Using Constrained Bilinear Quadratic Regulator for the Optimal Semi-active Control Problem

[+] Author and Article Information
Ido Halperin

Department of Civil Engineering, Faculty of Engineering, Ariel University, Ariel, 40700, Israel

Grigory Agranovich

Professor, Department of Electrical and Electronics Engineering, Faculty of Engineering, Ariel University, Ariel, 40700, Israel

Yuri Ribakov

Professor, Department of Civil Engineering, Faculty of Engineering, Ariel University, Ariel, 40700, Israel

1Corresponding author.

ASME doi:10.1115/1.4037168 History: Received August 31, 2016; Revised June 21, 2017


Semi-active systems provide an attractive solution for the structural vibration problem. A useful approach, aimed to simplify the control design, is to divide the control system into two parts: an actuator and a controller. The actuator generates a force that tracks a command which is generated by the controller. Such approach reduces the complexity of the control law design as it allows for complex properties of the actuator to be considered separately. In this study, the semi-active control design problem is treated in the framework of optimal control theory by using bilinear representation, a quadratic performance index and a constraint on the sign of the control signal. The optimal control signal is derived in a feedback form by using Krotov's method. To this end, a novel sequence of Krotov functions which suits the multi-input constrained bilinear-quadratic regulator problem is formulated by means of quadratic form and differential Lyapunov equations. An algorithm is proposed for the optimal control computation. A proof outline for the algorithm convergence is provided. The effectiveness of the suggested method is demonstrated by numerical example. The proposed method is recommended for optimal semi-active feedback design of vibrating plants with multiple semi-active actuators.

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