Robustness Gradients for Discrete-Time Control Systems

Abstract

This article addresses gradients for discrete-time control system design. First, the stability margin is investigated based on the minimum distance of the Mikhailov hodograph to the origin or on the minimum distance of the closed-loop poles to the unit circle. The gradients with respect to the output state controller matrix are derived and applied for stepwise, improving the dynamics of the closed-loop system. Second, the maximum admissible uncertainty of the plant is considered based on the unstructured type of uncertainty. For robustification, gradients to attain maximum admissible uncertainty are introduced.

Robustness and Dynamic Interaction

“…Following Weinmann (2006), the controller is changed towards reduction of the interaction energy. The system is simulated for the nominal and the perturbed process.…”

Stability Margin and Spherical Uncertainty

“…(For single-input single-output systems, h 0 corresponds to q à of Tesi et al 1995. ) The stability margin h 0 of a nominal (unperturbed) multivariable dynamic system of nth order with the coefficients matrix A cl of the closed loop results from executing the minimization (Weinmann 2005(Weinmann , 2006 …”