Application of discrete-time variable structure control in the vibration reduction of a flexible structure

This paper studies the application of using the discrete-time variable structure control method to reduce the vibration of the flexible structure. The structure is subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted, and the system is studied by the discrete-time model. Here, discrete sensors and actuators are used. We choose the modal filters as the state estimator to obtain the modal co-ordinates and modal velocities for the modal space control. A discrete-time variable structure controller with a disturbance force observer is adopted due to its distinguished robustness property of insensitiveness to parameter uncertainties and external disturbances. The included disturbance force observer can observe the unknown disturbance modal forces, which are used in the discrete-time variable structure control law to cancel out the excitations. The upperbound limitations of the unknown disturbances in the variable structure control, therefore, are no longer needed. The switching surface, in the discrete-time variable structure control system, is designed in an optimal sense. That is, along the switching surface, the cost function of the states is minimized. The investigation of this research focuses on the optimal switching surface design and the control performances of the discrete-time variable structure controller. The performance of estimating the disturbance modal forces and the robustness property of the control law are also discussed.