GA-based robust H2 controller design approach for active suspension systems

For the design problem of active suspension systems, the purpose of compensator is to suppress the road disturbances and to tolerate the different body mass. From the control viewpoints, this kind of compensators is equal to the robust controller for which the H₂ norm is minimized. In this paper, we attempt to use a Simple Genetic Algorithm (SGA) to find out the compensator. The notion is that all elements of compensator are randomly given. The compensator is determined by use of the fitness function which is composed of stability conditions, i.e., we determine the compensator according to the grade of stability. Thus we derive new stability conditions and convert them into numerals. To enhance the computing speed, we propose a Hierarchical Fitness Function Structure (HFFS) to merge these numerals into a unique fitness value. Based on these quantified stability conditions, HFFS and SGA, we can find the compensator without using complex mathematical derivation. Besides, we derive the new stability conditions by using the concept of family of polynomials, the generalized edge theorem, Hurwitz testing matrix and some simple control concept rather than using Lyapunov stability criteria. The purpose is to relax the stability constraints.