Digital controller design for time-delayed Bouc-Wen hysteretic systems

Bouc-Wen model is a popular analytical form to describe hysteretic system while the non-smooth absolute-value function terms in the model bring about challenges in control system design. Different from traditional piecewise approach, this paper presents a digital control design methodology based on a revised model with a universal smooth representation. In the proposed method, approximated scalar sign function in a smooth rational form is utilized to replace the non-smooth absolute-value function terms, resulting in an approximate description of Bouc-Wen model with adjustable accuracy and universal smoothness which facilitates the following linearization. Then the optimal linearization technique is adopted to obtain an accurate local linear model at any operating point. Next, an analog controller is developed based on the local linear model to attain the required control performance. Then through digital redesign, the analog controller is converted to the digital counterpart which is further capable of compensating time delays arising from controller computation, A/D and D/A conversion etc. The feasibility and effectiveness of the proposed method have been verified through simulations with two illustrative examples.