Peter Wellstead

Self-tuning pole/zero assignment regulators

In this paper a class of self-tuning regulators is considered which combines a simple recursive least squares estimator with a pole/zero assignment design rule. Two such algorithms are shown to have the self-tuning property (i ) detuned minimum variance regulators ; (ii ) pole-asaignment regulators. The use of these regulators in self-tuning can be of considerable benefit. In particular, case (i ) is useful when minimum variance strategies need unrealistically high-loop gains, since they permit an engineering trade-off between optimality and practicality. Case (ii ) is of use in regulating non-minimum phase systems or systems involving unknown time delays. Such systems are frequently encountered in discrete time control and cannot be handled by direct minimum variance methods.

Extended self-tuning algorithm

This article concerns the practical implications of an extended self-tuning property. The extension represents a refinement of existing asymptotic self-tuning properties, in the sense that it allows the designer to make arbitrary assumptions concerning the disturbance dynamics. The important practical consequence of this is that a simple pole-assignment self-tuner may now be designed which combines servo-tracking and regulatory closed-loop criteria. In the pure regulation case a priori parametrization of the noise dynamics can be used to aid convergence of the self-tuning algorithm. In addition, an implicit pole-assignment regulator is easily formulated from the extended self-tuner.

Non-parametric methods of system identification

The non-parametric identification of systems in terms of unparametrized representations such as the impulse response and frequency response is considered. Basic approaches are outlined in a retrospective setting as are the relationships between non-parametric and parametric identification models. The article concludes with an assessment of non-parametric methods which is conducted in terms of typical industrial applications.

Estimation of vehicle lateral velocity

Two techniques for the estimation of vehicle lateral velocity using state observers are considered. The first method uses a physical model of the vehicle handling. The physical model based observer produces noise free lateral velocity estimates, but can be sensitive to changes in the vehicle parameters. It produces reliable estimates in the vehicle linear handling region only. We show that the observer gain can be selected to make the observer insensitive to certain parameter variations. The second method uses a kinematic model relating longitudinal velocity, lateral velocity, longitudinal acceleration, lateral acceleration and yaw rate. This model contains no vehicle parameters, and hence the kinematic model based observer is unaffected by changes in the vehicle parameters. The observer produces reliable lateral velocity estimates throughout the linear and nonlinear handling regions, the estimates however are more noisy than those produced by the physical model based observer. The techniques are compared using simulated data for manoeuvers in the linear and nonlinear handling regions of the vehicle.

Least-squares identification of closed-loop systems

The problem of least-squares estimation of closed-loop systems is examined. The particular configuration considered is the single input-single output discrete linear system controlled by a linear, stationary feedback regulator. Results are obtained which determine the conditions for uniqueness and consistency of the least-squares estimates of the forward-path transfer function. In particular, it is shown that if two orthogonal unobservable noise sources are present, one in each path, the system is uniquely identifiable. When the feedback path is noise-free the uniqueness of the estimates is dependent upon the order of the regulator regression polynomials. The consistency of the estimates in the case of a white forward-path disturbance is assured provided that there is at least one delay term in the loop.

Correspondence item: An instrumental product moment test for model order estimation

The near singularity of the product moment matrix of observed input/output data provides a quick way of checking the order of a linear system. However, the technique becomes insensitive when significant amounts of extraneous noise are present, and while this difficulty can be alleviated it is only by additional computation and explicit use of a priori system knowledge. This short paper describes an instrumental variable modification to the product moment technique which overcomes these problems with a negligible amount of extra computation.

The dynamic systems approach to control and regulation of intracellular networks

Systems theory and cell biology have enjoyed a long relationship that has received renewed interest in recent years in the context of systems biology. The term ‘systems’ in systems biology comes from systems theory or dynamic systems theory: systems biology is defined through the application of systems‐ and signal‐oriented approaches for an understanding of inter‐ and intra‐cellular dynamic processes. The aim of the present text is to review the systems and control perspective of dynamic systems. The biologists conceptual framework for representing the variables of a biochemical reaction network, and for describing their relationships, are pathway maps. A principal goal of systems biology is to turn these static maps into dynamic models, which can provide insight into the temporal evolution of biochemical reaction networks. Towards this end, we review the case for differential equation models as a ‘natural’ representation of causal entailment in pathways. Block‐diagrams, commonly used in the engineering sciences, are introduced and compared to pathway maps. The stimulus–response representation of a molecular system is a necessary condition for an understanding of dynamic interactions among the components that make up a pathway. Using simple examples, we show how biochemical reactions are modelled in the dynamic systems framework and visualized using block‐diagrams.

An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements

An integrative, systems approach to the modelling of brain energy metabolism is presented. Mechanisms such as glutamate cycling between neurons and astrocytes and glycogen storage in astrocytes have been implemented. A unique feature of the model is its calibration using in vivo data of brain glucose and lactate from freely moving rats under various stimuli. The model has been used to perform simulated perturbation experiments that show that glycogen breakdown in astrocytes is significantly activated during sensory (tail pinch) stimulation. This mechanism provides an additional input of energy substrate during high consumption phases. By way of validation, data from the perfusion of 50 µM propranolol in the rat brain was compared with the model outputs. Propranolol affects the glucose dynamics during stimulation, and this was accurately reproduced in the model by a reduction in the glycogen breakdown in astrocytes. The model’s predictive capacity was verified by using data from a sensory stimulation (restraint) that was not used for model calibration. Finally, a sensitivity analysis was conducted on the model parameters, this showed that the control of energy metabolism and transport processes are critical in the metabolic behaviour of cerebral tissue.

The control systems structures of energy metabolism

The biochemical regulation of energy metabolism (EM) allows cells to modulate their energetic output depending on available substrates and requirements. To this end, numerous biomolecular mechanisms exist that allow the sensing of the energetic state and corresponding adjustment of enzymatic reaction rates. This regulation is known to induce dynamic systems properties such as oscillations or perfect adaptation. Although the various mechanisms of energy regulation have been studied in detail from many angles at the experimental and theoretical levels, no framework is available for the systematic analysis of EM from a control systems perspective. In this study, we have used principles well known in control to clarify the basic system features that govern EM. The major result is a subdivision of the biomolecular mechanisms of energy regulation in terms of widely used engineering control mechanisms: proportional, integral, derivative control, and structures: feedback, cascade and feed-forward control. Evidence for each mechanism and structure is demonstrated and the implications for systems properties are shown through simulations. As the equivalence between biological systems and control components presented here is generic, it is also hypothesized that our work could eventually have an applicability that is much wider than the focus of the current study.

The role of control and system theory in systems biology

The use of new technology and mathematics to study the systems of nature is one of the most significant scientific trends of the century. Driven by the need for more precise scientific understanding, advances in automated measurement are providing rich new sources of biological and physiological data. These data provide information to create mathematical models of increasing sophistication and realism—models that can emulate biological and physiological systems with sufficient accuracy to advance our understanding of living systems and disease mechanisms. New measurement and modelling methods set the stage for control and systems theory to play their role in seeking out the mechanisms and principles that regulate life. It is of inestimable importance for the future of control as a discipline that this role is performed in the correct manner. If we handle the area wisely then living systems will present a seemingly boundless range of important new problems—just as physical and engineering systems have done in previous centuries. But there is a crucial difficulty. Faced with a bewildering array of choices in an unfamiliar area, how does a researcher select a worthwhile and fruitful problem? This article is an attempt to help by offering a control-oriented guide to the labyrinthine world of biology/physiology and its control research opportunities.