Repetitive control for systems with uncertain period-time

Repetitive control is useful if periodic disturbances act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period-time is exactly known. For those cases where the period-time changes and cannot be measured directly by an auxiliary signal, a robust repetitive controller structure is proposed. It uses multiple memory-loops in a certain feedback configuration, such that small changes in period-time do not diminish the disturbance rejection properties. The robust repetitive controller shows good implementation results for a tracking control problem of a Compact Disc player.     

Delay-varying repetitive control with application to a walking piezo actuator

The performance of systems that exhibit repetitive disturbances can be significantly improved using repetitive control. If the repetitive disturbance is periodic with respect to time, perfect asymptotic disturbance rejection can be achieved by well-known methods. However, many systems have a repetitive nature with respect to a variable other than time. For this type of systems, we propose a delay-varying repetitive control (DVRC) method, which employs a time-varying delay in the repetitive controller that is continuously adjusted based on the repetitive variable. An H_∞ norm-based criterion is derived that guarantees stability of the time-varying delay system for a given range of variations of the repetitive delay. The strengths of this new repetitive control scheme are shown by applying it to a nanomotion stage driven by a walking piezo actuator.     

The consistency control of mold level in casting process

A new multiple periodic disturbance rejection control for casting process is proposed in this paper. Firstly, a high-precision multiple periodic disturbance detection method is designed. The accurate frequencies of the disturbance can be obtained. By using the disturbance observer and a group of filters with additional delay items, multiple periodic disturbance can be suppressed under time-delay environment. Then systematic control design is achieved based on the robust stability analysis. Finally, the efficiency of the proposed method is shown by comparisons between different methods and time-varying disturbance rejection in the consistency control of mold level.     

Generalized extended state observer–based repetitive control for systems with mismatched disturbances

A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.     

Period-robust repetitive model predictive control

Repetitive model predictive control (RMPC) incorporates the idea of repetitive control (RC) into the basic formulation of model predictive control (MPC) to enable the user to take full advantage of the constraint handling, multivariable control features of MPC in controlling a periodic process. The RMPC achieves perfect asymptotic setpoint tracking/disturbance rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance signal exactly. Even a small mismatch between the actual period of the process and the controller period can deteriorate the RMPCs performance significantly. The period mismatch can occur either from an inaccurate estimation of the actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of the sampling time. For such cases, an extension of RMPC called “period-robust” repetitive model predictive control (pr-RMPC) is proposed. It is based on the idea of using weighted, multiple memory loops in RC, such that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that, in case of a slight period mismatch, pr-RMPC achieves significant improvement over the standard RMPC in rejecting periodic disturbances.     

基于优化性能的重复控制器设计

提出一种基于优化性能的重复控制器设计方法.首先,对重复控制器中时滞环节的时延进行修正,以补偿由于低通滤波器的引入所带来的相位滞后,进而提高系统在参考/干扰信号基频处的增益,增强系统对基频信号的跟踪/抑制能力;其次,在重复控制器中加入超前校正环节,不仅拓宽了低通滤波器的带宽,而且提高了系统的高频增益,使得系统在高次谐波处的性能得以大幅提升.重复控制器的参数通过求解2个优化问题得到.在保证系统稳定的前提下,提出的设计方法最大限度地提升了系统的性能.针对光盘驱动器控制系统的仿真结果证实了该设计方法的有效性.     

Robust disturbance rejection in modified repetitive control system

This study concerns disturbance rejection for a modified repetitive control system (MRCS) that contains a strictly proper plant with time-varying uncertainties. Since an MRCS is affected by both periodic and aperiodic disturbances, and since the disturbances are often unknown, an equivalent-input-disturbance (EID)-based estimator was added to an MRCS to yield an EID-based MRCS that compensates for all types of disturbances. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of an EID estimate into the control input enables rejection of unknown periodic and aperiodic disturbances. A robust stability condition for the MRCS was established in the form of a linear matrix inequality, and the condition was used to design the parameters of the controller. This design method handles uncertainties and enables the preferential adjustment of the tracking and control performance of the MRCS. Simulation results demonstrate the validity of the method.     

重复学习控制及其在一类非线性系统中的应用

为跟踪或抑制仅周期已知的未知周期参考或扰动信号,提出一种新的重复学习控制方法,利用系统的稳态误差并通过迭代学习构造前馈补偿,实现了误差的渐近收敛,将所提出方法应用于一类常见的扰动信号和系统输出具有未知非线性关系的非线性系统,假设其满足连续里普希斯条件,利用重复学习控制器,系统的稳态误差可以减小到极低的程度,该方法控制精度高,实现简单,与传统的基于时延内模的重复控制方法相比,具有对非重复性干扰不敏感的优点,仿真结果验证了该方法的有效性。     

A hybrid observer for characterization and compensation of periodic disturbances

Usage of frequency based error correction methods for repetitive disturbances becomes popular in data storage devices that use a rotating mechanical power plant. Two distinct disturbance cancellation methods, disturbance observer (DOB) and adaptive feed forward control (AFC) are the most popular approaches used for current drive servo integration. DOB reduces error using a predetermined function that is calculated thorough a complicated process. Generally the response to disturbance and initiation of control action of DOB is relatively fast even if the amount of error reduction is limited. Meanwhile the error elimination capability of AFC for the repetitive disturbance is normally better than DOB as it utilizes a Fourier coefficients updating feature that supports an enhanced fine adaptation of a certain frequency disturbance. Of course, AFC suffers for disturbances that have neighboring close frequencies due to the inherent fundamental frequency dependencies of AFC formulation. In the present work, an attempt for combining benefits of AFC and DOB is made. This might enables control action not only to generate fast response to disturbance but also perform an accurate error rejection. This feature also provides to the closed loop system a frequency selection for enabling a strategic selective error rejection. The proposed method named Hybrid Disturbance Observer (HDOB) is compared to the traditional AFC and DOB.     

基于干扰补偿趋近律的离散滑模多周期重复控制

针对离散时间系统的多周期干扰抑制问题,提出一种离散滑模多周期重复控制器设计方法.利用非线性幂次函数设计新型离散趋近律,将周期差分等效干扰以加权形式嵌入到趋近律中,构造带干扰补偿作用的离散趋近律,并据此设计离散滑模多周期重复控制器.为了进行控制器参数整定和表征闭环系统的收敛性能,推导准滑模域边界层的表达式.所提出控制方法既能够消除多周期干扰信号,也能够减小准滑模域边界层.数值仿真验证了所提出控制方法的有效性.     

以幂次吸引的离散多周期重复控制

针对一类多周期干扰的抑制问题,提出一种基于幂次吸引律的离散多周期重复控制方法.多周期干扰由多个周期已知的周期干扰叠加而成.根据周期干扰的对称特性,构造出具有干扰抑制项的幂次吸引律,据此设计出子重复控制器,并以并联方式组合成多周期重复控制器,在消除多周期干扰的同时,有效地抑制慢时变非周期干扰带来的影响,改善控制品质;推导出幂次绝对吸引层和稳态误差带的具体表达式,用于刻画系统跟踪性能.仿真结果验证了所提控制方法的有效性.     

非参数不确定系统的双周期重复控制

针对一类扰动周期与参考信号周期之间无公共倍数的非参数不确定系统,为实现系统输出对参考信号的跟踪,本文提出一种双周期重复控制方法.基于Lyapunov方法设计控制器,结合鲁棒方法与双周期重复学习方法处理非参数不确定性与周期性扰动,利用无限幅学习方法估计时变参数.经过足够多个周期的重复运行后,可实现系统输出在整个参考信号重复周期上无误差地跟踪参考信号.最后,通过仿真示例验证所提控制方法的有效性.本文给出了闭环系统中无限幅学习量有界的数学证明,其结果优于多数现有文献中的L2意义下有界.     

Separated design of robust model predictive control for LPV systems with periodic disturbance

To eliminate the steady-state error of systems with periodic disturbance, the repetitive control (RC) is a useful approach. For practical applications, the controller is designed to both steer system output to a given set-point (or track a given reference signal) and reject periodic disturbance. The learning procedure of RC and the control action to steer system output to a set-point may influence each other and prolong the convergence time RC. In order to reduce this interaction, this paper proposes a separated design approach. A linear parameter varying (LPV) system is considered. A repetitive predictive control (RPC) and a robust model predictive control (RMPC) are separately designed, respectively, corresponding to reject the periodic disturbance and steer system output to the set-point. The convergence of the proposed RPC sub-controller is derived. The numerical examples show that the proposed design is effective.     

Implementation of repetitive controller for rejection of position-based periodic disturbances

Time-varying periodic motions have appeared in many industrial processes, such as cam-follower systems, in that the control system has to operate at a periodic variable velocity specified in terms of the angular position-domain. This paper employs a repetitive control for rejecting the time-varying periodic disturbances, and presents an implementation technique based on angular position which can generate a fixed number of cycles in real-time. This control technique can accommodate the period variation in a time-varying periodic signal such that variable samples per period for synchronization can be achieved by the regular fixed-time sampling rate. A technique using position information to manipulate the delayed data and an interpolation scheme to properly access data in the buffer memory is proposed. An anti-vibration control system with time-varying periodic disturbances is studied to illustrate control performance. The experimental results are given to illustrate that time-varying repetitive control can effectively eliminate steady-state errors within a few cycles.     

A systematic approach for robust repetitive controller design

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.     

基于椭圆吸引律的离散重复控制

针对离散时间系统的周期轨迹跟踪问题,提出一种基于椭圆吸引律的离散重复控制方法.该方法能有效减小抖振,并通过扰动扩张状态观测技术对系统的未知扰动进行有效抑制,采用重复控制技术对系统中存在的周期扰动完全消除.为了刻画系统误差动态性能,推导出单调减区域、绝对吸引层、稳态误差带的表达式以及系统跟踪误差进入稳态误差带的最大步长.通过数值仿真与直线伺服电机实验,验证所提出控制方法的有效性.     

高阶大惯性系统的线性自抗扰控制器设计

针对自抗扰控制器在热力系统高阶大惯性过程控制中效果不佳的问题,提出一种利用高阶系统模型信息进行补偿的自抗扰控制器设计方法.基于理论分析,给出各可调参数的物理意义及其定量化参数整定方法,并从观测误差、开环频率特性和参数稳定域等方面分析补偿自抗扰控制器能够提高控制效果的原因.仿真对比实验和鲁棒性检验结果表明,所提方法在设定值跟踪、抗扰能力和性能鲁棒性方面均优于PI/PID,同时能够显著改善低阶自抗扰控制器对高阶大惯性过程的控制效果,具有很好的工程推广潜力.     

DISTURBANCE COMPENSATION FOR TIME‐DELAY PROCESSES

In this paper, a general control scheme for disturbance rejection is presented. It is an extension of the disturbance observer used in mechatronics, and made applicable to time‐delay processes. It is shown that the proposed control scheme can achieve better load response in general and reject periodic disturbance asymptotically in particular. Stability analysis and disturbance rejection performance are provided. Simulation results confirm that the proposed method yields superior load response compared to the classical feedback system.     

重复控制系统中非周期扰动的抑制

为了改善重复控制系统中的扰动抑制性能,提出一种基于曲率模型的扰动估计新方法.该方法的主要特点是扰动的估计值直接与重复控制规则结合也不影响重复控制系统的稳定性.仿真结果显示该方法可以有效地抑制扰动.     

A robust adaptive feedforward control in repetitive control design for linear systems

This paper proposes a new adaptive feedforward cancellation (AFC) control that achieves periodic tracking and/or periodic disturbance rejection. The new control design is a direct scheme in the sense that it adaptively updates the desired control without estimating the unknown disturbance. The proposed new control has several advantages. First, its adaptation gain can be arbitrarily chosen without upsetting the system stability if given the exact system model. Second, it can be applied to not only minimum-phase systems, but also non-minimum phase systems. Third, the new control law is independent of where the disturbance enters the system. Finally, a robustness analysis is made to show that the proposed control is robust with respect to un-modelled dynamics.