Symbolic realization of asymptotic time-scale and eigenstructure assignment design method in multivariable control

Abstract

This paper reports on a symbolic realization of the asymptotic time-scale and eigenstructure assignment (ATEA) state feedback design technique for multivariable control. The resulting state feedback laws are parameterized in a scalar ε. Under these state feedback laws, the closed-loop system possesses a pre-specified time-scale and its eigenstructure approaches a pre-specified one, as the value of the parameter ε approaches zero. By appropriately specifying the time-scale and the eigenstructure, the feedback laws can be obtained to solve various control problems, such as the H ₂ and H _∞ suboptimal control, and almost disturbance decoupling problems. We present, in this paper, the software implementation of the ATEA design algorithm using the MATLAB symbolic programming technique. Our m-functions are capable of returning a result, which is explicitly expressed in terms of a symbolic variable epsilon, which represents ε. The controller design for a piezoelectric bimorph actuator is used to illustrate how the symbolic realization works.