Indirect adaptive techniques for fixed controller performance enhancement

Abstract

This paper develops the adaptive disturbance estimate feedback schemes of a companion paper for enhancing the performance of controllers designed by off-line techniques. The developments are based on the parametrization theory for the class of all stabilizing controllers for a nominal plant, and the dual class of plants stabilized by a nominal controller. Such parametrization allows us conveniently to parametrize plant uncertainties for on-line identification and control purposes, minimizing the effects of unmodelled dynamics. Based on these parametrizations, along with prefilteringwhich minimizesthe effect of unmodelled dynamics, standard adaptive stabilization, adaptive pole assignment, or adaptive linear quadratic schemesare shown to achieve controller enhancement. The idea is to exploit a priori information about a plant and design objectivesin an off-line design, and yet exploit the power of adaptive techniques to learn and tune on-line. Attention is focused on techniques for fixed but uncertain plants. IntroductionControl theory has tended to develop in two separate directions. Off-line robust control exploits the a priori information about a plant and the off-line power of computers to achieve robust controllers that achieve performance objectives. On-line adaptive control theory has as its ideal to learn and implement on-line whatever is necessary to achieve the control objectives. Most of the significant results developed are those for the input-output (black box) model. Adaptive schemes are known to work well for low-order models with simple objectives. Inclusion of a priori plant information does not always allow a convenient plant parametrization for on-line identification based on least squares, although the less well understood recursive prediction error schemes can be applied.There is still a need for methods to apply adaptive techniques efficiently to assist in the control of high-order plants when there is a priori plant information. The challenge addressed here, as by Moore (1988) andWittenmark (1988), is to find convenient parametrizations which allow adaptive techniques to work.In our earlier paper (Tay and Moore 1988) the problem of enhancing a fixed controller performance using additional filtering and standard recursive least-squares based algorithms is developed. Off-line and on-line controller designs are blended harmoniously together based on the theory for the class of all stabilizing controllers. In this paper, the approach of Tay and Moore (1988) is broadened to permit the blending of standard adaptive pole-assignment, or adaptive linear quadratic designs, or indeed any adaptive stabilizing scheme to achieve enhancement of off-line designed

Switching between stabilizing controllers

“…Then, because of Lemma 1, S(σ) is exponentially stable, uniformly over S and its state x and output u C remain bounded for every σ ∈ S. Because of (27), e T is then also bounded, as well as all other signals. Moreover, if r = d = n = 0 then e converges to zero exponentially fast, because of (28), and so does u C and all the remaining signals.…”

High Performance Control

“…The robust stabilization theory for the pair (K (Q), G(S)) was first developed in Tay, Moore and Horowitz (1989). Its generalization to plants P(S) incorporating a disturbance response, that is to pair (K (Q), P(S)), is straightforward, as is the application of the results to robust regulation.…”

Active Control and Closed-Loop Identification of Flutter Instability in a Typical Section Airfoil

“…Open-loop system identification techniques will give erroneous and biased estimates of G. One remedy is to estimate the closed-loop system Ps Gs= 1 GsKs from measurements of y and a persistently exciting reference signal r. The plant can then be calculated from the [12][13][14] …”