Parametric and Nonparametric Identification and Robust Control of a Rotational/Translational Actuator

RTAC benchmark problem considers a nonlinear fourth-order dynamical system involving the nonlinear interaction of a translational oscillator and an eccentric rotational proof mass. This problem has been posed to investigate the utility of a rotational proof mass actuator for stabilizing translational motion. In order to implement any of the model-based controllers proposed in the literature, the values of model parameters are required which are generally difficult to determine rigorously. In this paper, an approach to the least-squares estimation of system parameters is discussed and practically applied to the benchmark problem. Next, in order to design an H
∞
controller, the nonlinear system is modelled as a perturbed linear system using an effective identification scheme. Experimental results confirm that this approach can effectively condense the whole nonlinearities, uncertainties, and disturbances within the system into a favorable perturbation block. Finally, an effective mixed-sensitivity problem is developed for the system to satisfy all performance requirements as well as robust stability despite actuator saturation.