Model reference adaptive control for a flexible beam with time delay and uncertain parameters
摘要
Theoretical and experimental studies of model reference adaptive control of linear system with time delay and uncertain parameters are presented in this paper, where time delay is uncertain bounded delay. Firstly, the continuous time approximation method is used to handle the input-delay in the system. By means of the difference equation of control input with time-delay, the dynamic equation of the system with delay is changed to augmented state equation without delay in the form. Then, the state equation of a reference model is established based on the time-delay system and known variables, and the corresponding controller for the state equation of the reference model is designed using linear quadratic regulator method. At last, model reference adaptive controller with like-observer is carried out based on the linear quadratic regulator controller. Simulations and experiments on a flexible cantilever beam are carried out to demonstrate the effectiveness of the designed controller. Uncertainty of the first natural frequency of the beam and the uncertain time delay are both considered. The results show that the proposed method can effectively suppress the vibration of the cantilever beam, and the simulation and experiment results are in well agreement with each other.