Repetitive Control Law Research Articles

A Design Approach for Insensitivity to Disturbance Period Fluctuations Using Higher Order Repetitive Control

Repetitive control (RC) is well known as a method for tracking a periodic command as well as eliminating the influence of a periodic disturbance. An issue that can be encountered in applications is that the period of the disturbance can vary. In some cases one can monitor a drift in the disturbance period, but in other cases the period can fluctuate sufficiently fast that one wants an RC law that is robust to period fluctuations. Several studies address this problem using higher order RC incorporating a negative weight on errors from some previous period. This paper presents a systematic design procedure that can be used to improve RC robustness to disturbance period fluctuations. Methods are given to present the information needed to make the necessary tradeoffs when tuning the set of design parameters.

Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone

This paper extends the equivalent-input-disturbance (EID) approach to deal with the problem of aperiodic disturbance rejection for a plant with an input dead zone in a repetitive-control system so as to improve control performance for the tracking of a periodic signal. Since a dead zone greatly degrades control performance, we apply the EID approach to design a compensator for the nonlinearity by treating it as an input-dependent disturbance. An EID estimator is constructed by making the best use of a full-order generalized state observer (GSO). And a method of designing the GSO is explained. The EID estimate, which exhibits the synthetic effect of the nonlinearity and the aperiodic disturbance, is incorporated into a repetitive control law to compensate for the nonlinearity and the aperiodic disturbance. This method does not require any information about the dead zone. It guarantees perfect tracking for periodic reference input and satisfactory compensation of input dead zone and aperiodic disturbance at the same time. Simulation results demonstrate the effectiveness of this method.

Subspace Predictive Repetitive Control with Lifted Domain Identification for Wind Turbine Individual Pitch Control

Individual pitch control (IPC) is gaining increasing acceptance as a method for mitigation of periodic disturbances in wind turbines. This paper aims at formulating a repetitive control (RC) methodology capable of adapting online to changing turbine dynamics. This is achieved by performing system identification in a reduced-dimensional space using basis functions and using the identified parameters to synthesise an RC law to reject periodic disturbances: this methodology is termed Subspace Predictive Repetitive Control (SPRC). The method is tested on an industrial simulation test bench and is able to identify and perform load control on the turbine without affecting its power production.

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network (FBFN). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

Precision Tracking Control and Constraint Handling of Mechatronic Servo Systems Using Model Predictive Control

This paper presents precision tracking control and constraint handling of mechatronic servo systems using model predictive control. The current study revisits integral model predictive control, a common technique used in industrial process applications, from a motion control perspective for step tracking and constraint handling. To improve the control performance for periodic signal tracking, this paper integrates an internal model-based repetitive control law with the model predictive controller and transforms the original problem to a quadratic programming problem to deal with the given constraints. The current study applies the aforesaid controls to a piezoactuated system, implemented at a 10-kHz sampling rate. This research analyzes and discusses the experimental results of several controller design parameters affecting the control performance. Asymptotic error tracking and constraint handling results particularly demonstrate the effectiveness and potential of the model predictive controller for the servo design of fast mechatronic systems.

The Influence on Stability Robustness of Compromising on the Zero Tracking Error Requirement in Repetitive Control

Repetitive control (RC) can be used to design active vibration isolation mounts that aim to cancel the influence of spacecraft vibrations on fine pointing equipment. It can cancel the influence of slight imbalance in momentum wheels, reaction wheels, and CMGs. Because RC aims for zero error, it requires reasonably accurate knowledge of the system dynamics all the way to Nyquist frequency. As a result, special methods are needed to establish robustness to model error. A series of publications have demonstrated a method of averaging a cost function over models to increase the robustness. A previous paper improves on this by adjusting the learning rate as a function of frequency to further improve robustness, but there is still a hard limit on phase error. This paper considers yet one more approach, and all three can be used simultaneously. Here we compromise on the zero tracking error requirement for frequencies that require extra robustness. This allows one to extend this hard limit making RC tolerate larger model errors. A quadratic cost is used that penalizes not just the rate of change of the input function, but also the size of the input function. We first establish how to do this for the sister field of iterative learning control, and then the frequency response characteristics are produced for design of repetitive control. The method can improve tracking error for a frequency interval above the frequency at which one would otherwise have to cut off the learning because of model error. Model uncertainty can be used directly in the design process to produce stable RC laws for any level of uncertainty. The design approach differs from typical earlier work that used a sharp frequency cutoff, and instead uses a minimal amount of attenuation needed to produce stability.

Adaptive Repetitive Control of Nonlinearly Parameterized Systems Based on Fuzzy Basis Function Networks

In this note, an adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on fuzzy basis function networks (FBFNs). The parameters of the fuzzy rules are tuned with adaptive schemes. The adaptive repetitive control law is derived by using Lyapunov synthesis method to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, the controller singularity problem is solved as it avoids the nonlinear parameterization from entering into the adaptive control and repetitive control. The proposed approach has the added advantage that it does not require an exact structure of the system dynamics. The proposed controller is applied to control a model of permanent-magnet linear synchronous motor (PMLSM) subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method in terms of significant reduction in chattering while maintaining asymptotic convergence.

Repetitive learning control for triangular systems with unknown control directions

A backstepping repetitive learning control method is proposed for a class of high-order non-linear systems with triangular structure with unknown control coefficients. The Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control directions. A differential-difference repetitive control law is presented to avoid the difficulties encountered in the derivation of the fictitious control. It is proved that the output of controlled system converges to the desired trajectory asymptotically along the iterative learning axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.

Repetitive Learning Control for Nonlinear Systems with Unknown Control Directions

AbstractA repetitive learning control method combined with backstepping technology is proposed for a class of high-order nonlinear systems with triangular structure with unknown control coefficients. The Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control directions. A differential-difference repetitive control law is presented to avoid the difficulties encountered in the derivation of the fictitious control. It is shown that the output of the controlled system could converge to the desired trajectory asymptotically through repetitive learning.

Designing time invariant repetitive controllers using frequency raising of periodic coefficient projection algorithm

Many control systems are subject to periodic disturbances. Spacecraft isolation mounts for fine pointing equipment, attempt to isolate from vibrations caused by imbalance in three or four reaction wheels or control moment gyros. Repetitive control (RC) is a type of control that specifically targets the frequencies of a disturbance aiming to achieve zero error in its presence. Typical approaches have difficulty with stability robustness to model errors at high frequency, and are difficult to use with multiple unrelated frequencies. The Matched Basis Function Repetitive Control (MBFRC) developed here specifically addresses both difficulties. It uses the projection algorithm from adaptive control to determine the error frequency components of interest. This results in linear equations with periodic coefficients. By using the frequency raising method, it is shown that there is an equivalent linear time invariant transfer function model for the repetitive control law. This process designs pole-zero configurations for RC compensators that would be very hard to create by other means.

H<SUB align=right>∞ repetitive control of linear systems based on Two-Dimensional model

This paper concerns with the H ∞ repetitive control of linear system based on Two-Dimensional (2D) system theory. First, a 2D model is established to describe the control behaviour within a repetition period and the learning process between periods. Next, the problem of designing an H ∞ repetitive control law is formulated as an H ∞ state-feedback design problem for the 2D model. A new existence condition and method of designing an H ∞ state-feedback control law for the 2D model is presented. Moreover, this idea is extended to solve the problem of H ∞ repetitive control law for linear system. Finally, a numerical example was presented to illustrate the effectiveness of the presented method.

Advanced Programmed Motion Tracking Control of Nonholonomic Mechanical Systems

Trajectory tracking control of nonholonomic systems has been extended to tracking a desired motion. The desired motion is specified by equations of constraints, referred to as programmed, which may be differential equations of high order and may be nonholonomic. The strategy enables motion tracking control under the assumption that the system dynamics are accurately known. It is referred to as a model reference tracking control strategy for programmed motion. In this paper, adaptive and repetitive extensions of the strategy are proposed. Two selected advanced tracking control algorithms, i.e., the desired compensation adaptation law and the repetitive control law, which were originally dedicated to holonomic systems, are adapted to motion tracking control of nonholonomic systems. Simulation studies that illustrate programmed motion tracking control of systems with unknown parameters and the performance of repetitive motions are provided. A new performance measure to evaluate a programmed motion tracking performance is introduced.

Direct Model Reference Learning and Repetitive Control

Abstract Iterative learning and repetitive controllers learn to improve their performance when repeatedly executing a task. The learning process can be based on many different convergence concepts. However, the similarity of objective with adaptive control suggest the use of adaptive concepts. Here direct model reference adaptive control ideas are converted to produce discrete-time direct model reference learning control and direct model reference repetitive control laws with guaranteed convergence to zero tracking error. These control laws are used to modify the command going into a feedback control system, converging on whatever command is necessary to produce the desired output. The original adaptive control concepts used are for linear time invariant systems without deterministic disturbances, but the learning and repetitive control laws developed handle time varying systems with repetitive disturbances. Such general models are important since they can represent the behavior of nonlinear systems linea...

Asymptotic Rejection of Periodic Disturbances With Fixed or Varying Period

A constructive derivation of repetitive control is obtained, through attempting to derive a control law for asymptotic rejection of periodic disturbances. This derivation not only reveals a close relationship between iterative operator inversion and repetitive control, but also suggests a unified design method for a learning control algorithm. Also, based on the observation, digital repetitive control can be generalized to reject periodic disturbance whose period is not exactly an integer multiple of the sampling interval. This study introduces a delay filter in the digital repetitive control law, which optimally interpolates the signal between samples, thus effectively reconstructing the signal of the previous period and making the learning process of repetitive control successful. The proposed optimal delay filter can be updated easily according to different signal periods. Thus it is specifically suitable for on-line tuning when the signal period is changing. Compared with the available tuning methods, the proposed tuning method has excellent steady-state performance while maintaining fast transient and system robustness. The simulations on active noise cancellation within a duct confirm the superiority of this tuning method.

Adaptation rates for repetitive control schemes

In this note the effect of the adaptation gains on the rate at which a repetitive control law forces an error to zero is presented. Once determined, a design procedure is suggested for how to choose the gains for the repetitive control law. © 1997 by John Wiley & Sons, Ltd.

A Digital Segmented Repetitive Control Algorithm

This paper presents the structure and analysis of the segmented discrete-time repetitive controller. The repetitive controller is designed to reject periodic disturbance and/or track periodic reference signal with known period. Resulted from the Internal Model Principle, the repetitive control law is applied to the entire control path. However, when crucial segments within a control path are of concern, the segmented repetitive control law, which applies control actions only to those segments, can be utilized to save the memory space. It is shown that such a segmented repetitive control system is stable if the original nonsegmented one is stable.

Microcomputers do on-chip a-d conversion : Electronics p. 67 (20 July 1978)

In many applications of nanopositioning, such as scanning probe microscopy, tracking fast periodic reference trajectories with high accuracy is highly desirable. Repetitive control is a simple and effective control scheme to obtain good tracking of such reference trajectories. In order to implement repetitive control, a method for introducing time-delay is necessary. This can easily be implemented using a memory buffer with digital signal processing equipment. To achieve fast, high accuracy, and low noise performance, fast microcontrollers or field-programmable gate array hardware with fast high-resolution analog-to-digital and digital-to-analog converters are needed. As an inexpensive alternative to digital signal processing, the use of an analog bucket brigade device to implement the time-delay is investigated in this paper. Bucket brigade devices use switching to carry the input voltage over an array of capacitors, achieving a specified time-delay. Low-noise bucket brigade devices can achieve a signal-to-noise ratio around 80 dB, comparable to the actual performance when using 16-bit analog-to-digital converters. In this paper, the proposed control scheme utilizes a modified integral control law in conjunction with the repetitive control law. The overall control scheme ensures robustness towards plant uncertainty. Experimental results demonstrate the effectiveness of the overall control scheme and the analog implementation.