A New Optimal Sliding Mode Controller with Adjustable Gains based on Bolza-Meyer Criterion for Vibration Control

Abstract In this study, a new optimal control law associated with sliding mode control is developed based on basis of the Bolza-Meyer criterion. The salient characteristic of the proposed controller is to have gains adjustability, where the gain values can be larger than one. This leads to enhancing control system performances with a given cost function. It should be pointed out that conventional optimal controllers usually have constant gains of one or less than one, and hence the control system performances such as the requirement on convergence speed may not be satisfactory. After formulating the proposed optimal control law for polynomial time-varying control systems, computer simulations are carried out to validate the benefits of the proposed approach. Firstly, as an illustrative example, three crucial index values including control gain index, main input control index and the state index are investigated. Secondly, the proposed controller is applied to a vehicle seat suspension system with magneto-rheological damper to evaluate vibration control performances. In simulation studies, a comparison between the proposed approach and a state-of-the-art optimal controller is undertaken to demonstrate additional benefits such as less power and faster convergence of the proposed optimal controller.