Parametric output feedback control with response insensitivity

A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.     

Parametric state-feedback control with model reduction

A parametrization of the class of linear state-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is applied to a method of model reduction. By making the maximum number of the closed-loop modes unobservable, while retaining arbitrary assignment of the remaining modes, a lower-order transfer-function matrix is obtained. The technique may be used to reduce a broad class of multivariable systems to first-order multivariable systems. The main result is a class of mode) reducing fixed-gain state feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements.     

Parametric output feedback control with left eigenstructure insensitivity

It is shown by example that a closed-loop system eigenvalue may be made totally insensitive by making the corresponding left eigenmode insensitive, even though no closed-loop system right eigenmode may be made insensitive. This paper, therefore, formulates and solves a fundamental response insensitivity problem. It is established to what extent output feedback control can be used to render the closed-loop system left eigenstructure insensitive to possibly many, not necessarily small, parameter variations in the open-loop state-space model. It is explained that the results presented cannot be seen merely by transposing all the results in a previous paper on the corresponding issues for the right eigenstructure. A lemma is given that details the loss of design freedom that occurs when a closed-loop eigenvalue is assigned to a transmission zero. Sufficient conditions for the total insensitivity of a closed-loop dyad mode are given. It is shown by example that more closed-loop eigenvalues may be made insensitive by a mixture of parametric left and right eigenstructure insensitivity than by either alone. Multistage parametric eigenstructure-insensitive design is discussed.     

Parametric insensitivity and controlled invariance

Parametric insensitivity of state and output trajectories of linear systems is approached by employing an analysis method recently developed for imbedding a large class of structural properties usually expressed in terms of matrices into a unified geometric framework. Necessary and sufficient conditions useful for determining maximal state and output subspaces, where parameter insensitive trajectories range, are given. Moreover, a procedure for the synthesis of controllers which discriminate the trajectories according to their insensitivity to various parameters is proposed. It is also shown that such controllers are consistent with completely arbitrary pole assignment.     

Control system synthesis with response insensitivity

This paper considers the problem of finding a state feedback control law which arbitrarily assigns distinct eigenvalues and achieves output response insensitivity to small plant parameter variations. It is assumed that plant structural parameter dependence is known. Conditions for these objectives are expressed in terms of eigenvectors and equivalent controllability subspaces. A maximum number of possible insensitive terms in the output spectral representation with simultaneous arbitrary eigenvalue assignment is determined, and the problem is shown to be related to the dynamic cover problem. A design procedure employing dynamic compensation is presented. It is shown that dynamic compensation does not influence the number of possible observable, insensitive terms in the output spectral representation, but it can be used to satisfy the required insensitivity conditions. Incorporation of an observer to implement the control law introduces additional sensitivity constraints which can also be satisfied using the design technique.     

LPV state-feedback control of a control moment gyroscope

This paper presents the design and successful experimental validation of a linear parameter-varying (LPV) control strategy for a four-degrees-of-freedom control moment gyroscope (CMG). The MIMO plant is highly coupled and nonlinear. First, a linearized model with moving operating point is used to construct an LPV model. Then, a gridding-based LPV state-feedback control is designed that clearly outperforms linear time-invariant (LTI) controllers. Moreover, a way is proposed to select pre-filter gains for reference inputs that can be generalized to a large class of mechanical systems. Overall, the strategy allows a simple implementation in real-time and may be of interest for applications such as attitude control of a satellite. The method is applied to a laboratory scale CMG, and experimental results illustrate that the proposed LPV controller achieves indeed a better performance in a much wider range of operation than linear controllers reported in the literature.     

A state-feedback approach to event-based control

This paper proposes a new method for event-based state-feedback control in which a control input generator mimics a continuous feedback between two consecutive event times. The performance of the event-based control system is evaluated by comparing this loop with the continuous state-feedback loop. An upper bound of the difference between both loops is derived, which shows that the approximation of the continuous state-feedback loop by the event-based control loop can be made arbitrarily tight by appropriately choosing the threshold parameter of the event generator.     

Observer-based state-feedback control of timed Petri nets with deadlock recovery

This paper discusses the problem of controlling a timed Petri net whose marking cannot be measured but is estimated using an observer. The control objective is that of enforcing a set of generalized mutual exclusion constraints (GMEC) and all transitions are assumed to be controllable. We show that the use of marking estimates may significantly reduce the performance of the closed-loop system and in particular may lead to a deadlock. First, we present a linear algebraic characterization of deadlock markings based on siphon analysis. Second, we show how this characterization may be used to derive a procedure that may be invoked to recover from a controller induced deadlock. Finally, we assume that the timing delays associated to transitions are known and show how this knowledge can be used to improve the marking estimate and to recover the net from partial deadlocks. This procedure is similar to the one used for deadlock recovery and may be invoked whenever a transition has not fired for a time longer than its expected delay.     

Sampled-data H8 state-feedback control of systems with state delays

Sliding mode based feedback control has long been recognized as a powerful, yet easy-to-implement, control method to counteract non-vanishing external disturbances and unmodelled dynamics. Recently, research attention has focused on the development of sliding mode feedback control methods for various classes of infinite-dimensional systems. However, the existing methods are based on the assumption that distributed sensing and actuation is available, which significantly restricts their applicability to distributed process control applications. In this work, a sliding mode output feedback control method is developed for a class of linear infinite-dimensional systems with finite-dimensional unstable part using finite-dimensional sensing and actuation. Modal decomposition is initially used to decompose the original infinite-dimensional system into an interconnection of a finite-dimensional (possibly unstable) system and an infinite-dimensional stable system. Then, a sliding mode-based stabilizing state feedback controller is constructed on the basis of the finite-dimensional system. Subsequently, an infinite-dimensional Luenberger state observer, which utilizes a finite number of measurements, is constructed to provide estimates of the state of the infinite-dimensional system. Finally, an output feedback controller design is completed by coupling the infinite-dimensional Luenberger state observer and the sliding mode-based state feedback controller. Implementation, performance and robustness issues of the sliding-mode output feedback controller are illustrated in a simulation study of a distributed parameter system governed by the linearization around the spatially-uniform steady-state solution of the Kuramoto–Sivashinsky partial differential equation with periodic boundary conditions.     

Observer-based schemes for adaptive nonlinear state-feedback control

We combine recently proposed adaptive nonlinear controllers with two types of observer-based identifiers. The controllers guarantee an input-to-state stability property with respect to θ? and θ? and the observer-based identifiers independently guarantee boundedness of θ?. A stability enhancement in the observer is crucial in establishing stability properties.     

线性离散时滞系统的Gl2状态反馈控制

研究具有状态时滞的线性离散时不变系统的Gl2控制问题．基于简化的Gl2分析定理,Gl2控制问题被等价转化为H∞控制问题．通过LMI和构造Lyapunov函数,得到了Gl2性能的LMI表述．给出了使得时滞系统稳定且满足给定性能指标的无记忆Gl2状态反馈控制器存在的充分条件和设计方法．当系统具有独立范数有界扰动输入和全结构不确定性时,使用此方法设计得到的Gl2控制器比H∞控制器的保守性更小．算例验证了该方法的有效性.     

网络控制系统的H∞状态反馈控制器设计

研究了对网络控制系统如何设计H∞状态反馈控制器.这些网络控制系统中存在不确定的网络时延和数据包丢失.当网络时延和连续丢包有界时,可以将系统建模为具有时变输入时滞的系统,利用Lyapunov-Krasovskii泛函,推导出网络控制系统渐近稳定的充分条件.将这些充分条件转化为带等式约束的LMIs,并对他们进行迭代求解,就可以构造H∞控制器.与现有结果相比,在推导稳定性条件时本文对交叉项采取了更紧的界定,并且在设计控制器时无需知道调节参数.因此,本文提出的方法具有更低的保守性.仿真结果说明了本方法的正确性和有效性.     

Causal state-feedback parameterizations in robust model predictive control

In this paper, we investigate the problem of nonlinearity (and non-convexity) typically associated with linear state-feedback parameterizations in the Robust Model Predictive Control (RMPC) for uncertain systems. In particular, we propose two tractable approaches to compute an RMPC controller–consisting of both a causal, state-feedback gain and a control-perturbation component–for linear, discrete-time systems involving bounded disturbances and norm-bounded structured model-uncertainties along with hard constraints on the input and state. Both the state-feedback gain and the control-perturbation are explicitly considered as decision variables in the online optimization while avoiding nonlinearity and non-convexity in the formulation. The proposed RMPC controller–computed through LMI optimizations–is responsible for steering the uncertain system state to a terminal invariant set. Numerical examples from the literature demonstrate the advantages of the proposed scheme.     

Switched state-feedback control for continuous time-varying polytopic systems

This article deals with switched state-feedback ?₂ control design of continuous time-varying polytopic systems. More specifically, the main goal is to determine, simultaneously, a set of state-feedback gains and a switching rule to orchestrate them, rendering the closed-loop system globally asymptotically stable for all time-varying uncertain parameter under consideration and assuring a guaranteed ?₂ cost. A contribution of the present switched control technique compared to the gain scheduling, widely used in the literature, is that the online measurement of the uncertain parameter is not required and no assumption on its time derivative is imposed. The conditions are based on modified Lyapunov–Metzler inequalities and can be solved by line search coupled with LMIs. An academic example illustrates the theoretical results and compares the present technique with other techniques from literature.     

分子量分布的广义状态反馈跟踪控制

针对化工过程中分子量分布的跟踪控制问题, 提出了一种简单的广义状态反馈控制方法, 实现给定分子量分布的跟踪. 该方法充分利用复合动态支持向量机模型, 实现分子量分布函数在时间域和空间域上的分离, 从而将分布函数的跟踪问题转化为动态权值向量的时间域跟踪问题, 并设计了状态反馈与积分器相结合的控制结构, 采用线性矩阵不等式技术对闭环系统稳定性和跟踪性能进行分析. 仿真结果表明该方法的可行性.     

Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients

This paper investigates the adaptive state-feedback stabilization problem for a class of high-order stochastic non-linear systems with unknown lower and supper bounds for uncertain control coefficients. Under some weaker and reasonable assumptions, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution on [0,∞, the equilibrium of interest is globally stable in probability and the states can be regulated to the origin almost surely. A simulation example is given to show the systematic design and effectiveness of the controller.     

Necessary conditions for nonlinear block noninteracting control with stability via dynamic state-feedback

In this paper we give some necessary conditions to achieve noninteraction and stability via dynamic state-feedback for a wide class of nonlinear systems with block-partitioned outputs. Moreover, a class of regular dynamic state-feedback is defined and it is shown that the asymptotic stability of certain dynamics, together with the asymptotic stabilizability of certain system, is necessary to achieve noninteraction and stability via regular dynamic state-feedback. These two conditions, plus the asymptotic stabilizability of a suitable system, are shown to be also sufficient to solve the problem.     

Stability margins of singular perturbation systems via state-feedback control

The gain and phase margins of singular perturbation systems are analysed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control. The analysis is on the basis that there is a good relation between the minimum singular value of return difference transfer matrix and the stability margins. We begin with the examination of stability margins of subsystems and then show that state-feedback control design of subsystems could preserve gain and phase margins for the original full-order singularly perturbed system if the singular perturbation parameter epsiv; is sufficiently small. The effectiveness of ε on stability margins is formulated and determined. It is found that the effectiveness can be evaluated by a simple method. Two examples are exploited to illustrate the analytic results.