Multi-criteria optimal pole assignment robust controller design for uncertainty systems using an evolutionary algorithm

This paper presents the synthesis of an optimal robust controller design using the polynomial pole placement technique and multi-criteria optimisation procedure via an evolutionary computation algorithm – differential evolution. The main idea of the design is to provide a reliable fixed-order robust controller structure and an efficient closed-loop performance with a preselected nominally characteristic polynomial. The multi-criteria objective functions have quasi-convex properties that significantly improve convergence and the regularity of the optimal/sub-optimal solution. The fundamental aim of the proposed design is to optimise those quasi-convex functions with fixed closed-loop characteristic polynomials, the properties of which are unrelated and hard to present within formal algebraic frameworks. The objective functions are derived from different closed-loop criteria, such as robustness with metric H${\cal H}$∞, time performance indexes, controller structures, stability properties, etc. Finally, the design results from the example verify the efficiency of the controller design and also indicate broader possibilities for different optimisation criteria and control structures.