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.

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.

Deformation Control of Elastic Object by Robot Arm - High-Precision Deformation Control by Adaptive Feed-forward Control -

1998 ◽  
Vol 10 (3) ◽  
pp. 184-190
Author(s):  
Hiroyuki Kojima ◽  
◽  
Masakazu Kamei ◽  
Tsuneo Akuto ◽  
Keyword(s):  
Least Squares Method ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Phase Error ◽  
Identification Algorithm ◽  
Robot Arm ◽  
Deformation Control ◽  
Feed Forward Control ◽  
Adaptive Feedforward ◽  
Elastic Object

This paper derives the equations of motion of a horizontal three-link robot arm contacting an elastic object, then proposes deformation control for the elastic object by the robot arm. This deformation control involves feedback control of joint angles, feedforward control by robot arm dynamics, and adaptive feedforward control for unknown elastic object dynamics. An adaptive feedforward control law is devised using an online parameter identification algorithm based on the least squares method, zero phase error tracking control theory, and the Jacobian matrix of the robot arm. Numerical simulation and experimental results confirmed that deformation control error by the proposed adaptive control rapidly decreases with the passing of time.

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.

Nonlinear Feedforward Control for Electrohydraulic Actuators With Asymmetric Piston Areas

2016 ◽  
Author(s):  
Abhinav Tripathi ◽  
Zongxuan Sun
Keyword(s):  
Coming Out ◽  
Feedforward Control ◽  
Design Method ◽  
Phase Error ◽  
Differential Flatness ◽  
Pressure Feedback ◽  
Feedforward Controller ◽  
Linearized Model ◽  
Electrohydraulic Actuators ◽  
Zero Phase

This paper presents a new design method of a nonlinear feedforward controller for electrohydraulic actuators with asymmetric piston areas. While the use of flatness based inversion of the plant model to design a feedforward controller has been reported for electrohydraulic actuators with symmetric piston area, the extension of this method to actuators with asymmetric piston areas is non-trivial. In asymmetric electrohydraulic actuators, the areas of the hydraulic piston are different in the two chambers, and hence, the amount of fluid going into one chamber of the actuator is not equal to the amount of fluid coming out of the other. This asymmetry leads to loss of flatness, and hence, flatness based inversion of the plant is no longer possible. In this paper, we present a method for calculation of the feedforward control signal for a given trajectory by numerically solving the inverse problem for the system. We demonstrate the effectiveness of the proposed feedforward controller by simulation of trajectory tracking in an asymmetric electrohydraulic actuator. For benchmarking, the tracking performance has been compared with three other feedforward schemes: a linearized model based Zero Phase Error Tracking (ZPET) feedforward controller, a nonlinear feedforward controller implementing an approximate plant inversion based on differential flatness, and a pressure feedback based feedforward controller.

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 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 Review of Feedforward Control Approaches in Nanopositioning for High-Speed SPM

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Garrett M. Clayton ◽  
Szuchi Tien ◽  
Kam K. Leang ◽  
Qingze Zou ◽  
Santosh Devasia
Keyword(s):  
High Speed ◽  
Science Studies ◽  
Feedforward Control ◽  
Phase Error ◽  
Scanning Probe ◽  
Wide Range ◽  
High Bandwidth ◽  
Iterative Control ◽  
And Inversion ◽  
Zero Phase

Control can enable high-bandwidth nanopositioning needed to increase the operating speed of scanning probe microscopes (SPMs). High-speed SPMs can substantially impact the throughput of a wide range of emerging nanosciences and nanotechnologies. In particular, inversion-based control can find the feedforward input needed to account for the positioning dynamics and, thus, achieve the required precision and bandwidth. This article reviews inversion-based feedforward approaches used for high-speed SPMs such as optimal inversion that accounts for model uncertainty and inversion-based iterative control for repetitive applications. The article establishes connections to other existing methods such as zero-phase-error-tracking feedforward and robust feedforward. Additionally, the article reviews the use of feedforward in emerging applications such as SPM-based nanoscale combinatorial-science studies, image-based control for subnanometer-scale studies, and imaging of large soft biosamples with SPMs.

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.

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