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

• Design of fixed structure H∞ loop shaping controller using CMA-ES.
• Integral Time Absolute Error performance requirement is included as a constraint.
• ɛc-constraint relaxation method is incorporated to CMA-ES for handling the constraint.
• Flexibility to fix the controller structure in H∞ loop shaping controller design.
• The higher order controller implementation difficulties are also discussed.
• Statistical results of CMA-ES, non-smooth and Heuristic Kalman Algorithm are analyzed.

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.

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