Periodic Reference Signals Research Articles

Online automatic tuning of a proportional integral derivative controller based on an iterative learning control approach

A new approach is proposed for closed-loop automatic tuning of a proportional integral derivative (PID) controller based on an iterative learning control (ILC) approach. The method does not require the control loop to be detached for tuning, but it requires the input of a periodic reference signal. Such a reference signal can be the natural reference signal of the control system when it is used to execute a repetitive sequence, or it can be an excitation signal purely for tuning the PID controller. A modified ILC scheme iteratively changes the control signal by adjusting the reference signal only. Once a satisfactory performance is achieved, the PID controller is then tuned by fitting the controller to yield close input and output characteristics of the ILC component. Simulation and experimental results are furnished to illustrate the effectiveness of the proposed tuning method.

Iterative Learning Approach Toward Closed-Loop Automatic Tuning of PID Controllers

This paper proposes a new method for closed-loop automatic tuning of a proportional−integral−derivative (PID) controller based on a new iterative learning control (ILC) approach. The proposed approach is applicable to process control applications where there is usually a time-delay/lag phenomenon and where nonrepetitive step changes in the reference signal are far more common than repetitive ones assumed in most literature on ILC. The method does not require the control loop to be detached for tuning, but it requires the input of a periodic reference signal which can be specified by the user or derived from a relay feedback experiment. A modified ILC scheme iteratively changes the control signal by adjusting the reference signal only. The learning gain can be selected to satisfy a necessary and sufficient condition derived in the paper, based on the information available from the oscillations induced. Once a satisfactory performance is achieved, the PID controller is then tuned by fitting the controller to yield a fitting input and output characteristic of the ILC component. Simulation and experimental results are furnished to illustrate the effectiveness of the proposed tuning method.

Adaptive Repetitive Control for an Eccentricity Compensation of Optical Disk Drivers

This paper present an adaptive repetitive control scheme for optical disk drivers to track a periodic reference signal with dynamic change in period. Periodic disturbances can be adequately attenuated using the concept of repetitive control, provided the known period. Optical disk drivers support various speeds. So optical disk drivers have the varying periodic disturbance. To deal with time varying periodic disturbances, a proposed repetitive controller is turned based on repetitive control to change sampling frequency to follow the change of reference period The proposed adaptive repetitive control consists of two portions, the repetitive controller and the frequency multiplier, where the former uses a varying sampler operating at a variable sampling rate maintained at fixed multiple times of the disturbance frequency and the latter generate the vary sampling frequency based on the disturbance frequency. An adaptive repetitive control scheme is proposed, implemented on experimental set of an optical disk driver, and demonstrate the effectiveness of the proposed methods and the improvement of the random access time.

IDENTIFIABILITY ANALYSIS FOR NONLINEAR FEEDBACK LIMIT-CYCLE SYSTEMS USING HARMONIC BALANCE METHODS

This paper proposes a method for analyzing identifiability of inherently closed-loop systems with nonlinear feedback by determining the order of persistent excitation of the input to the linear part of the dynamics. The method is based on the harmonic balance and the double Fourier series which is used for approximately expressing the output of the nonlinearity in the feedback loop. It is shown that a multiplicative periodic reference signal enhances the identifiability of the system by the additional sinusoids with interweaving frequencies to the original unforced case.

Output regulation of periodic signals for DPS: an infinite-dimensional signal Generator

In this note, we consider output regulation and disturbance rejection of periodic signals via state feedback in the setting of exponentially stabilizable linear infinite-dimensional systems. We show that if an infinite-dimensional exogenous system is generating periodic reference signals, solvability of the state feedback regulation problem is equivalent to solvability of the so called equations. This result allows us to consider asymptotic tracking of periodic reference signals which only have absolutely summable Fourier coefficients, while in related existing work the reference signals are confined to be infinitely smooth. We also discuss solution of the regulator equations and construct the actual feedback law to achieve output regulation in the single-input-single-output (SISO) case: The output regulation problem is solvable if the transfer function of the stabilized plant does not have zeros at the frequencies i/spl omega//sub n/ of the periodic reference signals and if the sequence ([CR(i/spl omega//sub n/, A+BK)B]/sup -1/ /spl times/(Q/spl phi//sub n/-CR(i/spl omega//sub n/, A+BK)P/spl phi//sub n/)) /sub n/spl isin/z//spl isin/l/sup n2/. A one-dimensional heat equation is used as an illustrative example.

Torque-Ripple Reduction in PM Synchronous Motor Drives Using Repetitive Current Control

The paper deals with the torque-ripple reduction in a permanent magnet synchronous motor (PMSM) drive with distorted back electromotive force. A smooth torque is obtained by tracking a modified current reference which is periodic over one-sixth of the electrical time period in the synchronous reference frame. An accurate tracking involves, however, very high current loop bandwidth, which is usually not achievable with conventional linear controllers. In order to improve current tracking in the presence of periodic reference signals and disturbances, the paper proposes the application of repetitive techniques to the current control in a field-oriented PMSM drive, where the q-axis current reference has been modified to achieve constant torque. The paper investigates the advantages and pitfalls of the method, through a mathematical analysis and an experimental validation obtained on a laboratory prototype. Particular emphasis is placed on the adjustments that have been specifically studied to enhance the overall system performance.

Analog circuits to implement repetitive controllers for tracking and disturbance rejection of periodic signals

In this paper, simple analog circuits to implement a repetitive control scheme are discussed. The repetitive control has shown to be a useful tool for tracking of periodic reference signals and for compensation of periodic disturbances. The main advantages of the proposed circuitry are: 1) no digital conversion required; 2) easy tuning to the corresponding frequency; and 3) cost effectiveness. A description of the circuits and corresponding experimental frequency responses are given.

A repetitive-based controller for the boost converter to compensate the harmonic distortion of the output Voltage

A novel repetitive based-control strategy is proposed for the pulsewidth modulated (PWM) boost converter to compensate the output voltage ripple due to the harmonic distortion present in the input voltage. Repetitive control has shown to be a useful tool for tracking of periodic reference signals and for compensation of periodic disturbances, in other words, for harmonic compensation. The structure of the proposed controller is preserved as close as possible to the conventional one, which includes outer and inner control loops. Thus, in the proposed controller, the repetitive strategy appears as a refinement term added to the inner control loop. We show that the repetitive strategy can be built using a single analog delay integrated circuit, thus, simplifying enormously the implementation. The repetitive strategy is able to cancel almost every remaining harmonic distortion component while maintaining an acceptable dynamical performance and without inclusion of additional hardware in the power stage. Experimental results on a boost converter board, using a poorly regulated voltage source, are presented to assess the performance of our approach.

광 디스크 드라이브의 편심 보상을 위한 적응 반복 제어

본 논문에서는 변하는 주기 기준 신호를 추종하기 위한 광학 디스크 드라이브의 적응 반복 제어 기법을 제시한다. 주기가 알려진 주기적인 외란은 반복 제어 개념을 이용하면 충분히 제거할 수 있다. 광학 디스크 드라이브는 다양한 속도를 지원하기 때문에 변하는 주기의 외란을 가진다. 기준 주기 변화를 추종하기 위해 샘플링 주파수를 변화시키는 반복 제어를 기초로 하여 주기가 변하는 외란을 다루기 위한 적응 반복 제어를 제안한다. 제안한 제어 기법은 반복 제어기와 주파수 발생기고 구성된다. 전자는 외란 주파수의 고정 배수에서 동작하는 가변 샘플러를 사용하고 후자는 외란 주파수에 따라 변하는 샘플링 주파수를 발생한다. 광학 디스크 드라이브 제어 대한 실험 결과에서 제안한 기법의 우수성과 랜덤 탐색 시간의 개선을 보인다. This paper presents an adaptive repetitive control scheme for optical disk drives to track a variable periodic reference signal. Periodic disturbances can be adequately attenuated using the concept of repetitive control, provided the period is known. Because optical disk drives support various speeds, they have the varying periodic disturbances. Based on repetitive control to change sampling frequency to follow the change of reference period, an adaptive repetitive control is proposed in order to deal with such disturbances. The proposed control consists of the repetitive controller and the frequency generator. The former uses a varying sampler operating at fixed multiple times of the disturbance frequency and the latter generates the changeable sampling frequency based on the disturbance frequency. The experimental results on the control of an optical disk drive demonstrate the effectiveness of the proposed schemes and the improvement of random access time as well.

繰返し動作を考慮に入れたリニアスライダの適応型摩擦補償制御

繰返し動作を考慮に入れたリニアスライダの適応型摩擦補償制御

USING REPETITIVE CONTROL TO ELIMINATE PERIODIC DISTURBANCES IN DAMPER TEST RIGS

Repetitive Control is a relatively new technique for controlling systems that contain periodic reference signals or periodic disturbances. The fundamental idea behind the method is to use the internal model of the periodic signal to guarantee asymptotic reference tracking or disturbance rejection. In this paper two recent Repetitive Control algorithms are applied to a simulation model of a damper test rig. Damper test rigs are are widely used in the automotive industry to experimentally verify the mechanical durability properties of a given damper. These rigs, however, due to their mechanical setup, a tendency to generate internal periodic disturbances, which obviously have a negative effect on the reliability of the test results. The theoretical and simulation results in this paper show how Repetitive Control can be used to eliminate these periodic disturbances, resulting in a considerable increase in accuracy.

ADAPTIVE LEARNING CONTROL OF LINEAR SYSTEMS BY OUTPUT ERROR FEEDBACK

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output, minimum phase, observable linear systems. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: exponential tracking of both the input and the output reference signals is achieved if the Fourier series expansion is finite, while arbitrary small tracking errors are guaranteed otherwise.

Adaptive learning control of nonlinear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output, minimum phase, observable nonlinear systems with unknown smooth output dependent nonlinearities. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ’learns’ the input reference signal by identifying its Fourier coefficients: exponential tracking of both the input and output reference signals is achieved if the Fourier series expansion is finite while arbitrary small tracking errors are exponentially guaranteed otherwise.

An Approach to the Control of Periodically Cyclic Processes

Abstract Numerous solutions for the problem of controlling periodically cyclic processes (i.e. systems subject to periodic reference signals) already exist. However, most of them are quite sophisticated, hence unfavourable in practice. The following method is very simple, easily realisable, needs little prior knowledge of the system, works even with non-minimum-phase systems or systems with large dead time and has proved to function by some industrial applications.

Identification of resonant systems using periodic multiplicative reference signals

System identification of the forward path of a linear unity feedback system, which is almost unstable, is considered through the application of a periodic multiplicative reference signal. Motivation for this problem comes from the need to identify the linear acoustics of a combustion process on the verge of instability. The tools of cyclostationary signal analysis provide an entré to develop methods for understanding the problem and for determining requisite properties of the reference signal.

Digital repetitive learning controller for three-phase CVCF PWM inverter

In this paper, a plug-in digital repetitive leaning control scheme is proposed for three-phase constant-voltage constant-frequency (CVCF) pulsewidth modulation inverters to achieve high-quality sinusoidal output voltages. In the proposed control scheme, the repetitive controller (RC) is plugged into the stable one-sampling-ahead-preview-controlled three-phase CVCF inverter system using only two voltage sensors. The RC is designed to eliminate periodic disturbance and/or track periodic reference signal with zero tracking error, The design theory of plug-in repetitive learning controller is described systematically and the stability analysis or overall system is discussed. The merits of the controlled systems include features of minimized total harmonic distortion, robustness to parameter uncertainties, fast response, and fewer sensors. Simulation and experimental results are provided to illustrate the effectiveness of the proposed scheme.

Design and application of a continuous repetitive controller for rotating mechanisms

In this paper the continuous repetitive controller is designed to reject the periodic disturbance and track periodic reference signal for rotating mechanisms. The stability condition is derived and the system is shown to satisfy the internal model principle, which assures that the control output tracks a class of reference commands without a steady-state error if the generator for the references is included in the stable closed-loop system. In order to satisfy this principle, a periodic signal generator is placed in the feedback loop to reject periodic disturbances and to track repetitive reference signals. The best control method will be chosen from the viewpoint of suitability in the practical problems. Finally, the repetitive control algorithm is applied to both the slider-crank and quick-return mechanisms.

Nonlinear repetitive control

Repetitive controllers are generally applied to reject periodic disturbances and to track periodic reference signals with a known period. Their design is based on the internal model principle, proposed by Francis and Wonham (1975). This paper describes a new finite-dimensional SISO repetitive controller for two different classes of nonlinear plants. Simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the Nth harmonic frequency. A proof of robustness of the repetitive control system to small nonlinearities, like actuator nonlinearities, is provided.

A Repetitive-PD Controller for a Low Order Industrial Plant

This work reviews the concept of repetitive control applied to a low order industrial plant. This kind of control is used to track periodic reference signals and to reject periodic disturbance signals. Usually, these controllers are introduced in a plug-in fashion in cascade with a previous designed controller and the controlled plant. In this work a PD controller is used to stabilize the plant and the repetitive controller is added to obtain periodic disturbance signals rejection and tracking capabilities.

A Modified Filtered-X LMS Algorithm for Active Control of Periodic Noise with On-Line Cancellation Path Modelling

The filtered-x LMS algorithm (FXLMS) has been successfully applied to the active control of periodic and random noise and vibration. This paper presents a modified algorithm for active control of periodic noise based on the FXLMS algorithm which uses random noise for on-line cancellation path transfer function (CPTF) estimation. In the proposed algorithm, another two short adaptive filters are introduced. One is an adaptive noise cancellation filter, which is used to improve the convergence speed of the CPTF modelling filter in the presence of very large amplitude primary noise by cancelling the component of the error signal that is correlated with the primary noise. The other is an adaptive estimator, which is used to re-estimate the obtained CPTF (long FIR filter estimated by random noise) with a short FIR filter by using the periodic reference signal as the input. The traditional FXLMS algorithm is then used with the shortened FIR filter to filter the reference signal, thus providing significant processing flexibility in practical situations where the primary path transfer function changes much faster than the CPTF. Simulation results demonstrate the effectiveness of the proposed algorithm.