Robust model reference adaptive control in the presence of bounded uncertainty

Robustness is defined here as maintaining performance and stability in the presence of uncertainties associated with the modeling process, the control system, and its environment. Modeling uncertainties arise from parameter variations due to change in operating conditions and the margin of error associated with estimating model parameters based on analytical tools and experimental data.; A robust model reference adaptive control (MRAC) system is developed for both multi-input multi-output (MIMO) and single-input single-output (SISO) linear plants of order n in the presence of process disturbance, parameter variations, and measurement noise, all characterized by known bounds. For MIMO linear plants, it is assumed that all states are accessible. The objective of the robust adaptive control system is to assure bounded error between the plant output and the output of a stable reference model.; The design of the robust model reference adaptive control system is based on assumptions concerning the structure of the plant. The adaptive control system for MIMO linear plants whose states are accessible consists of feedback and feedforward gain matrices. On the other hand, for SISO linear plants in the presence of only output measurement rather than full state feedback, the adaptive control system is considerably more complicated. This arises from the need to introduce dynamics into the controller structure so that the transfer function of the plant together with the adaptive controller is identical to that of the reference model. The structure of the adaptive controller is divided into two cases. In the first case, the plant is assumed to have a transfer function of relative degree (number of poles {dollar}-{dollar} number of zeroes) unity and the reference model is chosen to be strictly positive real. The second case deals with plants having a relative degree greater than 1. In both cases, for perfect tracking or regulation the plant has to satisfy a few basic assumptions concerning minimum phase zeroes and the sign of the high frequency gain.; Lyapunov's direct method is used to verify an adaptation law which adjusts the parameters of the feedforward gain matrix and the feedback gain matrix in the MIMO case. This adaptation law uses the available signals of the plant and the reference model as well as the prior information available regarding the bounded disturbances to guarantee that the adaptive control system remains stable and the tracking error is bounded for arbitrary initial parameter values. In the SISO case, the adjustment of the controller parameters is carried out using an augmented error signal. Again, Lyapunov's direct method is used to confirm resulting stability. An important feature of these adaptation laws is that no persistent excitation is required for the tracking convergence properties of the resulting robust adaptive control system.; Simulation results are presented to demonstrate the theoretical developments.