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.

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.

Optimal Feedforward Prefilter With Frequency Domain Specification for Nonminimum Phase Systems

1996 ◽  
Vol 118 (4) ◽  
pp. 791-795 ◽  
Author(s):  
Dirk Torfs ◽  
Joris De Schutter
Keyword(s):  
Phase Error ◽  
Time Domain Analysis ◽  
Least Square ◽  
Superior Performance ◽  
Reference Trajectory ◽  
Nonminimum Phase ◽  
Nonminimum Phase Systems ◽  
Gain Error ◽  
Phase Systems ◽  
Zero Phase

The paper shows the influence of the location of unstable zeros on the tracking performance of feedforward prefilters. Unstable zeros are divided into a number of classes. It is shown that existing feedforward prefilters (Zero Phase Error Tracking Control (ZPETC), E-filter, Extended Bandwidth ZPETC, ...) perform well for two classes, but fail for a particular class of unstable zeros. For this class, a characteristic frequency, fc, exists such that the induced gain error attenuates all frequencies of the reference trajectory f ≤ fc and amplifies frequencies f > fc. Hence, it is impossible to freely select the tracking bandwidth. Therefore, an optimal feedforward prefilter for discrete time nonminimum phase systems is presented to deal with this class of unstable zeros. As in the ZPETC method, the prefilter compensates for unstable zeros in the inverse system model, retains the zero phase property, and introduces small gain errors. But in addition, the design minimizes a cost function for which a least square solution is found. A frequency and time domain analysis shows the superior performance of the presented optimal prefilter design even for trajectory with high frequency components.

scholarly journals Simulation and Experimental Studies on Perfect Tracking Optimal Control of an Electrohydraulic Actuator System

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
R. Ghazali ◽  
Y. M. Sam ◽  
M. F. Rahmat ◽  
Zulfatman ◽  
A. W. I. M. Hashim
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Tracking Control ◽  
Phase Error ◽  
Experimental Studies ◽  
Phase System ◽  
Nonminimum Phase ◽  
Gain Error ◽  
Feedforward Controller ◽  
Electrohydraulic Actuator

This paper presents a perfect tracking optimal control for discrete-time nonminimum phase of electrohydraulic actuator (EHA) system by adopting a combination of feedback and feedforward controller. A linear-quadratic regulator (LQR) is firstly designed as a feedback controller, and a feedforward controller is then proposed to eliminate the phase error emerged by the LQR controller during the tracking control. The feedforward controller is developed by implementing the zero phase error tracking control (ZPETC) technique in which the main difficulty arises from the nonminimum phase system with no stable inverse. Subsequently, the proposed controller is performed in simulation and experimental studies where the EHA system is represented in discrete-time model that has been obtained using system identification technique. It also shows that the controller offers better performance as compared to conventional PID controller in reducing phase and gain error that typically occurred in positioning or tracking systems.

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.

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.

The Effect of Adding Zeroes to Feedforward Controllers

1991 ◽  
Vol 113 (1) ◽  
pp. 6-10 ◽  
Author(s):  
B. Haack ◽  
M. Tomizuka
Keyword(s):  
Phase Error ◽  
Feedback System ◽  
Contour Error ◽  
Phase Lag ◽  
Contouring Accuracy ◽  
Feedforward Controller ◽  
Zero Phase

The effect of adding zeroes to two types of feedforward controllers, stable pole zero cancelling (SPZC) controllers and zero phase error tracking (ZPET) contollers, is discussed. When there are uncancellable zeroes in the feedback system, additional zeroes in the feedforward controller can reduce the tracking and/or the contour error. For multi-axis contouring with mismatched axis dynamics, a ZPET controller cancels the phase error and provides good contouring accuracy. With a SPZC controller which does not cancel the phase lag, the axes can be “matched” for equal phase lag by adding zeroes to the feedforward controller.

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 Controllers With Optimal Gain Characteristics

1993 ◽  
Vol 115 (3) ◽  
pp. 311-318 ◽  
Author(s):  
Y. Funahashi ◽  
M. Yamada
Keyword(s):  
Control System ◽  
Phase Error ◽  
Tracking Performance ◽  
Output Data ◽  
Tracking Controllers ◽  
Tracking Controller ◽  
Phase Property ◽  
Feedforward Controller ◽  
Step Type ◽  
Zero Phase

Recently, a digital feedforward controller, called a Zero Phase Error Tracking Controller (ZPETC), has been proposed. In this controller, the overall frequency response between the desired output and the controlled output exhibits zero phase shift for all frequencies by using a few steps of the future desired output data. In this paper, two extensions of ZPETC’s are proposed: a ZPETC with deadbeat tracking performance and an L2-Optimal ZPETC. These ZPETC’s can provide the overall control system with not only the above phase property but also the excellent tracking performance for a desired output and the superior gain property, respectively. Moreover, a ZPETC with both the excellent tracking performance for a step-type and ramp-type desired output and the superior gain property, called an L2-Optimal ZPETC with deadbeat tracking performance, is presented.

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.

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