Stability Condition and Synthesis Methods for Repetitive Control Systems

A design method for simple repetitive controllers for time-delay plants

“…That is, Manuscript received on July 31, 2008 ; revised on January 21, 2009. 1,2,3,4 The authors are with Department of Mechanical System Engineering, Gunma University 1-5-1 Tenjincho, Kiryu 376-8515 Japan., E-mail: yamada@me.gunma-u.ac.jp the repetitive control system follows the periodic reference input without steady state error, even if a periodic disturbance or uncertainty exists in the plant [1][2][3][4][5][6][7][8][9][10][11][12][13]. It is difficult to design stabilizing controllers for the plant, because the repetitive control system follows any periodic reference input without steady state error is a neutral type of time-delay control system [11].…”

“…It is difficult to design stabilizing controllers for the plant, because the repetitive control system follows any periodic reference input without steady state error is a neutral type of time-delay control system [11]. In order to design a repetitive control system that follows any periodic reference input without steady state error, the plant needs to be biproper [3][4][5][6][7][8][9][10][11]. In practice the plant is strictly proper.…”

“…In practice the plant is strictly proper. Many design methods of repetitive control systems for the strictly proper plants are given [3][4][5][6][7][8][9][10][11]. These studies are divided into two types.…”

“…These studies are divided into two types. One uses a low-pass filter [3][4][5][6][7][8][9][10] and the other uses an attenuator [11]. The latter is difficult to design because it uses a state variable time-delay in the repetitive controller [11].…”

“…The former has a simple structure and is easily designed. Therefore, the former type of repetitive control system is called the modified repetitive control systems [3][4][5][6][7][8][9][10].…”