Polytopic topic Bilinear System Modeling and Nonlinear H∞ Control Design for Semi-Active Suspension System

As an important class of nonlinear system, polytopic bilinear system is investigated. Combined with the properties of convex polytope, the nonlinear control for polytopic bilinear system is formulated by synthesizing nonlinear H_∞ controller which is designed for polytopic bilinear system at vertices. For a semi-active suspension system with controllable damping and variant stiffness elements, it is easily modeled as a polytopic bilinear system model. In this case, the desired nonlinear control properties are pursued in making effective use of the changeable damping property while the variant stiffness is taken as the affine parameter of polytopic model. Therefore, polytopic bilinear system model could be reduced to a feasible problem by polytopic convex decomposition. Then the control problem of bilinear system model is to find a solution of nonlinear H_∞ control. Here, the merits in using nonlinear H_∞ state feedback control are that it can confine the damping force output to 1^st and 3^rd phase planes where changeable damping force is produced and its nonlinear control output makes a fast state origin convergence in keeping small vibration and motion. In this paper, a practical control design demonstration for a polytopic bilinear suspension system is described after the theory description. The simulation study and experimental results demonstrate the effective control performance in improving ride comfort.