Repetitive Control Design Research Articles

Repetitive Learning Control Design and Period Uncertainties

AbstractThe aim of this brief is to show how stability proofs in the time‐domain involving suitable quadratic‐integral Lyapunov‐like functions can be derived in the repetitive control design scenario in the case of uncertain period for the reference signals/disturbances to be tracked/rejected. Even though the presented arguments are rather general, we apply them to the generalization of the proportional–integral–derivative (PID)‐like learning control that has been recently designed. The use of the presented results in multi‐link robot synchronization tasks provides simple and intuitive solutions to as yet unsolved problems.

Robust repetitive control design and its application on linear servo systems

A robust design method of the discrete-time plug-in repetitive control system is proposed. By modifying the stabilizing compensator, the robustness of the repetitive control system can be well ensured together with the zero-following error performance. The design method is simple and straightforward. Meanwhile, a novel robustness criterion for the discrete-time repetitive control system is introduced, and theoretical analysis is taken to compare the robustness of the proposed controller with the widely used zero phase error tracking controller (ZPETC). The proposed repetitive controller is implemented in a linear servo system. Simulation is performed to verify the theoretical analysis, and the experimental results show the effectiveness of the proposed controller.

Digital design of adaptive repetitive control of linear systems with time‐varying periodic disturbances

The repetitive control is well known for rejecting the periodic disturbances. However, most of the existing repetitive control algorithms assume that either the plant is known or the disturbance period is fixed. This study proposes the digital design of adaptive repetitive control for a class of linear systems subject to time-varying periodic disturbances, whose periods are assumed to be identifiable. The proposed control is based on the direct adaptive control scheme and the internal model principle. A comparative study is conducted and the effectiveness of the approach is verified in simulations and experiments on a servo motor system.

Design of observer-based discrete repetitive-control system based on 2D model

A discrete observer-based repetitive control (RC) design method for a linear system with uncertainties was presented based on two-dimensional (2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality (LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.

Repetitive Controller Design for Heat Exchanger.

Repetitive Controller Design for Heat Exchanger.

Analysis and design of repetitive controller based on regeneration spectrum and sensitivity function in active power filter system

Conventional repetitive controller can hardly obtain a fast dynamic response. In order to achieve a faster dynamic performance, an improved repetitive controller is proposed in this study. The controller adds a proportional link in parallel with the original repetitive control loop. Based on the regeneration spectrum theory and the sensitivity function, the stability, steady-state error and convergence of the control system are analysed. A parameter design method is also developed. The feasibility of the controller is shown in simulations and verified by the experimental works. The simulation and experiment results confirm that the improved repetitive controller and the parameter design method are effective in the active power filter design.

Design of Robust Repetitive Control With Time-Varying Sampling Periods

This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms.

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

SummaryThis paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.

Robust Repetitive Control for a Class of Nonlinear Systems with Input Deadzone

摘要: 针对一类输入含死区非线性特性的周期时变系统, 在周期时变参数不可参数化的情形下设计鲁棒重复控制器. 采用微分自适应律估计未知死区参数, 剩余的有界项通过鲁棒方法予以消除, 为避免出现颤振现象, 采用饱和函数替代符号函数. 在系统输出跟踪周期轨迹的情形下, 将非参数化不确定项转化为含周期时变参数的形式, 以达到利用周期学习律进行估计的目的. 理论分析与仿真结果表明, 采用部分饱和或全饱和学习算法均能实现输出误差有界收敛, 并保证闭环系统所有信号有界. 关键词: 输入死区 / 非参数化 / 周期时变参数 / 鲁棒重复控制

Position-Dependent Repetitive Control for Speed Ripple Reduction of Ultrasonic Motor

Ultrasonic motors are driven by the friction force between the rotor and the vibrator, which often induces speed fluctuations synchronizing with the rotor position periodically, namely, speed ripples. This paper employs the plug-in type repetitive control for rejecting the position-dependent periodic speed ripple and presents an implementation technique based on rotor position information. A mathematical description for characterizing the speed ripple is introduced using the Fourier series. A position-dependent repetitive controller design and an interpolation scheme to manipulate the delayed data based on the acquired rotor position are developed to improve control performance in speed ripple reduction. Simulation and experimental results are given to confirm the validity of the proposed repetitive control design and implementation.

Repetitive control of servo systems with time delays

In many industrial robotic servo applications there is a need to track periodic reference signals and/or reject periodic disturbances. Moreover, time-delays are usually unavoidable in control systems due to the sensoring and communication delays. This paper presents an alternative repetitive control design for systems with constant time-delays in both forward and feedback control channels, which are dedicated to track/reject periodic signals. An additional delay is introduced together with the plant delays to construct an internal model for periodic signals, and a simple compensator based on the plant model inverse is utilized to stabilize the closed-loop system. Sufficient stability conditions of the closed-loop system and the robustness analysis against modeling uncertainties are studied. The proposed idea is further extended for general time-delay systems with only a delay term in the forward control channel. The “plug-in” structure used in conventional repetitive control designs is avoided, so that it leads to a simpler control configuration, i.e. only a proportional parameter and the cutoff frequency of a low-pass filter are required to be selected. Simulations based on a hard disk drive system and practical experiments on a rotary robotic servo system are provided to evaluate the effectiveness of the proposed method.

Robustification of iterative learning control and repetitive control by averaging

This paper describes a recently developed averaging technique to robustify iterative learning and repetitive controllers. The robustified controllers are found by minimising cost functions that are averaged over either multiple analytical time-domain models or experimental frequency-domain data. The aim is to produce a technique that is simple and general, and can be applied to any iterative learning control (ILC) or repetitive control (RC) design that involves the minimisation of a cost function. Substantial improvement in convergence to zero tracking error in the presence of model uncertainties has been observed for both ILC and RC by this averaging technique.

Robust approach to repetitive controller design for uncertain feedback control systems

In many applications, add-on type repetitive controllers have been reported to have prominent capability of attenuating periodic disturbances and/or tracking periodic reference commands. However, the effective information such as performance weighting functions for the design of feedback controllers has not been considered sufficiently on the design of repetitive controllers. In this study, we deal with a problem of a robust repetitive controller design for an uncertain feedback control system using its explicit performance information. We first show that a robust stability condition of repetitive control systems has a similar form with the well-known robust performance condition of general feedback control systems. The repetitive controller is designed using the performance weighting function for the design of the robust feedback controller. It is also shown that a steady-state tracking error of the repetitive control system is described in a simple form without time-delay term. This result yields that the repetitive control system has a much larger loop gain in the steady state than the feedback control system. Moreover, this paper provides sufficient conditions ensuring that the power of the steady-state tracking error in the repetitive control system is less than or equal to that of the feedback control system. Based on the obtained results, we present repetitive controller design method using the design information of the feedback control system. Finally, application studies on the track-following control system of optical disk drives are performed to show the validity of the proposed method.

Control repetitivo digital de sistemas con frecuencia incierta o variante en el tiempo

Digital repetitive control is an internal model principle-based control technique that aims at tracking/rejecting periodic signals. A key assumption in traditional repetitive control designs is that the frequency of such signals is constant and known, its main drawback being the dramatic loss of performance that occurs when this frequency is uncertain or time-varying. This article reviews the most relevant proposals introduced so far to overcome this problem.

Accounting for hysteresis in repetitive control design: Nanopositioning example

This paper deals with designing a repetitive controller (RC) for tracking periodic reference trajectories for systems that exhibit hysteresis, such as piezoelectric actuators used in nanopositioning systems. Hysteresis can drastically limit the performance of an RC designed around a linear dynamics model, and thus the effect of hysteresis on the closed-loop stability of RC is analyzed and the allowable size of the hysteresis nonlinearity for a stable RC is quantified. But when the hysteresis effect exceeds the maximum bound, an inverse-hysteresis feedforward controller based on the Prandtl–Ishlinskii hysteresis model is used to compensate for the nonlinearity. The control method is implemented on a custom-designed nanopositioning stage. Experimental results show that by incorporating hysteresis compensation the stability margin and the rate of error reduction improve. Likewise, the maximum tracking error reduces by 71%, from 13.7% (using industry-standard integral control) to 3.9% (using RC with hysteresis compensation), underscoring the benefits of RC with hysteresis compensation.

Analysis and design of a robust odd-harmonic repetitive controller for an active filter under variable network frequency

Frequency variations in the electrical network may cause a dramatic performance decay in repetitive controlled active filters intended to remove odd-harmonic distortion in single-phase AC loads. This work presents an odd-harmonic repetitive controller for a shunt active power filter that addresses such a performance problem. This is achieved by means of an adaptive change of the sampling period of the digital controller. However, this action implies structural changes that may result in an overall destabilization of the closed-loop system. Hence, a small-gain theorem-based robust control design technique allows to obtain a controller which assures BIBO stability in the required sampling period interval. Experimental results validate the proposal.

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.

A common setting for the design of iterative learning and repetitive controllers with experimental verification

SUMMARYPrevious work has shown that the structure of repetitive control (RC) and that of iterative learning control (ILC) differ only in the location of an internal model of the disturbance. In this paper, it is shown how this common setting permits derivation of controllers in one domain based on an existing controller in the other. This is illustrated using the following case studies: 1) an RC scheme using a state feedback structure is derived based on an existing ILC scheme, which also uses state feedback (the underlying structure is first extended to comprise both current‐error feedback and previous‐error feedforward implementations); and 2) an ILC scheme using an output injection structure is developed based on an existing RC scheme, which uses state feedback, but differs from 1) by containing only a single internal model representation. All controllers are shown to have similar equivalent representations, with parameters derived by using linear quadratic regulator analysis. This correspondence enables comparison of the effect of the structure (ILC or RC, state feedback or output injection), number of internal models, and use of error (feedback or feedforward) on subsequent performance. This is undertaken using experimental results obtained using a gantry robot. Copyright © 2012 John Wiley & Sons, Ltd.

Bitmask aware compression of NISC control words

It is not always feasible to implement an application specific custom hardware due to cost and time considerations. No instruction set compiler (NISC) architecture is one of the promising directions to design a custom datapath for each application using its execution characteristics. A major challenge with NISC control words is that they tend to be at least 4–5 times larger than regular instruction size, thereby imposing higher memory requirement. A possible solution to counter this is to compress these control words to reduce the code size of the application. This paper proposes an efficient bitmask-based compression technique to drastically reduce the control word size while keeping the decompression overhead in an acceptable range. The main contributions of our approach are (i) smart encoding of constant and less frequently changing bits, (ii) efficient do not care resolution for maximum bitmask coverage using limited dictionary entries, (iii) run length encoding to significantly reduce repetitive control words and (iv) design of an efficient decompression engine to reduce the performance penalty. Our experimental results demonstrate that our approach improves compression efficiency by an average of 20% over the best known control word compression, giving a compression ratio of 25–35%. In addition, our technique only requires 1–3 on-chip RAMs, thus making it suitable for FPGA implementation.

Repetitive Control Design for MIMO Systems With Saturating Actuators

This paper addresses the problem of tracking and rejection of periodic signals for linear multi-input, multi-output systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure is considered. Conditions in a “quasi” linear matrix inequality form are proposed to simultaneously compute a stabilizing state feedback gain and an anti-windup gain. Provided that the references and disturbances belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the repetitive controller ensures the periodic tracking/rejection.