Covariance matrix adaptation evolution strategy based design of fixed structure robust H∞ loop shaping controller

Abstract

This paper proposes the application of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in fixed structure H∞ loop shaping controller design. Integral Time Absolute Error (ITAE) performance requirement is incorporated as a constraint with an objective of maximization of stability margin in the fixed structure H∞ loop shaping controller design problem. Pneumatic servo system, separating tower process and F18 fighter aircraft system are considered as test systems. The CMA-ES designed fixed structure H∞ loop-shaping controller is compared with the traditional H∞ loop shaping controller, non-smooth optimization and Heuristic Kalman Algorithm (HKA) based fixed structure H∞ loop shaping controllers in terms of stability margin. 20% perturbation in the nominal plant is used to validate the robustness of the CMA-ES designed H∞ loop shaping controller. The effect of Finite Word Length (FWL) is considered to show the implementation difficulties of controller in digital processors. Simulation results demonstrated that CMA-ES based fixed structure H∞ loop shaping controller is suitable for real time implementation with good robust stability and performance.