Constrained H̳₂ design via convex optimization with applications

Abstract

A convex optimization controller design method is presented which minimizes the closed-loop H2 norm, subject to constraints on the magnitude of closed-loop transfer functions and transient responses due to specified inputs. This method uses direct parameter optimization of the closed-loop Youla or Q-parameter where the variables are the coefficients of a stable orthogonal basis. The basis is constructed using the recently rediscovered Generalized Orthonormal Basis Functions (GOBF) that have found application in system identification. It is proposed that many typical control specifications including robustness to modeling error and gain and phase margins can be posed with two simple constraints in the frequency and time domain. With some approximation, this formulation allows the controller design problem to be cast as a quadratic program. Two example applications demonstrate the practical utility of this method for real systems. First this method is applied to the roll axis of the EOS-AM1 spacecraft attitude control system, with a set of performance and robustness specifications. The constrained H2 controller simultaneously meets the specifications where previous model-based control studies failed. Then a constrained H2 controller is designed for an active vibration isolation system for a spaceborne optical technology demonstration test stand. Mixed specifications are successfully incorporated into the design and the results are verified with experimental frequency data.