Robust Stability Condition of Repetitive Control Systems and Analysis on Steady-State Tracking Errors

2006 ◽  
Author(s):  
Tae-yong Doh ◽  
Jung Ryoo
Keyword(s):  
Steady State ◽  
Control Systems ◽  
Robust Stability ◽  
Stability Condition ◽  
Repetitive Control ◽  
Tracking Errors ◽  
State Tracking

scholarly journals Discrete-Time Phase Compensated Repetitive Control for Piezoactuators in Scanning Probe Microscopes

2008 ◽  
Author(s):  
Ug˘ur Arıdog˘an ◽  
Yingfeng Shan ◽  
Kam K. Leang
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Tracking Error ◽  
Repetitive Control ◽  
Scanning Probe ◽  
Two Phase ◽  
Operating Cycle ◽  
Phase Lead ◽  
State Tracking ◽  
Repetitive Controller

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or fabrication is periodic in time. Because of hysteresis and dynamic effects in the piezoactuator, the tracking error repeats from one scanning period to the next. Commercial SPMs typically employ PID feedback controllers to minimize the tracking error; however, the error repeats from one operating cycle to the next. Furthermore, the residual error can be excessively large, especially at high scan rates. A discrete-time repetitive controller was designed, analyzed, and implemented on an experimental SPM. The design of the RC incorporates two phase lead compensators to provide stability and to minimize the steady-state tracking error. Associated with the lead compensators are two parameters that can be adjusted to control the performance of the repetitive controller. Experimental tracking results are presented that compare the performance of PID, standard RC, and the modified RC with phase lead compensation. The results show that the modified RC reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared to PID control.

Setpoint Tracking Control With Discrete Actuators Using Controller Switching

2018 ◽  
Author(s):  
Y. Chida ◽  
R. Hara
Keyword(s):  
Steady State ◽  
Lyapunov Function ◽  
Control Problem ◽  
Numerical Simulations ◽  
Tracking Control ◽  
Control Structure ◽  
Control Method ◽  
Tracking Errors ◽  
State Tracking ◽  
Servo Controller

In the present paper, we discuss a setpoint tracking control problem for a plant with discrete actuators. When a conventional linear servo controller is applied to the plant, undesirable periodic vibrations similar to the limit cycle occasionally occur in the output response caused by synergy with the integration of the steady-state tracking errors and the quantized errors of the control inputs. To prevent an undesirable response, a novel control method is proposed, in which the controller switches the control structure based on the value of the Lyapunov function. The effectiveness of the proposed method was verified through numerical simulations.

Design and Analysis of Discrete-Time Repetitive Control for Scanning Probe Microscopes

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Ugur Aridogan ◽  
Yingfeng Shan ◽  
Kam K. Leang
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Pid Control ◽  
Tracking Error ◽  
Repetitive Control ◽  
Scanning Probe ◽  
Operating Cycle ◽  
Digital Implementation ◽  
Phase Lead ◽  
State Tracking

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or nanofabrication is periodic. Dynamic and hysteresis effects in the piezoactuator cause significant tracking error. To minimize the tracking error, commercial SPMs commonly use proportional-integral-derivative (PID) feedback controllers; however, the residual error of PID control can be excessively large, especially at high scan rates. In addition, the error repeats from one operating cycle to the next. To account for the periodic tracking error, a discrete-time RC is designed, analyzed, and implemented on an atomic force microscope (AFM). The advantages of RC include straightforward digital implementation and it can be plugged into an existing feedback control loop, such as PID, to enhance performance. The proposed RC incorporates two phase lead compensators to ensure robustness and minimize the steady-state tracking error. Simulation and experimental results from an AFM system compare the performance among (1) PID, (2) standard RC, and (3) the modified RC with phase lead compensation. The results show that the latter reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared with PID control.

Robust Performance Repetitive Control Systems

1998 ◽  
Vol 123 (3) ◽  
pp. 330-337 ◽  
Author(s):  
Jianwu Li ◽  
Tsu-Chin Tsao
Keyword(s):  
Control System ◽  
Control Systems ◽  
Robust Stability ◽  
Repetitive Control ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Control Design ◽  
Robust Performance ◽  
Feedback Form ◽  
Pure Delay

This paper addresses analysis and synthesis of robust stability and robust performance repetitive control systems. The repetitive control design problem is formulated as a standard feedback form in the linear fractional transformation form such that the standard numerical optimization software can be used to obtain the solution. The main idea of the robust repetitive control system design lies in introducing a fictitious complex uncertainty to replace the long delay chain in the internal model of the repetitive control system. This drastically reduces the order of the augmented plant for controller synthesis and hence generates a low order compensator, which in conjunction with the pure delay renders a repetitive controller that can be implemented efficiently in real time. The proposed approach can be applied to both the continuous and discrete-time domain repetitive control design for unstable open-loop plant. Sufficient conditions for the robust stability and robust performance repetitive control systems are presented. Conservatism analysis shows that the sufficient conditions become necessary when the pure delay approaches infinity. The robust repetitive control is applied to an electrohydraulic actuator for tracking periodic trajectories. Experimental results are presented to illustrate the design procedure and control system performance.

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