Zero Phase Error Tracking Control for Square Sampled-Data Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 506-509 ◽  
Author(s):  
H. Ali Pak ◽  
G. Q. Li
Keyword(s):  
Tracking Control ◽  
Control Algorithm ◽  
Phase Error ◽  
Data Systems ◽  
Sampled Data ◽  
Minimal Order ◽  
Phase Cancellation ◽  
Feedforward Controller ◽  
Zero Phase ◽  
Function Matrix

A multivariable version of the zero phase error tracking control algorithm is presented for sampled-data systems. The feedforward controller is based on the minimal-order inverse of a square system’s transfer function matrix. It is shown that, apart from phase cancellation, complete input/output decoupling will result from the use of the controller. Using a simulation study, the control algorithm’s performance is demonstrated for a multivariable positioning system.

A zero phase error tracking based path precompensation method for high-speed machining

2015 ◽  
Vol 230 (2) ◽  
pp. 230-239 ◽  
Author(s):  
Xuewei Li ◽  
Jun Zhang ◽  
Wanhua Zhao ◽  
Bingheng Lu
Keyword(s):  
Tracking Control ◽  
High Speed ◽  
Control Algorithm ◽  
Phase Error ◽  
Great Influence ◽  
Contour Error ◽  
Machining Accuracy ◽  
High Speed Machining ◽  
Feed System ◽  
Zero Phase

Contour error due to the dynamic characteristics of feed system has a great influence on machining accuracy, in high-speed machining. In this paper, a new path precompensation method is proposed using zero phase error tracking control algorithm to improve the contouring accuracy for multiaxis machining with large feed rates. In this method, the outputs are predicted with the identified position-loop models of feed systems, and a contour error calculator is designed to calculate contour error in each sample instance using the predicted output and reference input. In order to compensate the contour error resulting from the dynamic tracking error of feed systems, the contour error vector is decomposed orthogonally and the compensation components for individual axis are calculated using zero phase error tracking control algorithm. Simulations showed that contour errors can be significantly improved with small compensation using the new path precompensation method for linear, circular, and parabola contours. Experimental results showed that the new method can reduce contour error significantly and achieve a better compensation compared with zero phase error tracking control and cross-coupled path pre-compensation.

Extended Bandwidth Zero Phase Error Tracking Control of Nonminimal Phase Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 347-351 ◽  
Author(s):  
D. Torfs ◽  
J. De Schutter ◽  
J. Swevers
Keyword(s):  
Tracking Control ◽  
Control Algorithm ◽  
Phase Error ◽  
Tracking Error ◽  
Flexible Robot ◽  
Phase Errors ◽  
Gain Error ◽  
Small Gain ◽  
Phase Systems ◽  
Zero Phase

This paper describes a new feedforward algorithm for accurate tracking control of nonminimal phase systems. Accurate feedforward calculation involves a prefilter design using the inverse system model. Nonminimal phase systems cause problems with this prefilter design, because unstable zeros become unstable poles in the inverse model. The zero phase error tracking control algorithm (ZPETC) consists of a substitution scheme, which removes the unstable zeros. This scheme introduces a small gain error, which increases with frequency, but no phase error. This paper investigates additional properties which give more insight into the ZPETC algorithm, and allow to improve it. The improved algorithm is based on the same substitution scheme as ZPETC, but adds additional feedforward terms to compensate for the gain error. These additional terms increase the frequency range for which the overall transfer function has only limited gain error, without introducing phase errors. The additional feedforward terms repeatedly reduce the tracking error proportional to ε2, ε4, ε6, …, where ε is the ZPETC tracking error. The new feedforward algorithm or new substitution scheme is therefore called “extended bandwidth zero phase error tracking control algorithm” (EBZPETC). Experimental results on a one-link flexible robot compares both methods.

Zero Phase Error Tracking Algorithm for Digital Control

1987 ◽  
Vol 109 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Masayoshi Tomizuka
Keyword(s):  
Phase Shift ◽  
Motion Control ◽  
Closed Loop ◽  
Feedforward Control ◽  
Phase Error ◽  
Robotic Arms ◽  
Phase Cancellation ◽  
Feedforward Controller ◽  
General Motion ◽  
Zero Phase

A digital feedforward control algorithm for tracking desired time varying signals is presented. The feedforward controller cancels all the closed-loop poles and cancellable closed-loop zeros. For uncancellable zeros, which include zeros outside the unit circle, the feedforward controller cancels the phase shift induced by them. The phase cancellation assures that the frequency response between the desired output and actual output exhibits zero phase shift for all the frequencies. The algorithm is particularly suited to the general motion control problems including robotic arms and positioning tables. A typical motion control problem is used to show the effectiveness of the proposed feedforward controller.

Tracking Control of Non-Minimum Phase Systems Using Filtered Basis Functions: A NURBS-Based Approach

2015 ◽  
Author(s):  
Molong Duan ◽  
Keval S. Ramani ◽  
Chinedum E. Okwudire
Keyword(s):  
Tracking Control ◽  
Phase Error ◽  
Approximate Model ◽  
Basis Functions ◽  
Minimum Phase ◽  
Tracking Errors ◽  
Model Inversion ◽  
B Spline ◽  
Phase Systems ◽  
Zero Phase

This paper proposes an approach for minimizing tracking errors in systems with non-minimum phase (NMP) zeros by using filtered basis functions. The output of the tracking controller is represented as a linear combination of basis functions having unknown coefficients. The basis functions are forward filtered using the dynamics of the NMP system and their coefficients selected to minimize the errors in tracking a given trajectory. The control designer is free to choose any suitable set of basis functions but, in this paper, a set of basis functions derived from the widely-used non uniform rational B-spline (NURBS) curve is employed. Analyses and illustrative examples are presented to demonstrate the effectiveness of the proposed approach in comparison to popular approximate model inversion methods like zero phase error tracking control.

Concurrent Design of Continuous Zero Phase Error Tracking Controller and Sinusoidal Trajectory for Improved Tracking Control

1998 ◽  
Vol 123 (1) ◽  
pp. 127-129 ◽  
Author(s):  
Hyung-Soon Park ◽  
Pyung Hun Chang ◽  
Doo Yong Lee
Keyword(s):  
Continuous Time ◽  
Phase Error ◽  
Phase System ◽  
Pass Filter ◽  
Nonminimum Phase ◽  
Tracking Controller ◽  
Feedforward Controller ◽  
Gain Errors ◽  
High Pass ◽  
Zero Phase

A trajectory control strategy for a nonminimum phase system is proposed. A continuous-time version of the Zero Phase Error Tracking Controller (ZPETC), which is a well-known discrete-time feedforward controller, is considered. In the continuous-time case, the overall transfer function consisting of the ZPETC and the closed-loop plant exhibits high-pass filter characteristics. This introduces serious gain errors between the desired and actual output if the desired output is made directly as the ZPETC’s input. This paper proposes the use of a specially designed sinusoidal trajectory to compensate for the gain errors. The sinusoidal trajectory imparts a synergic effect to tracking performance when combined with the continuous ZPETC. Continuous ZPETC with sinusoidal trajectory is evaluated successfully by applying to a nonminimum phase plant, single link flexible arm.

Multi-Rate Feedforward Tracking Control for Plants With Nonminimum Phase Discrete Time Models

1999 ◽  
Vol 123 (3) ◽  
pp. 556-560 ◽  
Author(s):  
Yuping Gu ◽  
Masayoshi Tomizuka
Keyword(s):  
Discrete Time ◽  
Tracking Control ◽  
Performance Enhancement ◽  
Feedforward Control ◽  
Phase Error ◽  
Sampling Rate ◽  
Time Model ◽  
Rate System ◽  
Control Scheme ◽  
Feedforward Controller

This paper is concerned with performance enhancement of tracking control systems by multi-rate control. The feedback controller is updated at the same rate as the sampling rate of the output measurements. The feedforward controller processes the desired output signal for high accuracy tracking, and its output is updated at a rate N-times faster than the sampling rate of the output measurements. The discrete time model of the controlled plant may possess unstable zeros, and the zero phase error tracking controller (ZPETC) is used as a feedforward controller. Inter-sample behavior of the plant is included in evaluating the tracking performance of the multi-rate system. Illustrative examples are given to show advantages of the proposed multi-rate feedback/feedforward control scheme.

Simplified Realization of Zero Phase Error Tracking

2020 ◽  
Author(s):  
Masayoshi Tomizuka ◽  
Liting Sun
Keyword(s):  
Transfer Function ◽  
Tracking Control ◽  
Control Method ◽  
Feedforward Control ◽  
Phase Error ◽  
Time Varying ◽  
Time Transfer ◽  
Simple Implementation ◽  
Tracking Time ◽  
Zero Phase

Abstract Zero phase error tracking (ZPET) control has gained popularity as a simple yet effective feedforward control method for tracking time varying desired trajectories by the plant output. In this paper, we will show that the zero-order hold equivalent of continuous time transfer function, i.e. pulse transfer function, naturally has a property to realize zero phase effort tracking. This property is exploited to realize a simple implementation of zero phase error tracking control. The effectiveness of the proposed approach is demonstrated by simulations.

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