Disturbance rejection of non-minimum phase MIMO systems: An iterative tuning approach

An iterative tuning method is presented to obtain the multi-input multi-output (MIMO) feedforward controller coefficients to improve disturbance rejection in non-minimum phase (NMP) MIMO systems. In the NMP systems, eliminating the effect of disturbances may cause instability and also can impose extra costs to control the entire system. For this purpose, a simple feedforward controller structure is proposed. The unknown variables of the feedforward controller are calculated using LMIs such that the H∞ norm of the transfer function matrix from disturbance to output is minimized. By taking advantage of the frequency sampling techniques into account and using some iterative algorithms, a new tractable method is constructed to solve the problem. Also, a condition based on the right half plane (RHP) zero direction for the NMP system has been proposed to improve the disturbance rejection property of these systems. To obtain optimal coefficients, the algorithm is repeated several times to reach the best answer. The method employs convex technics and CVX software to perform calculations. The efficiency of the method is shown in various practical examples using different performance indicators such as integral of absolute error (IAE), integral of squared error (ISE), integral of time multiplied by absolute error (ITAE), integral of time multiplied by squared error (ITSE).