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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 is presented. 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 the high-order H∞ controller is minimized. However, because solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with a 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 that the control specifications are met to a large extent.
Date of Publication: April 2006