Direct Computation of the Performance Index for an Optimally Controlled Active Suspension with Preview Applied to a Half-Car Model

A quadratic integral performance index is defined for a linear active preview-type suspension and a series of matrix expressions derived for its evaluation by means of MATLAB or some similar computer program in the case of a unit step input to the system. The computation, which is both fast and accurate compared to simulation, requires the solution of Lyapunov- and Riccati-type equations. Some examples of numerical computation are given and these show excellent agreement with published results. The conclusion features a useful computer program.