ROBUST & OPTIMAL REGULATION USING A FEEDFORWARD-FEEDBACK SCHEME

Abstract

This work focuses on robust control systems design. Specifically, the robust regulation problem is solved using an H00 optimization approach. There are two aspects to this problem: namely robust disturbance rejection and robust tracking. A 2 degree-of-freedom (d.o.f.) controller is used for this purpose. The feedback compensator is designed to robustly stabilize the dosed-loop system and also to reject the disturbance (by minimizing the sensitivity function), while the feedforward compensator is designed independently for robust tracking. A method of solution to control systems design is to parametrize the class of all stabilizing compensators, from which an appropriate one satisfying additional desired objectives may be selected (here in an optimal fashion). The parametrization of all such solutions to the robust disturbance rejection and robust tracking problem are respectively given in Theorems 4.1 and 4.2. For the latter, we provide a new proof to link Vidysagar's [94] results for square plants with those of Sugie & Yoshikawa [86] which extends to nonsquare plants. Corollaries 4.1 to 4.3 specify the set of all compensators that achieves robust tracking. The latter two parametrizations are new. Minimizing the sensitivity function (for robust disturbance rejection) and tracking error alone is inadequate, as it does not consider other objectives like power constraints, robustness to plant uncertainty and so on. Thus we also looked into nominal performance vs control effort (or robust stability) trade-off for both cases. The idea of plant augmentation (Postlethwaite et al., 1990) is introduced to overcome the violation of the solvability conditions due to unstable reference or disturbance generators. For the 1 d.o.f. scheme, the robust disturbance rejection and robust tracking problems are equivalent. There is no advantage in using a 2 d.o.f. controller for achieving robust disturbance rejection alone since a stable feedforward compensator does not influence feedback properties. But for robust tracking, a 2 d.o.f. controller will result in a. cost no larger than that for a 1 d.o.f. scheme. Whether the feedback controller is optimal or not, the inclusion of the feedforward controller will result in the same optimal cost, though the actual feedforward controller parameters will be different. Thus, the extra d.o.f. in the former can be exploited to achieve simultaneously good disturbance rejection and good tracking. Stability and performance robustness of the controllers are also discussed. The conditions for performance robustness for the single-input single-output (SISO) case are summarized in Theorem 5.3. In particular, the sufficient conditions for robust tracking are our own. Finally, implementation issues like performance limitations, weighting function selection, and controller-order reduction are looked into. This work provides some understanding in using a 2 d.o.f. controller to solve, in particular, the robust regulation problem in an H00 optimaI control framework and also the issues involved.