线性离散周期系统满意估计

针对线性离散周期系统的状态估计问题,运用提升原理提取期望极点指标,同时期望估计误差系统满足稳态误差方差/H_∞混合指标,采用代数Riccati矩阵不等式法与数值递推算法对误差系统进行了上述指标的满意估计设计,并根据满意控制的基本理论将上述满意估计问题转化为线性矩阵不等式(LMI)的线性规划问题,从而运用LMI技术求解并设计了可行的满意估计,数值算例验证了相关算法.     

Output stabilization via pole placement of discrete-time linearperiodic systems

The output stabilization problem for discrete-time linear periodic systems is solved. Both the state-feedback control law and the state-predictor are based on a suitable time-invariant state-sampled reformulation associated with a periodic system. Preliminary concepts of periodic system theory are briefly recalled. In particular, the structural properties of a linear discrete-time periodic system are properly related to those of a time-invariant system associated with it. By resorting to such a time-invariant reformulation, the output stabilization problem via pole placement is solved. The stabilizing controller is constituted by a control law and an asymptotic state predictor, both of which are shown to be periodic     

A multirate controller design of linear periodic time delay systems

This paper presents a multirate controller design for a linear periodic system with multiple delays at input and output. The approach first converts the periodic time-delay system into a periodic delay-free system, and then stabilizes and optimizes it by a multirate controller with pulse compensation. A significant advantage of this approach is that by using multirate sampling, the controller can provide more substantial design freedoms, so that although the system does not provide complete state information, it remains possible to convert the controller design into the dual of a regular complete state feedback problem. This enables one to derive a simple algorithm for choosing the optimal parameters of the controller and, by use of the optimal pulse compensation, to improve the transient response.     

Synthesis of MIMO controllers for extending the stability range of periodic solutions in forced nonlinear systems

This paper deals with a central issue in bifurcations and chaos control applications, i.e., the stabilization of periodic motions in sinusoidally forced nonlinear systems. Specifically, the problem of designing multi-input-multi-output (MIMO) finite-dimensional linear time-invariant controllers maximizing the amplitude of the sinusoidal input for which the corresponding periodic solutions are guaranteed to be stable, is considered. By exploiting linearization techniques and the multi-variable circle criterion, a synthesis algorithm is developed to determine the controller which maximizes a suitable lower bound of the amplitude of the input. The algorithm requires the solution of a sequence of linear matrix inequalities (LMIs) of increasing size. The Brusselator oscillator is employed as a case study to show that the synthesized controllers, though optimizing a lower bound, provide quite satisfactory control performance.     

On stability and stabilization of periodic discrete-time systems with an application to satellite attitude control

An alternative stability analysis theorem for nonlinear periodic discrete-time systems is presented. The developed theorem offers a trade-off between conservatism and complexity of the corresponding stability test. In addition, it yields a tractable stabilizing controller synthesis method for linear periodic discrete-time systems subject to polytopic state and input constraints. It is proven that in this setting, the proposed synthesis method is strictly less conservative than available tractable synthesis methods. The application of the derived method to the satellite attitude control problem results in a large region of attraction.     

Decentralized control and state estimation of linear time-periodic systems

The main contributions of this article are the design of a decentralized controller and state estimator for linear time-periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time-invariant system by applying a time-lifting technique and designing a discrete-time decentralized controller and state estimator for the time-lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete-time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady-state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite-horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady-state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple-tank process and an extended 40-tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.     

Model-based periodic event-triggered stabilization for continuous-time stochastic nonlinear systems

In this paper, we investigate a model-based periodic event-triggered control framework for continuous-time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete-time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete-time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean-square exponentially stabilization for continuous-time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.     

An LMI approach to stabilization of linear discrete-time periodic systems

The problem of stabilization of linear discrete-time periodic systems is considered. LMI based conditions for stabilization via static periodic state feedback as well as via static periodic output feedback are presented. In the case of state feedback, the conditions are necessary and sufficient whereas for output feedback the result is only sufficient as it depends on the particular state-space representation used to describe the system. The problem of quadratic stabilization in the presence of either norm-bounded or polytopic parameter uncertainty is also treated. As an application of the output feedback stabilization technique, we consider the problem of designing a stabilizing (respectively, quadratically stabilizing) static periodic output feedback controller for linear time-invariant discrete-time systems which are not stabilizable (respectively, quadratically stabilizable) by static constant output feedback.     

Control and state observation of periodic linear multimodal systems

This paper investigates the control and state observation problem for periodic linear controllable and observable multimodal systems. For a controllable periodic linear multimodal system, this paper proposes an alternative minimum-norm dynamic state feedback control scheme for state transition matrix assignment. Also presented is a new design of state observers for an observable periodic linear multimodal system. Finally, an analysis of closed-loop behaviour of controlled periodic linear multimodal systems using a state-estimate is given     

期望指标下一类线性周期系统鲁棒状态估计

针对满足多重区域指标约束的鲁棒滤波问题 ,以离散线性周期系统为研究对象 ,利用周期系统参数在某区间变化的特性 ,将周期系统满足极点或极点 /协方差指标的估计问题转化为区间系统的鲁棒估计问题。采用线性矩阵不等式 (L MIs)法进行凸优化 ,求解对应区间系统的满意估计增益 ,并设计相应鲁棒状态估计器。数值算例验证了相关的结论。     

Fixed-time output regulation of linear delay systems by smooth time-varying control

This article investigates the fixed-time output regulation problem (FxTORP) for linear systems in the presence of input delay. A linear controller consisting of the linear periodic delayed feedback (PDF) gain and the feedforward gain obtained by solving regulator equations is designed, such that FxTORP is addressed. If only the measurable output can be used for feedback, a linear observer with periodic coefficient and artificial delay is designed so that its state converges to the state of the augmented system at a prescribed finite time. Based on the estimated state, the output regulation problem can also be solved by using observer-based output feedback. The most significant advantages of this article are that the PDF gain can be taken as smooth and the output regulation problem is achieved within a prespecified regulation time. Finally, a simulation example is given to substantiate the validity of the proposed approaches.     

一类离散时间切换线性系统的无差拍控制

研究一类带多控制器和多传感器离散时间线性系统的无差拍控制.对能控系统,通过适当的状态坐标变换获得系统矩阵的块三角结构,再设计状态反馈和周期切换策略使得状态反馈矩阵在有限周期内为零,从而保证闭环系统的无差拍稳定.进一步,对能观系统,设计具有有限时间精确估计的动态输出反馈,通过适当的周期切换策略实现闭环系统的无差拍稳定.最后,给出一个例子以验证所提设计方法的有效性.     

Discrete time linear optimal multi-periodic repetitive control: a benchmark tracking solution

The use of optimal control tracking methodologies for the development of feedback control schemes for arbitrary discrete-time linear systems is considered for the special case when the demand signal is multi-periodic, i.e. can be expressed as a finite sum of periodic signals of different but known frequencies. By embedding the reference signal into plant dynamics, the problem is reduced to a classical linear quadratic control problem which yields an explicit formula for a globally stabilizing tracking controller. Asymptotic perfect tracking is guaranteed by the presence of the familiar internal model of the demand signal dynamics within the control structure. Transfer function analysis of the controller indicates that it consists of an inner state feedback loop plus an error actuated forward path control element containing the internal model.     

一种有限对象集的输出通道任意增益/相角裕度调节方法

针对一类有限多输入多输出线性时不变对象集,提出一种调节输出通道增益/相角裕度的方法.采用增益相角裕度测试器理论,将问题转化为有限不确定对象集的稳定性问题;基于连续线性二次调节器理论,设计针对单个对象的输出反馈控制器;利用周期控制方法,设计针对有限对象集的线性周期控制器.该控制器可使有限对象集的所有反馈控制回路在输出通道同时实现任意大的增益裕度和直到90°的相角裕度.仿真结果表明了该方法的有效性.     

缸内直喷汽油机的自抗扰轨压跟踪控制器设计

获得期望的共轨压力是保证缸内直喷发动机(GDI)稳定工作和喷油量精确控制的一个重要前提. 本文针对缸内直喷汽油发动机轨压控制问题, 首先通过动力学分析建立了共轨燃油喷射系统的数学模型; 由于系统中存在有较强的非线性和不确定性, 采用基于模型但对模型的精确形式依赖较小的自抗扰控制技术设计轨压跟踪控制器,其中线性扩张状态观测器(ESO) 对系统存在的总扰动和不确定性进行了估计, 非线性误差反馈控制(NLSEF) 则采用反馈补偿实现扰动的抑制. 最后, 通过给定不同的参考轨压对控制器的有效性进行验证, 仿真结果表明控制性能是满意的.     

Pole placement adaptive control with persistent jumps in the plant parameters

In this paper we consider the problem of adaptively stabilizing, and providing step tracking for, an uncertain linear time-varying system. We propose an adaptive pole placement controller which solves the problem for a single-input single-output plant whose parameters switch at a moderate rate among the elements of a compact set. The output feedback controller incorporates an integrator, and its action emulates the behaviour of a pole placement state feedback compensator; the controller is periodic and mildly nonlinear, is easy to implement, is noise tolerant, and tolerates a degree of unmodelled dynamics.     

Supervised Multi‐Rejector of Periodic Disturbances for Nonlinear Systems Using Decoupled State Multimodel

In this paper, a multi‐rejector of periodic disturbances is proposed for discrete‐time nonlinear systems represented by a decoupled state multimodel. We report a decoupled state multimodel repetitive‐predictive control based on a supervised algorithm to ensure reference trajectory tracking and periodic disturbances rejection. Partial predictors associated to the local controllers make the best choice of the most valid partial controller that meets the desired closed loop performances. The effectiveness of the supervised multi‐rejector is shown via a simulation example. The obtained results are satisfactory and show a good rejection of periodic disturbances and reference trajectory tracking.     

线性周期系统特征指数的配置

线性周期系统的稳定性完全由它的特征指数决定,该文研究如何配置线性周期系统的特征指数,为了配置特征指数,首先需要用旋转变换将原系统化简成块能控标准形.在块能控标准形的基础上文中提出一种设计周期状态反馈的方法,可以任意配置线性周期系统的特征指数.文章还给出了一个线性周期系统特征指数可以任意配置的充分条件.此设计方法曾应用于磁控小卫星的控制器设计,仿真结果表明,采用该文提出的设计方法控制线性周期系统是非常有效的.     

Periodic motion planning and control for underactuated mechanical systems

We consider the problem of periodic motion planning and of designing stabilising feedback control laws for such motions in underactuated mechanical systems. A novel periodic motion planning method is proposed. Each state is parametrised by a truncated Fourier series. Then we use numerical optimisation to search for the parameters of the trigonometric polynomial exploiting the measure of discrepancy in satisfying the passive dynamics equations as a performance index. Thus an almost feasible periodic motion is found. Then a linear controller is designed and stability analysis is given to verify that solutions of the closed-loop system stay inside a tube around the planned approximately feasible periodic trajectory. Experimental results for a double rotary pendulum are shown, while numerical simulations are given for models of a spacecraft with liquid sloshing and of a chain of mass spring system.     

Robust compensation of time delayed plant by continuous‐time high frequency periodic controller with negligible output ripples

The present work addresses the problem of ensuring robust stability to time delayed plants, compensated with continuous‐time high frequency periodic controller. An efficient design methodology is proposed to synthesize the periodic controller for robust compensation of time delayed linear time‐invariant plants. The periodic controller, by virtue of its loop zero‐placement capability, is shown to achieve superior gain as well as phase/delay margin compensation, especially for non‐minimum phase plants having right half plane poles and zeros in close vicinity to each other. The periodic controller is considered in the observable canonical form which results in realizable bounded control input as well as ensuring insignificant periodic oscillations in the plant output. As a consequence, this paper, furthermore, establishes the fact that the periodic controller designed and synthesized with the proposed methodology can be implemented in real‐time with an assurance of model matching and robust zero‐error tracking. Simulation and experimental results are illustrated to establish the veracity of the claims. The closed‐loop system comprising of time‐delayed linear time‐invariant plant with the periodic controller is analyzed employing the averaging principle and presented here explicitly in a meticulous approach. Copyright © 2015 John Wiley & Sons, Ltd.