H-INFINITY-CONSTRAINED QUASI-LINEAR QUADRATIC GAUSSIAN CONTROL WITH LOOP TRANSFER RECOVERY

In this paper we propose a new nonlinear controller design method, cal led quasi-linear quadratic Gaussian/H-infinity/loop transfer recovery (QLQG/H-infinity/LTR), for nonlinear multivariable systems with hard n onlinearities such as Coulomb friction and dead-zones. We consider H-i nfinity-constraints for the optimization of statistically linearized s ystems, by replacing the covariance Lyapunov equation by a modified Ri ccati equation, whose solution leads to an upper bound QLQG performanc e. As a result, the nonlinear correction term is included in the Ricca ti equation which, in general, is excessively difficult to solve. nume rically. To solve this problem, we use the modified loop shaping techn ique and derive analytic proofs of the LTR condition. Finally, the H-i nfinity-constrained nonlinear controller is synthesized by an inverse random input describing function technique (IRIDF). The proposed desig n method for a hard nonlinear multivariable systems has better robustn ess to unstructured uncertainty and hard nonlinearities than the QLQG/ LTR method. A flexible link system with Coulomb frictions serves as a design example for our methodology.