Robust-optimal active vibration controllers design for the uncertain flexible mechanical systems possessing integrity via genetic algorithm

In this paper, a robust-optimal control approach is proposed to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under mode truncation, linear time-varying parameter uncertainties in both the controlled and residual parts, feedback gain perturbations, estimator gain perturbations and partial actuator failures. A sufficient condition is proposed to ensure that the flexible mechanical systems with time-varying structured parameter uncertainties are asymptotically stable against partial actuator failures. Systems which have such a property of keeping stable under partial actuator failures are said to possess integrity, and this is an inherent property of MIMO systems. Based on the robust stability constraint and the minimization of a defined H2 performance, a hybrid Taguchi-genetic algorithm (HTGA) is applied to solve the optimal state feedback controller and observer design problem of uncertain flexible mechanical systems. A design example of a flexible rotor system is given to demonstrate the applicability of the proposed approach. It is shown that the proposed approach can obtain satisfactory results.