Classical and Simple Adaptive Control for Nonminimum Phase Autopilot Design

Abstract

Ar ecent publication uses a difficult design example to show that fuzzy logic might have advantages when compared with classical compensators. Although in this particular case the application was shown to be successful, convergence of the fuzzy-logic algorithm, as well as other time-varying controllers, cannot not be guaranteed unless some preliminary conditions are satisfied. It will be shown that further exploitation of the classical design can improve robust performance. This result is then used to create sufficient conditions that guarantee convergence with time-varying controllers, and it is then shown that simple adaptive control methods can further improve performance and maintain it in changing environments. I. Introduction A RECENT publication 1 has presented successful applications of fuzzy-logic control design in a nonminimum phase autopilot with uncertainty of parameters. The authors use this difficult design case to show that fuzzy logic has advantages when compared with a classical compensator or with the ubiquitous proportional‐ integral‐derivative (PID) design when uncertainty is concerned. Although this particular fuzzy-logic application was successful, it is well known that convergence with nonstationary controllers, including adaptive and fuzzy-logic algorithms, is not inherently guaranteed. This paper intends to show that further exploitation of the basic knowledge of the plant and the uncertainty can be used to improve the performance of a classical control design and also to create sufficient conditions that guarantee convergence of time-varying controllers. The results are presented here in connection with simple adaptive control that is shown to achieve improved performance along with the guarantee of stability. Successful implementations of simple direct adaptive control techniques in various domains of application have been presented over the past two decades in the technical literature. This simpleadaptive-control (SAC) methodology has been introduced by Sobel et al. 2 and further developed by Barkana et al. 3 and Barkana and Kaufman. 4,5 These techniques have also been extended by Wenn and Balas 6 and Balas 7 to infinite-dimensional systems. Those successful applications of low-order adaptive controllers to large-scale examples have led to successful implementations of SAC in such diverse applications as flexible structures, 8−15 flight control, 16,17