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Structural Engineering and Mechanics
  Volume 20, Number 2, May30 2005 , pages 191-207

Active control of a flexible structure with time delay
Guo-Ping Cai and Simon X. Yang

    Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.
Key Words
    flexible structure; variable structure control; time delay.
Guo-Ping Cai; Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China
Simon X. Yang; Advanced Robotics and Intelligent Systems (ARIS) Lab, School of Engineering, University of Guelph, Guelph, Ontario N1G 2W1, Canada

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