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Simultaneous optimisation of the low-pass filter and state-feedback controller in a robust repetitive-control system

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4 Author(s)
She, J.-H. ; Sch. of Comput. Sci., Tokyo Univ. of Technol., Tokyo, Japan ; Wu, M. ; Lan, Y.-H. ; He, Y.

A low-pass filter is inserted in a repetitive controller to guarantee the stability of the modified repetitive-control system. The control precision strongly depends on the parameter of the filter. This study presents a method of simultaneously optimising the parameters of the low-pass filter and state feedback of a modified repetitive-control system in which the plant contains a class of uncertainties. First, the relationship between the control precision of a repetitive-control system and a low-pass filter is explained. Next, a linear matrix inequality (LMI)-based robust-stability condition is derived for fixed state-feedback gains. This condition is transformed into a generalised eigenvalue problem and is used to calculate the maximum cut-off angular frequency of the low-pass filter. Then, another LMI-based robust-stability condition is derived for a fixed low-pass filter, and is employed to find H static-state-feedback gains. Moreover, an iterative algorithm that combines these two robust-stability conditions is designed that yields the largest bandwidth while guaranteeing closed-loop robust stability. The conservativeness of the result produced by the algorithm is the same as that of the less conservative of the two robust-stability conditions. Finally, two numerical examples demonstrate the validity of the method.

Published in:

Control Theory & Applications, IET  (Volume:4 ,  Issue: 8 )