Robust Control Algorithm for Linear MIMO Plants in Conditions of Saturation of the Control Signal

Abstract

The paper describes the robust control algorithm for the linear dynamic multi input multi output plants in the conditions of parametric uncertainties, external bounded disturbances and saturation of the input signal. Firstly, the author proposed the disturbance compensation algorithm, which ensured tracking of a plant output to the reference signal with a given accuracy without constraints in the control signal. It is shown that the structure of the control law does not depend on the dynamical order of the plant model. Therefore, the proposed algorithm can be used for the structural uncertainty plants. Besides, the proposed result generalizes some control algorithms, such as the consecutive compensator designed by A. A. Bobtsov, the algorithm based on a high gain observer proposed by H. Khalil and the auxiliary loop algorithm designed by A. M. Tsykunov. Secondly, the proposed algorithm is generalized for the case, when a control signal belongs to the given bounded set. The approximation algorithm of saturation of nonlinearity and the disturbance compensation algorithm for the design of the control law are used. The conditions depending on the parameters of the plant, the reference model and the algorithm for implementation of the control system under perturbations and control constraints are presented. The author considers two examples for the single input single output plant and the multi input multi output plant. The simulation results illustrate the efficiency of the proposed algorithm and confirm the analytical results. The theorem of the sum of the stable polynomials proposed by A. Feuer, A. S. Morse, K. S. Narendra and L. S. Valavani is generalized on the structural uncertainty polynomials and matrix polynomials for the proof of the closed-loop stability.