applied to dynamically dual vibration absorbers. Illustrative experiments using both a hinged rigid beam and a flexible cantilever beam are presented.

Bond graphs can be used to build thermodynamically-compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this study suggests that they can play the same rôle in the modelling, analysis and synthesis of biomolecular systems. The particular structure of bond graphs arising from biomolecular systems is established and used to elucidate the relation between thermodynamically closed and open systems. Block diagram representations of the dynamics implied by these bond graphs are used to reveal implicit feedback structures and are linearised to allow the application of control-theoretical methods. Two concepts of modularity are examined: computational modularity where physical correctness is retained and behavioural modularity where module behaviour (such as ultrasensitivity) is retained. As well as providing computational modularity, bond graphs provide a natural formulation of behavioural modularity and reveal the sources of retroactivity. A bond graph approach to reducing retroactivity, and thus inter-module interaction, is shown to require a power supply such as that provided by the ATP ⇌ ADP + Pi reaction. The mitogen-activated protein kinase cascade (Raf-MEK-ERK pathway) is used as an illustrative example.

Keywords: biology computing;bond graphs;enzymes;hierarchical systems;molecular biophysics;physiological models;thermodynamics;ATP⇌ADP + Pi reaction;Michaelis-Menten kinetics;Raf-MEK-ERK pathway;behavioural modularity;biomolecular systems;block diagram representations;computational modularity;intermodule interaction;mitogen-activated protein kinase cascade;modular bond-graph modelling;retroactivity;signalling networks;thermodynamically-compliant hierarchical models

Engineering systems modeling and analysis based on the bond graph approach has been applied to biomolecular systems. In this context, the notion of a Faraday-equivalent chemical potential is introduced which allows chemical potential to be expressed in an analogous manner to electrical volts thus allowing engineering intuition to be applied to biomolecular systems. Redox reactions, and their representation by half-reactions, are key components of biological systems which involve both electrical and chemical domains. A bond graph interpretation of redox reactions is given which combines bond graphs with the Faraday-equivalent chemical potential. This approach is particularly relevant when the biomolecular system implements chemoelectrical transduction – for example chemiosmosis within the key metabolic pathway of mitochondria: oxidative phosphorylation. An alternative way of implementing computational modularity using bond graphs is introduced and used to give a physically based model of the mitochondrial electron transport chain To illustrate the overall approach, this model is analyzed using the Faraday-equivalent chemical potential approach and engineering intuition is used to guide affinity equalisation: a energy based analysis of the mitochondrial electron transport chain.

Keywords: Analytical models;Biological system modeling;Chemicals;Computational modeling;Context;Electric potential;Protons;Biological system modeling;computational systems biology;systems biology

Keywords: Computer Science - Systems and Control, Quantitative Biology - Quantitative Methods

Decomposition of biomolecular reaction networks into pathways is a powerful approach to the analysis of metabolic and signalling networks. Current approaches based on analysis of the stoichiometric matrix reveal information about steady-state mass flows (reaction rates) through the network. In this work, we show how pathway analysis of biomolecular networks can be extended using an energy-based approach to provide information about energy flows through the network. This energy-based approach is developed using the engineering-inspired bond graph methodology to represent biomolecular reaction networks. The approach is introduced using glycolysis as an exemplar; and is then applied to analyse the efficiency of free energy transduction in a biomolecular cycle model of a transporter protein [sodium-glucose transport protein 1 (SGLT1)]. The overall aim of our work is to present a framework for modelling and analysis of biomolecular reactions and processes which considers energy flows and losses as well as mass transport.

Energy-based bond graph modelling of biomolecular systems is extended to include chemoelectrical transduction thus enabling integrated thermodynamically compliant modelling of chemoelectrical systems in general and excitable membranes in particular. Our general approach is illustrated by recreating a well-known model of an excitable membrane. This model is used to investigate the energy consumed during a membrane action potential thus contributing to the current debate on the trade-off between the speed of an action potential event and energy consumption. The influx of Na+ is often taken as a proxy for energy consumption; in contrast, this study presents an energy-based model of action potentials. As the energy-based approach avoids the assumptions underlying the proxy approach it can be directly used to compute energy consumption in both healthy and diseased neurons. These results are illustrated by comparing the energy consumption of healthy and degenerative retinal ganglion cells using both simulated and in vitro data.

Keywords: biochemistry;bioelectric potentials;biomembrane transport;eye;molecular biophysics;neurophysiology;sodium;Na;biomolecular systems;chemoelectrical energy transduction;chemoelectrical systems;degenerative retinal ganglion cells;diseased neurons;energy consumption;energy-based bond graph modelling;excitable membranes;healthy neurons;healthy retinal ganglion cells;integrated thermodynamically compliant modelling;membrane action potential

The human operator is described adequately by linear translation of sensory input to motor output. Motor output also always includes a non-linear remnant resulting from random sensorimotor noise from multiple sources, and non-linear input transformations, for example thresholds or refractory periods. Recent evidence showed that manual tracking incurs substantial, serial, refractoriness (insensitivity to sensory information of 350 and 550 ms for 1st and 2nd order systems respectively). Our two questions are: (i) What are the comparative merits of explaining the non-linear remnant using noise or non-linear transformations? (ii) Can non-linear transformations represent serial motor decision making within the sensorimotor feedback loop intrinsic to tracking? Twelve participants (instructed to act in three prescribed ways) manually controlled two systems (1st and 2nd order) subject to a periodic multi-sine disturbance. Joystick power was analysed using three models, continuous-linear-control (CC), continuous-linear-control with calculated noise spectrum (CCN), and intermittent control with aperiodic sampling triggered by prediction error thresholds (IC). Unlike the linear mechanism, the intermittent control mechanism explained the majority of total power (linear and remnant) (77–87 vs. 8–48, IC vs. CC). Between conditions, IC used thresholds and distributions of open loop intervals consistent with, respectively, instructions and previous measured, model independent values; whereas CCN required changes in noise spectrum deviating from broadband, signal dependent noise. We conclude that manual tracking uses open loop predictive control with aperiodic sampling. Because aperiodic sampling is inherent to serial decision making within previously identified, specific frontal, striatal and parietal networks we suggest that these structures are intimately involved in visuo-manual tracking.

Keywords: motor control, intermittent control, variability

A new approach to compute the equilibria and the steady-states of biomolecular systems modeled by bond graphs is presented. The approach is illustrated using a model of a biomolecular cycle representing a membrane transporter and a model of the mitochondrial electron transport chain.

Keywords: Biological system modeling;Chemicals;Electric potential;Kinetic theory;Mathematical model;Nanobioscience;Steady-state;Biological system modeling;computational systems biology;systems biology

The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction network concept of complexes. Both closed and open systems are discussed. The method is illustrated using a simple enzyme-catalysed reaction and a trans-membrane transporter.

Keywords: Chemicals;Junctions;Substrates;Standards;Nanobioscience;Biological system modeling;Open systems

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a extquoteleftconserved moietyextquoteright. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of thermodynamics. However, many mathematical models of transporters, especially those incorporated into whole-cell models, are not thermodynamically consistent, leading to unrealistic behaviour. In this paper we use a physics-based modelling framework, in which the transfer of energy is explicitly accounted for, to develop thermodynamically consistent models of transporters. We then apply this methodology to model two specific transporters: the cardiac sarcoplasmic/endoplasmic Ca2+ ATPase (SERCA) and the cardiac Na+/K+ ATPase.

Keywords: Bond graph, Biochemistry, Chemical reaction network, Biomedical engineering, Systems biology

Advances in systems biology and whole-cell modelling demand increasingly comprehensive mathematical models of cellular biochemistry. Such models require the development of simplified representations of specific processes which capture essential biophysical features but without unnecessarily complexity. Recently there has been renewed interest in thermodynamically-based modelling of cellular processes. Here we present an approach to developing of simplified yet thermodynamically consistent (hence physically plausible) models which can readily be incorporated into large scale biochemical descriptions but which do not require full mechanistic detail of the underlying processes. We illustrate the approach through development of a simplified, physically plausible model of the mitochondrial electron transport chain and show that the simplified model behaves like the full system.

Keywords: Systems biology, Thermodynamical modelling, Bond graph, Computational biology

Interactions among biomolecules, electrons, and protons are essential to many fundamental processes sustaining life. It is therefore of interest to build mathematical models of these bioelectrical processes not only to enhance understanding but also to enable computer models to complement in vitro and in vivo experiments. Such models can never be entirely accurate; it is nevertheless important that the models are compatible with physical principles. Network Thermodynamics, as implemented with bond graphs, provide one approach to creating physically compatible mathematical models of bioelectrical systems. This is illustrated using simple models of ion channels, redox reactions, proton pumps, and electrogenic membrane transporters thus demonstrating that the approach can be used to build mathematical and computer models of a wide range of bioelectrical systems.

The Na+/K+ATPase is an essential component of cardiac electrophysiology, maintaining physiological Na+ and K+ concentrations over successive heart beats. Terkildsen et al. (2007) developed a model of the ventricular myocyte Na+/K+ ATPase to study extracellular potassium accumulation during ischaemia, demonstrating the ability to recapitulate a wide range of experimental data, but unfortunately there was no archived code associated with the original manuscript. Here we detail an updated version of the model and provide CellML and MATLAB code to ensure reproducibility and reusability. We note some errors within the original formulation which have been corrected to ensure that the model is thermodynamically consistent, and although this required some reparameterisation, the resulting model still provides a good fit to experimental measurements that demonstrate the dependence of Na+/K+ ATPase pumping rate upon membrane voltage and metabolite concentrations. To demonstrate thermodynamic consistency we also developed a bond graph version of the model. We hope that these models will be useful for community efforts to assemble a whole-cell cardiomyocyte model which facilitates the investigation of cellular energetics.

Like all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

Energy-based modelling brings engineering insight to the understanding of biomolecular systems. It is shown how well-established control engineering concepts, such as loop-gain, arise from energy feedback loops and are therefore amenable to control engineering insight. In particular, a novel method is introduced to allow the transfer function based approach of classical linear control to be utilised in the analysis of feedback systems modelled by network thermodynamics and thus amalgamate energy-based modelling with control systems analysis. The approach is illustrated using a class of metabolic cycles with activation and inhibition leading to the concept of Cyclic Flow Modulation.

Keywords: Biological system modeling;Junctions;Transfer functions;Thermodynamics;Mathematical model;Feedback loop;Analytical models;Biological system modeling;computational systems biology;systems biology;negative feedback

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Author summary The biochemistry within a cell is complex, being composed of numerous biomolecules and reactions. In order to develop fully detailed mathematical models of cells, smaller submodels need to be constructed and connected together. Software and standards can assist in this endeavour, but challenges remain in ensuring that submodels are both consistent with each other and consistent with the fundamental conservation laws of physics. In this paper, we propose a new approach using bond graphs from engineering. In this approach, connections between models are defined using physical conservation laws. We show that this approach is compatible with current software approaches in the field, and can therefore be readily used to incorporate physical consistency into existing model integration methodologies. We illustrate the utility of this approach in streamlining the development of models for a signalling network (the MAPK cascade) and a metabolic network (the glycolysis pathway). The advantage of this approach is that models can be developed in a scalable manner while also ensuring consistency with the laws of physics, enhancing the range of data available to train models. This approach can be used to quickly construct detailed and accurate models of cells, facilitating future advances in biotechnology and personalised medicine.

Edmund Crampin (1973-2021) was at the forefront of Systems Biology research and his work will influence the field for years to come. This paper brings together and summarises the seminal work of his group in applying energy-based bond graph methods to biological systems. In particular, this paper: (a) motivates the need to consider energy in modelling biology; (b) introduces bond graphs as a methodology for achieving this; (c) describes extensions to modelling electrochemical transduction; (d) outlines how bond graph models can be constructed in a modular manner and (e) describes stoichiometric approaches to deriving fundamental properties of reaction networks. These concepts are illustrated using a new bond graph model of photosynthesis in chloroplasts.

Keywords: Systems biology, Bond graph, Energy-based, Photosynthesis, Electrochemical transduction

Advection, the transport of a substance by the flow of a fluid, is a key process in biological systems. The energy-based bond graph approach to modelling chemical transformation within reaction networks is extended to include transport and thus advection. The approach is illustrated using a simple model of advection via circulating flow and by a simple pharmacokinetic model of anaesthetic gas uptake. This extension provides a physically consistent framework for linking advective flows with the fluxes associated with chemical reactions within the context of physiological systems in general and the human physiome in particular.

Intermittent control combines open-loop trajectories with feedback at discrete time instances determined by events. Among other applications, it has recently been used to model quiet standing in humans where the system was assumed to be time-invariant. This article expands this work to the time-variant case by introducing an adaptive intermittent controller that exploits the well-known self-tuning architecture of adaptive control with a Kalman filter to perform online state and parameter estimation. Simulation and experimental results using a rotational inverted pendulum show advantages of the intermittent controllers compared to continuous feedback control since the former can provide persistent excitation due to their internal triggering mechanism, even when no external reference changes or disturbances are applied. Moreover, the results show that the event thresholds of intermittent control can be used to adjust the degree of responsiveness of the adaptation in the system, becoming a tool to balance the trade-off between steady-state performance and flexibility against parametric changes, addressing the stability–plasticity dilemma of adaptation and learning in control.

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.

The bond graph approach has been recognized as a useful conceptual basis for understanding the behaviour of living entities modelled as a system with hierarchical interacting parts exchanging energy. One such behaviour is oscillation, which underpins many essential biological functions. In this paper, energy-based modelling of biochemical systems using the bond graph approach is combined with classical feedback control theory to give a novel approach to the analysis, and potentially synthesis, of biochemical oscillators. It is shown that oscillation is dependent on the interplay between active and passive feedback and this interplay is formalized using classical frequency-response analysis of feedback systems. In particular, the phase margin is suggested as a simple scalar indicator of the presence or absence of oscillations; it is shown how this indicator can be used to investigate the effect of both the structure and parameters of biochemical system on oscillation. It follows that the combination of classical feedback control theory and the bond graph approach to systems biology gives a novel analysis and design methodology for biochemical oscillators. The approach is illustrated using an introductory example similar to the Goodwin oscillator, the Sel’kov model of glycolytic oscillations and the repressilator.

Bond graphs provide an energy-based methodology for modelling complex systems hierarchically; at the moment, the method allows biological systems with both chemical and electrical subsystems to be modelled. Herein, the bond graph approach is extended to include chemomechanical transduction thus extending the range of biological systems to be modelled. Actin filament polymerization and force generation is used as an example of chemomechanical transduction, and it is shown that the TF (transformer) bond graph component provides a practical, and conceptually simple, alternative to the Brownian ratchet approach of Peskin, Odell, Oster and Mogilner. Furthermore, it is shown that the bond graph approach leads to the same equation as the Brownian ratchet approach in the simplest case. The approach is illustrated by showing that flexibility and non-normal incidence can be modelled by simply adding additional bond graph components and that compliance leads to non-convexity of the force–velocity curve. Energy flows are fundamental to life; for this reason, the energy-based approach is utilized to investigate the power transmission by the actin filament and its corresponding efficiency. The bond graph model is fitted to experimental data by adjusting the model physical parameters.

Ageing is one of the most significant risk factors for heart disease; however, it is still not clear how the human heart changes with age. Taking advantage of a unique set of pre-mortem, cryopreserved, non-diseased human hearts, we performed omics analyses (transcriptomics, proteomics, metabolomics, and lipidomics), coupled with biologically informed computational modelling in younger (<25 years old) and older hearts (>50 years old) to describe the molecular landscape of human cardiac ageing. In older hearts, we observed a downregulation of proteins involved in calcium signalling and the contractile apparatus. Furthermore, we found a potential dysregulation of central carbon generation of fuel, glycolysis, and fatty acids oxidation, along with an increase in long-chain fatty acids. This study presents and analyses the first molecular data set of normal human cardiac ageing, which has relevant implications for understanding the human cardiac ageing process and the development of age-related heart disease.

Keywords: ageing, age-OME, excitation-contraction coupling, human heart, metabolism, omics

Synthetic biology aims to engineer novel functionalities into biological systems. While the approach has been predominantly applied to single cells, a richer set of biological phenomena can be engineered by applying synthetic biology to cell populations. To rationally design cell populations, we require mathematical models that link between intracellular biochemistry and intercellular interactions. In this study, we develop a kinetic model of gene expression that is suitable for incorporation into agent-based models of cell populations. To be scalable to large cell populations, models of gene expression should be both computationally efficient and compliant with the laws of physics. We satisfy the first requirement by applying a model reduction scheme to translation and the second requirement by formulating models using bond graphs, a modelling approach that ensures thermodynamic consistency. Our reduced model is significantly faster to simulate than the full model and reproduces important behaviours of the full model. We couple separate models of gene expression to build models of the toggle switch and repressilator. With these models, we explore the effects of resource availability and cell-to-cell heterogeneity on circuit behaviour. The modelling approaches developed here are a bridge towards engineering collective cell behaviours such as synchronization and division of labour.