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.

Adaptive Zero Phase Error Tracking Algorithm for Digital Control

1987 ◽  
Vol 109 (4) ◽  
pp. 349-354 ◽  
Author(s):  
Tsu-Chin Tsao ◽  
Masayoshi Tomizuka
Keyword(s):  
Closed Loop ◽  
Phase Error ◽  
Feedback Controller ◽  
Loop System ◽  
Phase Lag ◽  
Closed Loop System ◽  
Loop Dynamics ◽  
Feedforward Controller ◽  
Adaptive Feedforward ◽  
Zero Phase

This paper describes an adaptive feedforward controller to let the output of a plant with stable and unstable zeros track a time varying desired output. The dynamics of the closed loop system consisting of the plant and the feedback controller are assumed unknown or slowly varying due to changes on the plant parameters. In the control scheme proposed in this paper, the feedforward controller is adaptive while the feedback controller is fixed under the assumption that the closed loop system remains stable at all times. With a few samples of future reference input data available, the preview action of the adaptive feedforward controller cancels the phase lag caused by the closed loop dynamics and attains the zero phase error tracking performance (i.e., the plant output is in phase with any sinusoidal desired output) asymptotically.

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.

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.

High-Speed End Milling Using a Feedforward Control Architecture

1996 ◽  
Vol 118 (2) ◽  
pp. 178-187 ◽  
Author(s):  
E. D. Tung ◽  
M. Tomizuka ◽  
Y. Urushisaki
Keyword(s):  
High Speed ◽  
Feedforward Control ◽  
End Milling ◽  
Phase Error ◽  
Cutting Speed ◽  
Frequency Domain Analysis ◽  
Maximum Speed ◽  
Drive Control ◽  
Machining Errors ◽  
Feedforward Controller

Experiments are performed for end milling aluminum at 15,000 RPM spindle speed (1,508 m/min cutting speed) and up to 3 m/min table feedrate using an experimental machine tool control system. A digital feedforward controller for feed drive control incorporates the Zero Phase Error Tracking Controller (ZPETC) and feedforward friction compensation. The controller achieves near-perfect (±3 μm) tracking over a 26 mm trajectory with a maximum speed of 2 m/min. The maximum contouring error for a 26 mm diameter circle at this speed is less than 4 μm. Tracking and contouring experiments are conducted for table feedrates as high as 10 m/min. Frequency domain analysis demonstrates that the feedforward controller achieves a bandwidth of 10 Hz without phase distortion. In a direct comparison of accuracy, the machining errors in specimens produced by the experimental controller were up to 20 times smaller than the errors in specimens machined by an industrial CNC.

scholarly journals Adaptive Feedforward Control of a Pressure Compensated Differential Cylinder

2020 ◽  
Vol 10 (21) ◽  
pp. 7847
Author(s):  
Konrad Johan Jensen ◽  
Morten Kjeld Ebbesen ◽  
Michael Rygaard Hansen
Keyword(s):  
Control System ◽  
Root Mean Square ◽  
Motion Control ◽  
Experimental Verification ◽  
Feedforward Control ◽  
Position Error ◽  
Mean Square ◽  
Model Uncertainties ◽  
Feedforward Controller ◽  
Adaptive Feedforward

This paper presents the design, simulation and experimental verification of adaptive feedforward motion control for a hydraulic differential cylinder. The proposed solution is implemented on a hydraulic loader crane. Based on common adaptation methods, a typical electro-hydraulic motion control system has been extended with a novel adaptive feedforward controller that has two separate feedforward states, i.e, one for each direction of motion. Simulations show convergence of the feedforward states, as well as 23% reduction in root mean square (RMS) cylinder position error compared to a fixed gain feedforward controller. The experiments show an even more pronounced advantage of the proposed controller, with an 80% reduction in RMS cylinder position error, and that the separate feedforward states are able to adapt to model uncertainties in both directions of motion.

Precision motion control of permanent magnet linear synchronous motor servo system based on an integrated controller with inertia variation compensation

2012 ◽  
Vol 227 (7) ◽  
pp. 1481-1494 ◽  
Author(s):  
Zhijun Li ◽  
Chengying Liu ◽  
Fanwei Meng ◽  
Kai Zhou
Keyword(s):  
Permanent Magnet ◽  
Motion Control ◽  
Disturbance Observer ◽  
Phase Error ◽  
Servo System ◽  
Tracking Performance ◽  
Tracking Controller ◽  
Integrated Controller ◽  
Feed Forward Controller ◽  
Zero Phase

To achieve high robustness and precise motion control of permanent magnet linear synchronous motor servo system, an integrated controller is presented, including a velocity feed forward controller, a zero phase error tracking controller, a disturbance observer and inertia variation compensator. The velocity feed forward controller and the zero phase error tracking controller are included to improve tracking performance and the disturbance observer is involved to enhance disturbance rejection. However, both the zero phase error tracking controller and the disturbance observer are sensitive to inertia variation which often occurs in servo systems. So, an inertia compensator, which consists of a perfect tracking controller for the current loop and a compensation gain, is proposed to retain tracking performance. Detailed experiments are conducted on a PMLSM servo system to confirm the effectiveness of the integrated controller.

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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