Multiple Model Adaptive Control Design A Computer Algebra Approach

Abstract

Abstract-The multiple model adaptive control (MMAC) method potentially has the ability of providing excellent control performance over a wide range of parameter variations. A key part in the design of a MMAC system is the choice of candidate models. In this work, a method to optimally determine these candidate models is proposed. The method exploits the relationship between Grobner bases and polynomial spectral factorization through the notion of sum of roots. Using computer algebra techniques, the symbolic solution to the Algebraic Riccati Equation, and hence the H 2 optimal control problem, can be obtained. The symbolic solution gives the relationship between the optimal controller gains and the uncertain parameters. Hence, the candidate controllers in the MMAC system could be selected based on this relationship to best counter the parameter variations. To illustrate the effectiveness of the proposed method, a case study of a MMAC implementation on a quarter car active suspension with varying sprung mass is presented. The candidate controllers chosen using the proposed method was compared to a similar MMAC system where the candidate controllers were chosen based on equal sprung mass spacing. Simulations were performed under varying sprung masses, and using changing road profiles as a disturbance input. The performance criteria were vertical sprung mass acceleration, tyre force and suspension deflection. The results demonstrated the advantages of the proposed method where improved performances were obtained for all three criteria.