Control of systems subject to uncertainty and constraints

Abstract

All practical control systems are subject to constraints, namely constraints aris¬ing from the actuator’s limited range and rate capacity (input constraints) or from imposed operational limits on plant variables (output constraints). A linear control system typically yields the desirable small signal performance. However, the presence of input constraints often causes undesirable large signal behavior and potential insta¬bility. An anti-windup control consists of a remedial solution that mitigates the effect of input constraints on the closed-loop without affecting the small signal behavior. Conversely, an override control addresses the control problem involving output con¬straints and also follows the idea that large signal control objectives do not alter small signal performance. Importantly, these two remedial control methodologies must in¬corporate model uncertainty into their design to be considered reliable in practice. In this dissertation, shared principles of design for the remedial compensation problem are identified which simplify the picture when analyzing, comparing and synthesiz¬ing for the variety of existing remedial schemes. Two performance objectives, each one related to a different type of remedial compensation, and a general structural representation associated with both remedial compensation problems will be consid¬ered. The effect of remedial control on the closed-loop will be evaluated in terms of two general frameworks which permit the unification and comparison of all known remedial compensation schemes. The difference systems describing the performance objectives will be further employed for comparison of remedial compensation schemes under uncertainty considerations and also for synthesis of compensators. On the ba¬sis of the difference systems and the general structure for remedial compensation, systematic remedial compensation synthesis algorithms for anti-windup and override compensation will be given and compared. Successful application of the proposed robust remedial control synthesis algorithms will be demonstrated via simulation.