Showing papers by "Richard H. Middleton published in 1999"

Properties of single input, two output feedback systems

Abstract: We describe properties of linear multivariable feedback systems for which the plant has a single control input and two measured outputs. Particular attention is paid to 'algebraic' design tradeoffs that occur between different feedback properties at the same frequency. To describe these tradeoffs, we use concepts of plant and controller direction and alignment. We show that if plant/controller alignment is poor, then closed loop response to noise and disturbances will be large unless the loop gain is sufficiently small. Moreover, the closed loop system will exhibit large interactions. We also describe a dual set of results that are applicable to feedback systems for which the plant has two control inputs and a single measured output.

Performance limitations in the feedback control of a class of resonant systems

Abstract: There has been a large literature on the feedback control of flexible and resonant systems. Such systems arise naturally when system weight and or response speed issues push designers toward lighter, faster structures for a range of mechanical systems. Feedback control of such systems is often proposed to ameliorate the effects of the resonance. We investigate the extent to which the dynamic structure of a simple class of resonant systems limits the achievable feedback control performance for such systems. It turns out that in the class of systems considered, there is a trade off between three common control objectives, namely: (i) good initial transient response (that is the absence of large overshoot or undershoot in the initial rise time), (ii) fast response, (iii) good settling behaviour (that is, the absence of very slow modes in the step response).

Adaptive stabilization of uncertain discrete-time systems via switching control: The method of localization

Abstract: This chapter presents a new systematic switching control approach to adaptive stabilization of uncertain discrete-time systems. The approach is based on a method of localization that is conceptually different from supervisory adaptive control schemes and other existing switching control schemes. The proposed approach allows for slow parameter drifting, infrequent large parameter jumps, and unknown bound on exogenous disturbances. The unique feature of the localization-based switching adaptive control, proposed in the chapter, is its rapid model falsification capability. In the LTI case this is manifested in the ability of the switching controller to quickly converge to a suitable stabilizing controller. It is believed that the approach is applicable to a wide class of linear time invariant and time-varying systems with good transient performance.

Feedback systems with an almost rank deficient plant

Abstract: Consider properties of a feedback system for which the plant is almost rank deficient at a given frequency. We introduce a measure of input redundancy, and investigate its dependence upon scaling. Feedback properties are shown to be governed by two plant/controller alignment angles. We suggest ways to choose the controller based upon plant properties in order that these angles be satisfactory.

Cheap control performance of a class of non-right-invertible nonlinear systems

Abstract: For strict-feedback nonlinear systems, this paper shows that it is impossible to reduce to zero the optimal cost in the regulation of more states than the number of control inputs in the system, even using unrestricted control effort. By constructing a near optimal cheap control law, we characterise the infimum value of the optimal regulation cost as the optimal value of a reduced-order regulator problem where the states with lower relative degree drive those with higher relative degree. We illustrate our results with two examples of practical interest: the optimal regulation of the rotational motion of a free rigid body, and the optimal control of a magnetic suspension system.

A novel approach to systematic switching control design for a class of hybrid systems

Abstract: We propose and investigate a new systematic switching control design method applicable to a class of nonlinear discrete time hybrid systems. The main objective of this paper is to present a systematic algebraic approach to stabilizability analysis for the systems.

Performance limitations in a class of single-input two-output nonlinear systems

Abstract: This paper shows that there exists a structural limitation in reducing the integral of the squared regulation error in strict-feedback nonlinear systems with more outputs (that is, performance variables) than inputs. This limitation arises from the fact that, in these systems, some outputs are controlled only indirectly through other outputs with lower relative degree. It is then impossible to uniformly reduce the overall regulation cost to zero, the infimum value of which is characterised by a reduced-order optimal regulation problem. Although essentially nonlinear, the results are similar in nature and have direct connections with their linear counterparts.

Properties of finite rank operators that arise in approximation of integral operators related to linear dynamical systems

Abstract: In this paper we present an integral operator that arises in the context of linear dynamical systems, which describes the time evolution of the state probability density function. We propose a finite rank approximation to this integral operator and show that this finite rank operator converges in norm to the integral operator. We discuss Markov chains arising from this finite rank approximation, and show that the eigenvalues of the transition matrices of these Markov chains converge to the eigenvalues of the integral operator as the number of divisions in the statediscretization is increased. AMS subject classification. 93C30.