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.

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.

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.

A Control Strategy of a Two Degrees-of-Freedom Heavy Duty Parallel Manipulator

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Jun Wu ◽  
Dong Wang ◽  
Liping Wang
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Control Method ◽  
Feedforward Control ◽  
Phase Error ◽  
Time Lag ◽  
Kinematic Model ◽  
System Stability ◽  
Heavy Duty ◽  
Inverse Dynamic

The motion accuracy of a heavy duty parallel manipulator is usually low due to time lag and the difficulty to real-time measure the position of the end-effector. In this paper, a dynamic modeling of this system with consideration of the link flexible deformation is proposed, and a double-feedforward control is presented. The link deformation is considered in the kinematic model. Taking link deformation into account, the dynamic model is derived for real-time application, and the inverse dynamic compensator is designed. The zero phase error tracking controller (ZPETC) is introduced as the second compensator. The system stability is investigated by simulations. The control method is compared with the kinematic-based control without consideration of link deformation. The results show that the maximum contouring error reduces from 7.5mm to 10μm. Thus, the tracking performance is improved when using the method proposed in this paper.

Tool Positioning for Noncircular Cutting With Lathe

1987 ◽  
Vol 109 (2) ◽  
pp. 176-179 ◽  
Author(s):  
M. Tomizuka ◽  
M. S. Chen ◽  
S. Renn ◽  
T. C. Tsao
Keyword(s):  
Cross Sections ◽  
Control Algorithm ◽  
Least Squares Method ◽  
Feedforward Control ◽  
Phase Error ◽  
Control Law ◽  
Time Model ◽  
Tool Positioning ◽  
Tool Position ◽  
Zero Phase

This paper presents the design and implementation of a digital controller for a lathe to machine workpieces with noncircular cross sections. Noncircular cutting is accomplished by controlling the radial tool position in the direction normal to the surface of workpiece. A discrete time model for the tool carriage in the radial direction is obtained by a least squares method applied to input and output data. The model is used for designing digital feedback and feedforward controllers. The zero phase error tracking control algorithm is applied as a feedforward control law for positioning of the tool along desired time varying signals. The effectiveness of the proposed controller is demonstrated by experiment and simulation.

Zero Phase Robust Control of XY Table Linear Servo System

2013 ◽  
Vol 419 ◽  
pp. 713-717
Author(s):  
Xi Mei Zhao ◽  
Ming Ming Jiang ◽  
Hong Yi Li ◽  
Hao Liu
Keyword(s):  
Disturbance Observer ◽  
Position Control ◽  
Control Method ◽  
Phase Error ◽  
Tracking Error ◽  
Servo System ◽  
Direct Drive ◽  
Tracking Accuracy ◽  
Control Scheme ◽  
Zero Phase

For direct drive XY table servo system, position control is designed. Considering the error which is caused by the disturbance of the system, friction factor and so on. The control method combing the zero phase error tracking controller (ZPETC) with the disturbance observer (DOB) is adopted. The system tracking error is reduced by adopting ZPETC, and through influences of disturbance to the system is diminished by the disturbance observer. Thus the tracking accuracy and robustness of the system are improved. Simulation results show that this control scheme is effective. It can obviously improve the accuracy of the system.

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