Practical output regulation for bounded linear infinite-dimensional state space systems

We develop the mathematical foundations of practical state space output regulation for bounded infinite-dimensional linear systems. By practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy. Our main results are general upper bounds for the norms perturbations to the parameters of the exosystem, the plant and a controller which achieves exact output regulation. These bounds depend explicitly on the desired tracking accuracy ε>0. In this paper, all perturbations are assumed to be bounded, additive and linear. Our results apply for both feedforward and error feedback controllers, and for arbitrary bounded uniformly continuous reference/disturbance signals.     

Deadbeat control with disturbance rejection

A deadbeat control problem with disturbance rejection is considered for a SISO discrete time plant. Disturbances are supposed to enter into the input to the plant and the output from the plant. The two-degree-of-freedom controllers are employed to internally stabilize the feedback control system, to make the output of the plant track a reference signal and to reject the disturbances in the sense of the deadbeat response. Necessary and sufficient conditions for the problem to have a solution are shown. And the set of all controllers meeting the design requirements are represented using two free polynomials.     

Robust adaptive feedforward control and achievable tracking for systems with time delays

A feedback/feedforward controller architecture is developed that characterises the achievable reference tracking of real time inputs for both minimum phase and non-minimum phase systems with time delays, when there are no modelling errors or external disturbances. This characterisation is obtained by factoring the plant into its minimum phase, non-minimum phase, and time delay components, which are used to design two feedforward controllers that inject signals into two points of the feedback loop. Design constraints are provided that determine both the types of signals that may be achieved, and the feedforward controllers that will generate that output. Of course, in practice, both modelling errors and external disturbances will be present. In this case, we develop robust analysis tools that both guide the feedback controller design process, and provide rigorous robust tracking performance that guarantees for the overall resulting closed-loop system. Robust methods for designing the feedforward controllers are presented, and numerical examples are provided. The performance of this architecture depends strongly on the choice of design parameters, and the accuracy of the plant model used. Hence, the use of adaptation methods is also considered, and it is shown that they can readily be employed to improve the performance of this control methodology.     

A feedforward–feedback controller for infinite‐dimensional systems and regulation of bounded uniformly continuous signals

We design a controller for infinite‐dimensional linear systems (with bounded control, observation and feedthrough operators) which, under certain assumptions, achieves asymptotic tracking of arbitrary bounded uniformly continuous reference signals in the presence of disturbances. The proposed controller is of feedforward–feedback type: The dynamic feedback part is used to stabilize the closed‐loop system consisting of the plant and the controller, whereas the feedforward part is tuned using the regulator equations to achieve the regulation of desired signals. We also completely solve the regulator equations for SISO systems, and we discuss robustness properties of the proposed controller. A useful feature in our design is that the feedforward part of the controller can be designed independently of the feedback part. This automatically leads to a degree of robustness in the stabilizing part of the controller, which is not present in the existing state feedback controllers solving the same output regulation problem. Copyright © 2006 John Wiley & Sons, Ltd.     

Piecewise Fuzzy Anti-Windup Dynamic Output Feedback Control of Nonlinear Processes With Amplitude and Rate Actuator Saturations

In this paper, a novel anti-windup dynamic output compensator is developed to deal with the robust H _infin output feedback control problem of nonlinear processes with amplitude and rate actuator saturations and external disturbances. Via fuzzy modeling of nonlinear systems, the proposed piecewise fuzzy anti-windup dynamic output feedback controller is designed based on piecewise quadratic Lyapunov functions. It is shown that with sector conditions, robust output feedback stabilization of an input-constrained nonlinear process can be formulated as a convex optimization problem subject to linear matrix inequalities. Simulation study on a strongly nonlinear continuously stirred tank reactor (CSTR) benchmark plant is given to show the performance of the proposed anti-windup dynamic compensator.     

具有干扰输入的大型互联线性系统的分散有限时间镇定

借助于大型互联线性系统有限时间稳定性的定义,对具有干扰输入的大型互联线性系统引入了分散有限时间镇定的概念,并对一类具有干扰输入的大型互联不确定线性系统进行了分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式（LMI）方法,提出了一个充分条件.当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.     

An algorithmic method for the selection of multivariable process control structures

In process systems, the selection of suitable sets of manipulated and controlled variables and the design of their interconnection, known as the control structure selection problem, is an important structural optimisation problem. The operating performance of a plant depends on the control structure selected as well as the characteristics of the disturbances acting on the plant. The economic penalty associated with the variability of main process variables close to active constraints is used in this work in order to develop a quantitative measure for the ranking of alternative control structures. Based on this measure, a general methodology is presented for the generation of promising control structures where general centralised, linear time invariant, output feedback controllers are used to form the closed loop system. The special case of optimal static output feedback controllers is further investigated in this paper. Furthermore, the problem of selecting proper weights in forming quadratic integral performance indices in designing optimal multivariable controllers is addressed. The validity and usefulness of the method is demonstrated through a number of case studies.     

Output Feedback Controller Design for systems with Amplitude and Rate Control Constraints

A method for synthesizing dynamic output feedback controllers for continuous time systems presenting actuators constrained in both amplitude and rate is proposed here. The considered controller structure is composed of a saturating integrator block connected to a linear compensator output, delivering a signal to the actuator input inside all its bounds. Considering that the plant is submitted to L ₂ bounded disturbances, linear matrix inequality conditions are proposed in order to ensure both external and internal stability of the closed loop system.     

Solutions to the output regulation problem of linear singular systems

In this paper, we revisit the output regulation problem for linear singular systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated. We derive a necessary and sufficient condition for the regulation problem to be solvable via either full information feedback or error feedback. Then we show how full information feedback and error feedback controllers can be constructed explicitly.     

Incremental passivity and output regulation for switched nonlinear systems

This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.     

Pareto suboptimal controllers against coalitions of disturbances

We consider a multi-criteria problem of suppressing disturbances with linear feedback with respect to the state or output measured with noise. We assume that the system has N potentially possible inputs for disturbances from given classes, and the criteria are induced norms of operators generated by the system from the corresponding input to the common target output. We obtain necessary Pareto optimality conditions. We show that based on scalar optimization of the suppression level for the disturbances that act on all inputs we can synthesize Pareto suboptimal controllers whose relative losses compared to Pareto optimal controllers do not exceed 1 ? \(\sqrt N /N\). Our results generalize to the case when disturbances from different classes may form coalitions.     

Distributed output regulation for multi-agent systems with norm-bounded uncertainties

In this paper, we consider the distributed robust output regulation problem for multi-agent systems (MASs). It is involved with a group of heterogeneous high-order linear uncertain systems and an linear exosystem. The regulated output is a combination of the output of MAS and the exosystem, which is defined based on controlling demands. Distributed controllers are designed to ensure that the regulated output converges to the origin and meanwhile the closed-loop MAS is stable. The sufficient conditions for the solvability of distributed output regulation problem are given in terms of linear matrix inequalities. And algorithms are proposed to design distributed dynamic controllers with state feedback and output feedback, via the help of internal models. It is shown that, for any time-invariant norm-bounded uncertainties, the given controllers can realise the objective of output regulation.     

Design of feedforward controllers for multivariable plants

Simple methods for the design of feedforward controllers to achieve steady-state disturbance rejection and command tracking in stable multivariable plants are developed in this paper. The controllers are represented by simple and low-order transfer functions and are not based on reconstruction of the states of the commands and disturbances. For unstable plants, it is shown that the present method can be applied directly when an additional feedback controller is employed to stabilize the plant. The feedback and feedforward controllers do not affect each other and can be designed independently based on the open-loop plant to achieve stability, disturbance rejection and command tracking, respectively. Numerical examples are given for illustration.     

On Adaptive Output Feedback Controf Robotic Manipulators with Online Disturbance Estimation

The problem of disturbance estimation and compensation for adaptive output feedback type controllers are investigated. Specifically two adaptive output feedback controllers designed for robotic manipulators are extended to compensate external disturbances which are common in robotic applications with repetitive task. The uncertain disturbance term in the robot dynamics is modeled as a fixed term plus a combination of sinusoidal signals. The overall stability and convergence of the tracking error for both controllers is ensured via Lyapunov based analysis. Extensive simulation studies are presented to illustrate the feasibility of the proposed method.     

H∞ multiple objective robust controllers forinfinite-horizon single measurement single control input problems

A graphical method is introduced that solves the robust infinite horizon H_∞ multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H_∞ control problem. The new method links between the theories of H_∞ and quantitative feedback theory (QFT). It can be used to design robust H_∞ controllers with almost no overdesign, and it provides a convenient solution of H_∞ multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input, or the measurement output     

Robust controller synthesis for systems with input nonlinearities: a trade-off between gain variation and parametric uncertainty

A feedback control-system design problem involving input nonlinearities and structured plant parameter uncertainities is considered. Multivariable absolute stability theory is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design that accounts for input time-varying sector bounded nonlinearities. The principal result is a sufficient condition for characterizing dynamic controllers of a fixed dimension which are guaranteed to provide robust stability for plant parametric variations and absolute stabilization for input nonlinearities. The proposed framework provides a systematic design trade-off between classical robustness guarantees (i.e., gain and phase margins) versus parametric robustness. Furthermore, the framework is directly applicable to uncertain systems with saturating controls and provides fixed-order dynamic output feedback controllers with guaranteed domains of attraction. © 1998 John Wiley & Sons, Ltd.     

脉冲切换系统的鲁棒H∞动态输出反馈控制

考虑了脉冲切换系统的鲁棒H∞控制问题.该系统的状态矩阵和控制矩阵都有不确定性和扰动.利用线性矩阵不等式(LMI)、H∞控制理论、Lyapunov函数和变量替换方法,对这类系统给出了鲁棒稳定且具有γ鲁棒性能的充分条件.然后,使用MATLAB软件设计出H∞鲁棒动态输出反馈控制器和脉冲控制矩阵.最后通过一个仿真算例验证了文中结论的有效性.     

Design of output feedback controllers for sampled-data fuzzy systems

In this paper, the design problem of output feedback controllers for sampled-data fuzzy models is considered. We consider the case where the premise variable coincides with the state variable. We give observers and output feedback controllers for an approximation of the original system. We then apply the observers and output feedback controllers to the original system and give sufficient conditions for the asymptotic convergence and stability respectively. A design example is given to illustrate the theory.     

Internal behaviour provided by nonlinear l1-optimal controllers

An l₁-optimal linear time-invariant (LTI) compensator may have an order significantly higher than that of the plant, even when the state is measurable. Recently there has been work exploring the use of nonlinear static feedback controllers which provide near optimal performance. Here we consider a class of nonlinear state feedback controllers and derive superposition-like bounds on both the plant state and the controlled output in the event that the plant initial condition, the disturbance, and the noise are all non-zero.     

The robust control of a servomechanism problem for linear time-invariant multivariable systems

Necessary and sufficient conditions are found for there to exist a robust controller for a linear, time-invariant, multivariable system (plant) so that asymptotic tracking/regulation occurs independent of input disturbances and arbitrary perturbations in the plant parameters of the system. In this problem, the class of plant parameter perturbations allowed is quite large; in particular, any perturbations in the plant data are allowed as long as the resultant closed-loop system remains stable. A complete characterization of all such robust controllers is made. It is shown that any robust controller must consist of two devices 1) a servocompensator and 2) a stabilizing compensator. The servocompensator is a feedback compensator with error input consisting of a number of unstable subsystems (equal to the number of outputs to be regulated) with identical dynamics which depend on the disturbances and reference inputs to the system. The sorvocompensator is a compensator in its own right, quite distinct from an observer and corresponds to a generalization of the integral controller of classical control theory. The sole purpose of the stabilizing compensator is to stabilize the resultant system obtained by applying the servocompensator to the plant. It is shown that there exists a robust controller for "almost all" systems provided that the number of independent plant inputs is not less than the number of independent plant outputs to be regulated, and that the outputs to be regulated are contained in the measurable outputs of the system; if either of these two conditions is not satisfied, there exists no robust controller for the system.