Richard H. Middleton

Design issues in adaptive control

An integrated approach to the design of practical adaptive control algorithms is presented. Many existing ideas are brought together, and the effect of various design parameters available to a user is explored. The theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators. It is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics. >

Improved finite word length characteristics in digital control using delta operators

This paper examines some of the consequences of finite word lengths in digital control. It is shown that, in many cases of practical importance, the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach. This latter approach is shown to give better coefficient representation and less roundoff noise in many cases. We thus argue that the shift operator and its associated Z -transform can be replaced by delta operators and their associated transform which we designate a Δ-transform. An added advantage of this approach is that discrete designs and transforms converge to their continuous-time counterparts as the sampling rate is increased.

Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels

There has recently been significant interest in feedback stabilization problems over communication channels, including several with bit rate limited feedback. Motivated by considering one source of such bit rate limits, we study the problem of stabilization over a signal-to-noise ratio (SNR) constrained channel. We discuss both continuous and discrete time cases, and show that for either state feedback, or for output feedback delay-free, minimum phase plants, there are limitations on the ability to stabilize an unstable plant over an SNR constrained channel. These limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity bit rate over the same channel.

Adaptive computed torque control for rigid link manipulators

Abstract In this paper we shall examine the adaptive control of rigid link manipulator systems. Linear estimation techniques together with a computed torque control law are shown to give a globally convergent adaptive system which does not require measurements of accelerations.

Transient stability enhancement and voltage regulation of power systems

Improvement of the transient stability and voltage regulation of a single-machine-infinite-bus power system under the effects of a symmetrical three-phase short-circuit fault is detailed. The dynamical model of the system is described. A design strategy for nonlinear controllers is considered, and the design of a nonlinear variable-structure excitation controller is described. Simulation results obtained using the nonlinear excitation controller are given, and a new nonlinear coordinated controller is proposed. Simulation results obtained by using the nonlinear coordinated controller are presented. >

Trade-offs in linear control system design

Abstract For some time now, many practitioners and researchers in the control area have been aware that unstable open loop poles, non-minimum phase zeros, and/or time delays make control systems design difficult. In this paper we examine the nature of these difficulties by discussing the results of Freudenberg and Looze (1987, 1988) and Sung and Hara (1988) on integral constraints on sensitivity functions. One of the key conclusions here is a set of rules of thumb, giving limitations on the closed loop bandwidth which are imposed by unstable open loop poles, non-minimum phase zeros and/or time delays.

High-speed digital signal processing and control

An attempt is made to organize and survey recent work, and to present it in a unified and accessible form. The need for a new approach suitable for high-speed processing is discussed in the context of several applications in control and communications, and a historical perspective of the use of difference operators in numerical analysis is presented. The general systems calculus, based on divided-different operators is introduced to unify the continuous-time and discrete-time systems theories. This calculus is then used as a framework to treat the three problems of system state estimation; system identification and time-series modeling; and control system design. Realization aspects of algorithms based on the difference operator representation, including such issues as coefficient rounding and implementation with standard hardware, are also discussed. >

Brief Networked control design for linear systems

In this paper we study a systematic networked control method designed specifically to handle the constraints of the networked realization of a linear time invariant control system. The general structure of the proposed controller requires switching between the open loop and closed loop subsystems of the controller which is dictated by the behaviour of the communication network.

Rapprochement between continuous and discrete model reference adaptive control

Abstract In the literature to date there is a dichotomy between results on continuous- and discrete-time model reference control. This is highlighted in the case of continuous-time systems having relative degree greater than one. It is known that, for rapid sampling, these systems always give rise to a non-stably invertible discrete-time system and thus discrete model reference control is ruled out. On the other hand, there are many results pertaining to continuous-time model reference control of such systems. This apparent paradox can be resolved by a slight modification to the discrete-time model format as shown later. This alternative model is used to develop a new discrete model reference adaptive control law and a convergence analysis for the algorithm is presented.

Adaptive control of time-varying linear systems

The authors present a global bounded-input-bounded-state stability theory for a class of continuously adapting controllers applied to time-varying linear systems. This gives theoretical support to the application of many of the algorithms used in practice. A key feature of the analysis is that no persistence of excitation requirement is needed. >