Repetitive Control for Systems with Nonzero Relative Degree

A design method for robust stabilizing simple multi-period repetitive controllers for time-delay plants

“…That is, the repetitive control system follows the periodic reference input without steady state error, even if there exists a periodic disturbance or the plant has uncertainty [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Because a repetitive control system follows any periodic reference input without steady state error is a neutral type of time-delay control system, it is difficult to design stabilizing controllers for the plant [3].…”

“…Because a repetitive control system follows any periodic reference input without steady state error is a neutral type of time-delay control system, it is difficult to design stabilizing controllers for the plant [3]. To design a repetitive control system that follows any periodic reference input without steady state error, the plant needs to be biproper [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Since many actual control plants are strictly proper, many design methods are given in [1][2][3][4][5][6], [8][9][10][11][12][13][14].…”

The Parameterization of All Stabilizing Modified Repetitive Controllers for Multiple-Input/Multiple-Output Plants

“…To design a repetitive control system that follows any periodic reference input without steady state error, the plant needs to be biproper (3) - (11) . Ikeda and Takano (12), (13) pointed out that it has physical difficulty that the output follows any periodic reference input without steady state error. In addition they showed that the repetitive control system is L 2 stable for periodic signal that does not include infinite frequency signals if the relative degree of controller is one.…”

A design method of robust stabilizing simple multi-period repetitive controllers

“…A repetitive control system is a type of servomechanism for a periodic reference input for the periodic signal without steady state error (Inoue et al, 1981;Omata et al, 1987;Watanabe and Yamatari, 1986;Hara et al, 1988;Yamamoto and Hara, 1988;Nakano et al, 1989;Ikeda and Takano, 1990;Yamamoto and Hara, 1992;Yamamoto, 1993;Katoh and Funahashi, 1996;Weiss, 1997). That is, the repetitive control system follows the periodic reference input without steady state error, even if there exists a periodic disturbance or the plant has uncertainty (Inoue et al, 1981;Omata et al, 1987;Watanabe and Yamatari, 1986;Yamamoto and Hara, 1988;Nakano et al, 1989;Ikeda and Takano, 1990;Yamamoto and Hara, 1992;Yamamoto, 1993;Katoh and Funahashi, 1996;Weiss, 1997). The repetitive control system was proposed for 'high accuracy control for magnet power supply of proton synchrotron in recurrent operation' (Inoue et al, 1981).…”