Adaptive optimal control algorithm for vibrational systems under nonlinear friction

In this paper a novel control algorithm for vibration attenuation is presented. Proposed scheme is developed to control linear systems with presence of external disturbance. The goal of the control is to steer the system to prescribed reference trajectory by minimizing associated quadratic performance index. The synthesis of the control law consists of two steps. At the first step, past measures of disturbance are used to develop local linear approximation of dynamics of disturbance signal. Weights of the associated auto-regressive model are calculated by the least-square algorithm. At the second step, calculated model is used to obtain linear time-invariant approximation of the control system. The receding horizon control law is then calculated by using finite horizon Linear Quadratic Regulator. The algorithm is verified numerically for torsional vibrating system under nonlinear, time-varying friction. The results of simulation are compared to a standard Linear Quadratic Gaussian control.