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.

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.

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.

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.

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.

Pseudo-Causal Tracking Control of a Nonminimum Phase System

2009 ◽  
Author(s):  
Pengfei Wang ◽  
M. Necip Sahinkaya ◽  
Sam Akehurst
Keyword(s):  
Transfer Function ◽  
Test Facility ◽  
Phase System ◽  
Hardware In The Loop ◽  
Nonminimum Phase ◽  
Software Models ◽  
Continuously Variable Transmissions ◽  
Future Value ◽  
Novel Method ◽  
Feedforward Controller

A novel method is described to implement noncausal feedforward compensators causally, i.e. without requiring any future value of the reference input trajectory. A hardware-in-the loop test facility developed for continuously variable transmissions is utilized in this paper. The test facility includes two induction motors to emulate engine and vehicle characteristics. Software models of an engine and vehicle, running in real-time, provide reference torque and speed signals for the motors, which are connected to a transmission that is the hardware in the loop. Speed control of the output motor that emulates the vehicle dynamics is used to demonstrate an application of the proposed technique. A feedforward compensator, based on transfer function inversion, is used to compensate for the nonminimum phase motor and drive system dynamics. The vehicle model cannot be run ahead of time to provide the future values required by the noncausal inversion technique because it requires the current torque at the output of the transmission. Therefore, the feedforward controller has to be applied causally. A frequency domain estimation technique and a multi-frequency test signal are utilized to estimate, within the frequency range of interest, a low relative order transfer function of the closed loop system incorporating a manually added delay in the feedback loop. A noncausal feedforward controller is designed for the delayed output of the system based on the identified transfer function. It has been shown experimentally that this compensator offers excellent tracking performance of the motor when subjected a multi-frequency speed demand signal.

Sine phase compensation combining an amplitude phase controller and a discrete feed-forward compensator for electro-hydraulic shaking tables

2017 ◽  
Vol 40 (11) ◽  
pp. 3377-3389 ◽  
Author(s):  
Ge Li ◽  
Gang Shen ◽  
Zhen-Cai Zhu ◽  
Xiang Li ◽  
Wan-Shun Zang
Keyword(s):  
Control Strategy ◽  
Phase Error ◽  
Phase Delay ◽  
Shaking Table ◽  
Response Signal ◽  
Feed Forward ◽  
Amplitude Attenuation ◽  
Tracking Controller ◽  
Phase Deviation ◽  
Zero Phase

This article presents a novel control strategy on an electro-hydraulic shaking table under the acceleration control combining an amplitude phase controller and a zero phase error tracking controller with a discrete feed-forward compensator. Because of the electro-hydraulic system’s nonlinearity, phase delay and amplitude attenuation exist in the acceleration response signal inevitably when the electro-hydraulic shaking table system is excited by a sine vibration signal. Moreover, the phase delay of the electro-hydraulic shaking table is composed of phase deviation and actuator delay. For improving the acceleration tracking accuracy, an amplitude phase controller is employed to compensate the phase deviation and amplitude attenuation by introducing weights to adjust the reference signal. Meanwhile, the discrete feed-forward compensator is applied to compensate the actuator delay. As an offline compensator, the zero phase error tracking controller is employed to compensate the phase delay of the response signal and improve the convergence speed of the proposed controller. Overall, the proposed control strategy combines the merits of these three controllers with better tracking performance demonstrated by simulation and experimental results.

Feedforward Tracking Controller Design Based on the Identification of Low Frequency Dynamics

1993 ◽  
Vol 115 (3) ◽  
pp. 348-356 ◽  
Author(s):  
E. D. Tung ◽  
M. Tomizuka
Keyword(s):  
High Speed ◽  
Linear Models ◽  
Controller Design ◽  
Phase Error ◽  
Low Frequency ◽  
Reference Trajectory ◽  
Accurate Identification ◽  
Tracking Controller ◽  
Feed Drive System ◽  
Zero Phase

Several methodologies are proposed for identifying the dynamics of a machine tool feed drive system in the low frequency region. An accurate identification is necessary for the design of a feedforward tracking controller, which achieves unity gain and zero phase shift for the overall system in the relevant frequency band. In machine tools and other mechanical systems, the spectrum of the reference trajectory is composed of low frequency signals. Standard least squares fits are shown to heavily penalize high frequency misfit. Linear models described by the output-error (OE) and Autoregressive Moving Average with eXogenous Input (ARMAX) models display better closeness-of-fit properties at low frequency. Based on the identification, a feedforward compensator is designed using the Zero Phase Error Tracking Controller (ZPETC). The feedforward compensator is experimentally shown to achieve near-perfect tracking and contouring of high-speed trajectories on a machining center X-Y bed.

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