Abstract A Robust Universal Controller 1.pdf

A Robust Universal Controller1 S. H. Lam Princeton University Department of Mechanical and Aerospace Engineering Princeton, NJ 08544 lam@princeton.edu Abstract The present paper advocates the use of ODE-based (instead of algebra-based) constraints on the output variables of a controlled system, and the use of dynamic control laws (instead of static control laws)—when fi- nite but small errors in honoring the constraints are considered acceptable. It is assumed that the sensor signals are reliable and have good signal-to-noise ratios, that the controller has ample computational power, and that the hardware/software “sampling time” ts is much smaller than the system characteristic time tg. A uni- versal dynamic control law is proposed which does not require detailed knowledge of the system itself—and is therefore completely robust with respect to uncertain- ties of the system—provided the control problem to be solved is reasonable. The meaning of the equivocal word “reasonable” will be explained. 1 Introduction The approach advocated by this paper is based on the concatenation of two new ideas: ? Instead of imposing algebra-based constraints on the sensor signals, a set of ODE-based constraints are specified. ? Instead of looking for static control laws, the new approach looks for dynamic control laws which ap- proximately honor the ODE-based constraints. With this new approach, the only information about a dynamic system needed by the controller is some “sur- rogate” of the extended pulse-response matrix Bmi (t) (defined in §2.3 later by Eq. (7c)) which is closely 1Supported by NSF Grant #MSS-9302294 and AFOSR URI Grant F49620-93-1-0427. Presented at the 1997 ASME IMECE, Dallas, Texas. related—but is not identical—to the so-called “de- coupling matrix” (Isidori, 1995). Most importantly, this Bmi (t) matrix can be determined on-the-fly—in principle—directly by the controller itself (see §2.3). Unlike most current adaptive control theories (Ioan- nou and Sun, 1996; Mar