Multi-variable System Of Direct Model Reference Adaptive Control

This paper mainly deals with two theoretical problem of adaptive control: direct model reference adaptive control for multiple-input-multiple-output (MIMO) systems of uniform relative degree two and direct model reference adaptive control for multiple-input-multiple-output(MIMO) specific systems of uniform relative degree three, which is composed of the following two parts.1. The design and analysis of the direct model reference adaptive control with relative degree two.Consider the following LTI systemwhere G_p(s) is the transfer matrix of the plant and it has uniform relative degree n^* = 2, that is, lim_{sâ†'∞}s²G_p(s) = K_p, where the nonsingular matrix K_p is referred to as the HFG matrix .Control objective is to design an output feedback control u such that all the signals in the closed-loop system are all uniformly bounded and the output y can track the following reference model output y_m as close as possiblefor any reference signal r(t), where r(t) is uniformly bounded. To meet the control objective, the assumptions of the system, the reference model are needed in the second chapter.In this part, for the general systems with relative degree n^*=2, the problem of direct model reference adaptive control is considered. The parametrization based on the LDU and LDS factorization reduces the design of a square MIMO MRAC to the design of m single-input-single-output(SISO) MRAC, stability and tracking performance of the closed-loop plant are analyzed rigorously. The effectiveness of the control scheme is demonstrated by a simulation example.2.The design and analysis of the direct model reference adaptive control with relative degree three.Compared with the system with relative degree two, we consider a identical system, but where G_p(s) is the transfer matrix of the plant and it has uniform relative degree n^* = 3, that is, lim_{sâ†'∞}s³G_p(s) = K_p. where the nonsingular upper triangular matrix K_p is referred to as the HFG matrix.Control objective is to design an output feedback control u such that all the signals in the closed-loop system are all uniformly bounded and the output y can track reference model output y_m as close as possible. To meet the control objective, the assumptions of the system, the reference model are needed in the three chapter.To the system with relative degree three, there are some difficulties. If we imitate the control law of the system with relative degree two, which involves (?), that is not available for measurement. Consequently the control law cannot be implemented and the choice of control law is not feasible.Therefore, to the system with relative degree three, we introduce 'nonlinear damping' based on stability considerations. By designing 'nonlinear damping', a closed-loop system is obtained. Based on the system, a design scheme of adaptive output feedback controller is given. It is proved that all the signals in the closed-loop system are bounded, and the output of each subsystem converges to zero. The effectiveness of the control scheme is demonstrated by a simulation example.