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.

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.

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

Algorithms ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Yong-Hong Lan ◽  
Jun-Jun Xia ◽  
Yue-Xiang Shi
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

Analysis and Synthesis of Discrete-Time Repetitive Controllers

1989 ◽  
Vol 111 (3) ◽  
pp. 353-358 ◽  
Author(s):  
Masayoshi Tomizuka ◽  
Tsu-Chin Tsao ◽  
Kok-Kia Chew
Keyword(s):  
Discrete Time ◽  
Tracking Error ◽  
Disk File ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Analysis And Synthesis ◽  
Holding Device ◽  
Low Pass ◽  
Actuator System ◽  
Repetitive Controller

Repetitive control is formulated and analyzed in the discrete-time domain. Sufficiency conditions for the asymptotic convergence of a class of repetitive controllers are given. The “plug-in” repetitive controller is introduced and applied to track-following in a disk-file actuator system. Inter-sample ripples in the tracking error were present when the “plug-in” repetitive controller was installed. The performance is enhanced, however, when the zero-holding device is followed by a low-pass filter or replaced by a delayed first-order hold.

scholarly journals Quadratic Optimality of the Zero-Phase Repetitive Control

2000 ◽  
Vol 123 (3) ◽  
pp. 554-555 ◽  
Author(s):  
Hakan Ko¨rog˘lu ◽  
O¨mer Morgu¨l
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Zero Phase ◽  
Repetitive Controller

We consider the quadratically optimal repetitive control problem in discrete-time and show that the existing zero-phase repetitive controller is quadratically optimal for stable plants.

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