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.

Generalized Optimal Zero Phase Error Tracking Controller Design

1999 ◽  
Vol 121 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Manabu Yamada ◽  
Yasuyuki Funahashi ◽  
Zaier Riadh
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Phase Error ◽  
Least Square Method ◽  
Inequality Constraint ◽  
Least Square ◽  
New Approach ◽  
Ordinary Least Square ◽  
Feedforward Controller ◽  
Zero Phase

This paper presents a simple design method of discrete-time feedforward controllers that provide the overall transfer function with the following frequency characteristics. (i) The phase is equal to zero for all frequencies. (ii) The gain is equal to one at given frequencies. (iii) The error between the gain and unity for a given frequency range is minimized under given preview steps. The contributions of this paper are as follows. First, a new approach based on the spectral factorization is proposed and the class of all controllers satisfying the above conditions (i) and (ii) is parametrized using the solution of a Diophantine equation, i.e., the controller is obtained in an explicit form. With this explicit parametrization, the optimal feedforward controller is obtained by an ordinary least square method. The design method proposed in this paper is simple and straightforward, whereas the design method in previous result requires the solution of an optimization problem with troublesome inequality constraint and involves trial and error. Secondly, the frequencies at which the gain is made equal to unity can be chosen arbitrarily, while, in previous result, the frequency is restricted to zero. Finally, the effectiveness of the proposed controller is demonstrated by simulation.

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.

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.

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.

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 Error Tracking System With Arbitrarily Specified Gain Characteristics

1997 ◽  
Vol 119 (2) ◽  
pp. 260-264 ◽  
Author(s):  
Manabu Yamada ◽  
Yasuyuki Funahashi ◽  
Shin-ichi Fujiwara
Keyword(s):  
Unsolved Problem ◽  
Tracking System ◽  
Phase Error ◽  
Simple Algorithm ◽  
Nonminimum Phase ◽  
Minimum Value ◽  
Maximum Value ◽  
Feedforward Controller ◽  
Simulation Results ◽  
Zero Phase

This paper considers a design problem of discrete-time preview feedforward controllers such that the gain characteristics of the overall system is within an arbitrarily specified bound subject to the zero phase error condition for a plant having nonminimum phase zeros. In order to solve this problem, a feedforward controller termed Optimal-Feedforward Controller with Zero Phase Error Tracking Controller (Optimal-FCZPETC) is introduced. With this controller, the phase characteristics of the overall system is zero for all frequencies and the maximum value of the gap between the gain of the overall system and unity, which is ideal gain characteristics, is minimized under given preview steps. The choice of the preview steps is an unsolved problem. In this paper, we investigate the Optimal-FCZPETC from the viewpoint of the preview steps. The contribution is to give explicitly the minimum value of the maximum gap between the gain of the overall system and unity for given preview steps and to show that the minimum value can be made arbitrarily small as the preview steps increase. As a result, a simple algorithm is proposed to find the minimum preview steps such that the gain characteristics of the overall system is within an arbitrarily specified bound. The effectiveness is shown by simulation results.

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