Digital repetitive plug-in controller for odd-harmonic periodic references and disturbances

This work develops a digital repetitive plug-in controller for odd-harmonic discrete-time periodic references and disturbances. The controller presents a novel structure and it has a lower data memory occupation than the usual repetitive controllers because it takes advantage of the particular characteristics of the signals to track or attenuate. A sufficient criterion of stability, several hints for its practical application and an example are also included in the work.     

Quasi-sliding mode based repetitive control for nonlinear continuous-time systems with rejection of periodic disturbances

A Quasi-Sliding Mode (QSM) based tracking control method for tackling Multiple-Input Multiple-Output (MIMO) nonlinear continuous-time systems with un-matching system uncertainties and exogenous disturbances is proposed. The presented Repetitive Control (RC) scheme ensures robust system stability when the system is subject to non-periodic uncertainties and exogenous disturbances. The complete rejection of periodic exogenous disturbances and a perfect tracking of non-periodic reference trajectories are achievable. In this paper, a practical application to a mass-spring-damper system is used to illustrate the validity of the proposed QSM based RC method.     

Spatial observer-based repetitive controller: An active disturbance rejection approach

Linear Repetitive Control has proven to be an effective strategy to compensate for periodic disturbances in mechatronic systems that operate at constant speed; however, it renders very poor performance in varying speed applications. In this work, a Repetitive Controller based on a Generalized Proportional Integral (GPI) observer under Active Disturbance Rejection approach is presented and formulated in spatial domain. The inclusion of the linear GPI observer makes possible to see the spatial non-linear system as a simplified linear one by means of an on-line estimated unified disturbance term. Experimental results show that the presented linear approach successfully rejects periodic disturbances under varying speed conditions.     

A new adaptive control for periodic tracking/disturbance rejection

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. Second, it can be applied to not only minimum‐phase systems, but also non‐minimum phase systems. Finally, it is shown that the proposed AFC control is independent of where the disturbance enters the system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Nonlinear control for robust rejection of periodic disturbances

Consider a linear plant with a strictly proper rational transfer function and an input which is a known periodic waveform of unknown amplitude and phase. In the case when the periodic waveform has infinitely many non-zero harmonics, it is pointed out that for a wide class of linear, time-invariant (infinite-dimensional) controllers, it is not possible to robustly stabilize the plant and achieve asymptotic rejection of the disturbance. For a specific linear plant and a triangular wave disturbance, it is shown by construction that the problem is soluble with a nonlinear controller. Robustness is measured using the gap metric robust stability margin.     

Dealing with periodic disturbances in controls of mechanical systems

Periodic disturbances are common in control of mechanical systems. Such disturbances may be due to rotational elements such as motors and vibratory elements. When the period of a periodic disturbance is fixed and known in advance, repetitive control can be used for attenuating their effect. The most popular repetitive controller is based on the internal model principle. When the period is not fixed and unknown, adaptation capability must be introduced. This paper presents some fundamental issues and new challenges in the design of controllers to deal with periodic disturbances along with applications to mechanical systems.     

基于二维混合模型的改进型重复控制器设计

针对一类线性系统,提出一种基于连续/离散二维混合模型的改进型重复控制系统设计方法.首先,通过分析重复控制系统中独立存在的控制行为和学习行为,建立了连续/离散二维混合模型,并将重复控制设计问题转化为一类连续/离散二维系统的状态反馈控制问题;然后,基于对重复控制过程的分析和二维模型,提出一种新型重复控制系统结构,并将重复控制器的设计问题转化为连续/离散二维混合系统的状态反馈设计问题;最后,应用二维Lyapunov泛函理论和线性矩阵不等式方法,获得了重复控制器参数求解方法.     

A repetitive controller for discrete-time passive systems

This work proposes and studies a new repetitive controller for discrete-time systems which are required to track or to attenuate periodic signals. The main characteristic of the proposed controller is its passivity. This fact implies closed-loop stable behavior when it is used with discrete-time passive plants. The work also discusses the energetic structure, the frequency response and the time response of the proposed controller structure. A numerical example is included to illustrate its practical use.     

Asymptotic rejection of unmatched general periodic disturbances with nonlinear Lipschitz internal models

This article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with Lipschitz output nonlinearities for the internal model design. It is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions. Based on this observation, a nonlinear observer design with output Lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input-to-state stable zero dynamics. A number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear Lipschitz internal model can be applied. Two examples are included to demonstrate the proposed design strategies.     

Asymptotic rejection of unmatched general periodic disturbances in a class of non-minimum-phase non-linear systems

This article deals with asymptotic rejection of unmatched general periodic disturbances in nonminimum phase non-linear output feedback systems. The steady state responses are defined for unstable systems subject to general periodic disturbances, and the generalised gain and phase are defined for stable systems subject to general periodic disturbances. Based on the new definitions, new results are obtained for the equivalent input disturbance and disturbance estimation. An L _p -convergent estimate of the equivalent input disturbance is incorporated in the control design to ensure the asymptotic rejection of unmatched general periodic disturbances while maintaining the stability of the non-linear system.     

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.     

Optimal feedforward controller design for periodic inputs

This article presents an optimal design methodology for feedforward controllers that face periodic reference/disturbance inputs. The feedforward controller is parametrised as a finite impulse response filter, and its parameters are computed to minimise the worst-case tracking error in the presence of uncertainty on the input period and the plant model. Numerical results indicate that for nonminimum-phase systems exploiting the periodic input characteristics in the feedforward controller design is worthwhile, and reveal the superiority of the developed design methodology with respect to current design approaches when period-time and/or plant uncertainty is present.     

High-order repetitive control for discrete-time linear switched systems

This paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.     

Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete‐time repetitive controller design for time‐delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time‐delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed‐loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low‐pass filter are required to be chosen. The closed‐loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Linear periodic controller design for decentralized control systems

In the decentralized control of linear time-invariant (LTI) systems, a decentralized fixed mode (DFM) is a system mode which is immoveable using an LTI controller, while a quotient DFM (QDFM) is one which is immoveable using any form of nonlinear time-varying compensation. If a system has no unstable DFMs, there are well-known procedures for designing an LTI stabilizing controller; for systems which have unstable DFMs but no unstable QDFMs, we provide a simple design algorithm which yields a linear periodic sampled-data stabilizing controller.     

气动加载系统的积分型线性自抗扰控制

气动加载系统是复杂的非线性时变系统,可变参数和不确定性比较多,本文采用积分型线性自抗扰控制器(I--LADRC)对气动加载系统进行控制.自抗扰控制器(active disturbance rejection controller,ADRC)结构简单,不依赖于被控对象精确的数学模型,可以很好补偿被控系统内外各种不确定性.加入积分环节用来弥补ADRC在时变系统控制中存在的不足.在采用VC++6.0的工控试验平台上,将I--LADRC应用于气动加载系统中,分别在加载压力为恒值、方波和正弦波时进行空载和加载实验,并将得到的实验结果与PID控制算法进行比较,实验结果表明该控制算法不仅响应速度快,精度高,并且还具有较强的鲁棒性,具有良好的工程应用前景.     

Asymptotic rejection of asymmetric periodic disturbances in output-feedback nonlinear systems

This paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns. This class of disturbances covers asymmetric wave forms in the half-period such as alternating sawtooth wave form, some disturbances which are generated from nonlinear oscillation such as Van de Pol oscillators, as well as disturbances with symmetric half-period wave forms such as sinusoidal disturbances and triangular disturbances etc. The systems considered in this paper can be transformed to the nonlinear output feedback form. The amplitude and phase of the disturbances are unknown. The novel concept of integral phase shift is introduced together with the newly introduced half-period integration operator to investigate the invariant properties of asymmetric periodic disturbances. They are used for the estimation of unknown disturbances in the systems, together with observer design techniques to deal with nonlinearity. The proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance, and ensures the overall stability of the system.     

Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion (FSE) are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions (such as global Lipschitz c...     

Generating self-excited oscillations for underactuated mechanical systems via two-relay controller

A tool for the design of a periodic motion in an underactuated mechanical system via generating a self-excited oscillation of a desired amplitude and frequency by means of the variable structure control is proposed. First, an approximate approach based on the describing function method is given, which requires that the mechanical plant should be a linear low-pass filter–the hypothesis that usually holds when the oscillations are relatively fast. The method based on the locus of a perturbed relay systems provides an exact model of the oscillations when the plant is linear. Finally, the Poincaré map's design provides the value of the controller parameters ensuring the locally orbitally stable periodic motions for an arbitrary mechanical plant. The proposed approach is shown by the controller design and experiments on the Furuta pendulum.