Two-Dimensional Exact Model Matching With Application to Repetitive Control

1994 ◽  
Vol 116 (1) ◽  
pp. 2-9 ◽  
Author(s):  
David M. Alter ◽  
Tsu-Chin Tsao
Keyword(s):  
Controller Design ◽  
Reference Model ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Delayed Feedback ◽  
Model Matching ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Exact Model ◽  
Repetitive Controller

This paper concerns matching a system with time-delayed feedback to a rational transfer function model and its application to repetitive controller design. Necessary and sufficient conditions on the order of the plant, reference model, and controller are obtained for the existence of causal and stabilizing exact model matching solutions. The results are applied to robust repetitive controller design, in which a delayed feedback is introduced in the repetitive controller for rejecting periodic disturbances while simultaneously achieving input-output model matching. Furthermore, the 2-D model matching method also renders computationally efficient solutions. Also addressed are some subtle points on the selection of a low-pass filter required for robust stability. Finally, the approach is experimentally applied for turning noncircular shapes.

Tracking Performance Improvement of Repetitive Controller for Nano-Manipulating Systems With Time Delays

2019 ◽  
Author(s):  
Pengbo Liu ◽  
Peng Yan
Keyword(s):  
Time Delay ◽  
Performance Improvement ◽  
Controller Design ◽  
Repetitive Control ◽  
Tracking Performance ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Performance Improvements ◽  
Low Pass ◽  
Repetitive Controller

Abstract This paper investigates the robust repetitive controller design with improved tracking performance for nano-manipulating systems with time delay. In order to handle the time delay caused by the analog-to-digital (A/D) conversion of the capacitive sensors with ultra high precision, we modify the conventional repetitive control structure where the design of low pass filter is formulated as an H∞ optimization problem. For the purpose of tracking performance improvement, we further modify the structure of the low pass filter by shaping the sensitivity functions of the closed-loop system. With consideration of the existing of model uncertainties, the design of the modified low pass filter is also formulated as an H∞ optimization of infinite dimensional systems. The effectiveness of the proposed repetitive control architecture is further verified by real time experiments on a piezo driven nano-stage, where significant tracking performance improvements are demonstrated comparing with the traditional repetitive controller.

Characterization of Low-pass Filters on Local Fields of Positive Characteristic

2016 ◽  
Vol 59 (3) ◽  
pp. 528-541 ◽  
Author(s):  
Qaiser Jahan
Keyword(s):  
Positive Characteristic ◽  
Sufficient Conditions ◽  
Local Fields ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Necessary And Sufficient ◽  
Low Pass Filters ◽  
The Scaling Function

AbstractIn this article, we give necessary and sufficient conditions on a function to be a low-pass filter on a local field K of positive characteristic associated with the scaling function for multiresolution analysis of L2(K). We use probability and martingale methods to provide such a characterization.

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 Dynamic Compensator-Based Output Feedback Controller Design for Uncertain Systems with Adjustable Robustness

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Jeang-Lin Chang ◽  
Tsui-Chou Wu
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Mimo Systems ◽  
Input Saturation ◽  
Feedback Stabilization ◽  
Pass Filter ◽  
Low Pass Filter ◽  
System States ◽  
Filter Property ◽  
Uniformly Ultimate Boundedness

A low-order dynamics compensator-based output feedback stabilization method for a class of uncertain linear MIMO systems with mismatched disturbances is presented. Since all the system states are not measurable, the proposed controller inherently has low-pass filter property in which it can successfully replace the derivative terms of the system output and hence effectively estimate the input disturbance. The control scheme proposed here can simultaneously consider the input saturation problem and obtain the desired performance. Although the system has unknown uncertainties and disturbances, the uniformly ultimate boundedness of system states in the closed-loop system is analytically shown using the Lyapunov method. Finally, two numerical examples are presented to demonstrate the applicability of the proposed scheme.

scholarly journals Adaptive Data-Driven Control for Linear Time Varying Systems

Machines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 167
Author(s):  
Talal Abdalla
Keyword(s):  
Design Problem ◽  
Controller Design ◽  
Reference Model ◽  
Linear Time ◽  
Convex Relaxation ◽  
Data Driven ◽  
Time Varying ◽  
Model Matching ◽  
Control Approach ◽  
Time Varying Systems

In this paper, we propose an adaptive data-driven control approach for linear time varying systems, affected by bounded measurement noise. The plant to be controlled is assumed to be unknown, and no information in regard to its time varying behaviour is exploited. First, using set-membership identification techniques, we formulate the controller design problem through a model-matching scheme, i.e., designing a controller such that the closed-loop behaviour matches that of a given reference model. The problem is then reformulated as to derive a controller that corresponds to the minimum variation bounding its parameters. Finally, a convex relaxation approach is proposed to solve the formulated controller design problem by means of linear programming. The effectiveness of the proposed scheme is demonstrated by means of two simulation examples.

Two time-scale observer-based robust motion controller design and realization of a linear actuator

2016 ◽  
Vol 40 (11) ◽  
pp. 3241-3251 ◽  
Author(s):  
Nan Wang ◽  
Weiyang Lin ◽  
Jinyong Yu ◽  
An Zhang ◽  
Chao Ye
Keyword(s):  
Time Scale ◽  
Controller Design ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Velocity Signal ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Signal Tracking ◽  
Time Scale Separation ◽  
Low Pass

In this paper, an observer-based sliding mode controller is proposed for a high-accuracy motion plant to suppress the disturbances and improve the tracking performance. In particular, a two time-scale separation technology, which can recover the disturbance state in a faster time scale, is utilized to compensate the disturbances and improve the system robustness. The parameter identification is carried out to obtain the model coefficients with a high fitting rate. Such an identified model can allow the engineers to tune the controller’s gains highly enough when the system suffers from the measurement noises. Instead of the traditional low-pass filter, a differentiator is introduced for the velocity signal prediction and its discrete-time version is provided to attenuate the noises effect. To verify the effectiveness of the proposed approach, an adaptive robust control law is compared with the proposed one in terms of dynamic positioning error, robustness and rapid signal tracking, and the superiority and advantages can be illustrated by the experimental results.

TIME-DELAYED FEEDBACK CONTROL OF TIME-DELAY CHAOTIC SYSTEMS

2003 ◽  
Vol 13 (01) ◽  
pp. 193-205 ◽  
Author(s):  
XINPING GUAN ◽  
CAILIAN CHEN ◽  
HAIPENG PENG ◽  
ZHENGPING FAN
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Error Control ◽  
Chaotic Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Time Delayed Feedback

This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable fixed point and to tracking an unstable periodic orbit, respectively. Some numerical examples are provided to demonstrate the effectiveness of the presented method.

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