A Low-Order H∞ Controller Design for an Active Suspension System via Linear Matrix Inequalities

Abstract

We present an application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H ∞ controller subject to the H ∞-norm of a frequency-weighted error between the approximated controller and high-order H ∞ controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a semidefinite program, so that it can be solved efficiently Application to the active suspension system of the Automatic Laboratory of Grenoble provides a fourth-order controller. The experimental results show the control specifications are met to a large extent.