A stable one-step-ahead predictive control of non-linear systems

In this paper stability of one-step ahead predictive controllers based on non-linear models is established. It is shown that, under conditions which can be fulfilled by most industrial plants, the closed-loop system is robustly stable in the presence of plant uncertainties and input–output constraints. There is no requirement that the plant should be open-loop stable and the analysis is valid for general forms of non-linear system representation including the case out when the problem is constraint-free. The effectiveness of controllers designed according to the algorithm analyzed in this paper is demonstrated on a recognized benchmark problem and on a simulation of a continuous-stirred tank reactor (CSTR). In both examples a radial basis function neural network is employed as the non-linear system model.

Filtering techniques in self-tuning

In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description. This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case. At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.

Relationship between åström control and the kalman linear regulator — Caines revisited

The relationship between minimum variance and minimum expected quadratic loss feedback controllers for linear univariate discrete-time stochastic systems is reviewed by taking the approach used by Caines. It is shown how the two methods can be regarded as providing identical control actions as long as a noise-free measurement state-space model is employed.

Adaptive deadbeat control of stochastic systems

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Dynamic recurrent neural network for system identification and control

A dynamic recurrent neural network (DRNN) that can be viewed as a generalisation of the Hopfield neural network is proposed to identify and control a class of control affine systems. In this approach, the identified network is used in the context of the differential geometric control to synthesise a state feedback that cancels the nonlinear terms of the plant yielding a linear plant which can then be controlled using a standard PID controller.

Predictive algorithm for the roll control autopilot of a jet fighter aircraft

Predictive controllers are often only applicable for open-loop stable systems. In this paper two such controllers are designed to operate on open-loop critically stable systems, each of which is used to find the control inputs for the roll control autopilot of a jet fighter aircraft. It is shown how it is quite possible for good predictive control to be achieved on open-loop critically stable systems.

Multi-microprocessor control of processes with pure time delay

In 1967 a novel scheme was proposed for controlling processes with large pure time delay (Fellgett et al, 1967) and some of the constituent parts of the scheme were investigated (Swann, 1970; Atkinson et al, 1973). At that time the available computational facilities were inadequate for the scheme to be implemented practically, but with the advent of modern microcomputers the scheme becomes feasible. This paper describes recent work (Mitchell, 1987) in implementing the scheme in a new multi-microprocessor configuration and shows the improved performance it provides compared with conventional three-term controllers.

Modelling human dynamics in-situ for rehabilitation and therapy robots

This paper outlines some rehabilitation applications of manipulators and identifies that new approaches demand that the robot make an intimate contact with the user. Design of new generations of manipulators with programmable compliance along with higher level controllers that can set the compliance appropriately for the task, are both feasible propositions. We must thus gain a greater insight into the way in which a person interacts with a machine, particularly given that the interaction may be non-passive. We are primarily interested in the change in wrist and arm dynamics as the person co-contracts his/her muscles. It is observed that this leads to a change in stiffness that can push an actuated interface into a limit cycle. We use both experimental results gathered from a PHANToM haptic interface and a mathematical model to observe this effect. Results are relevant to the fields of rehabilitation and therapy robots, haptic interfaces, and telerobotics

Language dominance and lexical diversity: how bilinguals and L2 learners differ in their knowledge and use of French lexical and functional items

This chapter compares lexical diversity of French words used by Dutch-French bilinguals, English-French bilinguals and Flemish L2 learners of French.