Probabilistic Control for the Active-Mass-Driver Benchmark Model

A probability-based robust control design methodology is presented that is applied to the 'benchmark system', which is a high-fidelity model of an active-mass-driver laboratory structure. For the controller design, the objective is to maximize the probability that the uncertain structure/controller system achieves satisfactory performance when subject to uncertain excitation. The controller's robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model with the probability of that model, then integrating over the set of possible models. This is accomplished in an efficient manner using an asymptotic approximation. The probable performance is then maximized over the class of constant-gain acceleration-feedback controllers to find the optimal controller. This control design method is applied to a reduced-order model of the benchmark system to obtain four controllers, two that are designed on the basis of a 'nominal' system model and two 'robust' ones that consider model uncertainty. The performance is evaluated for the closed-loop systems that are subject to various excitations.