Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

Semiglobal stabilization and output regulation of singular linear systems with input saturation

The semi-global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed. A reduced-order normal system is obtained by a standard coordinate transformation. It is further shown that the controller that solves the stabilization (output regulation) problem of the reduced-order normal systems also solves the stabilization (output regulation) problem of the original singular systems.     

西门子变频器的应用 第3讲 MM4系列变频器在PID中的应用

PID控制是闭环控制中的一种常见形式。反馈信号取自传动系统的输出端,当输出量偏离所要求的给定值时,反馈信号成比例变化。在输入端,给定信号与反馈信号相比较,存在一个偏差值。对该偏差值,经过PID调节,变频器通过改变输出频率,迅速、准确地消除传动系统的偏差,回复到给定值。本文阐述了MM4系列变频器的PID功能。     

一类奇异非线性变结构控制系统的跟踪问题

首次利用变结构控制方法研究了一类奇异非线性系统的模型跟踪问题，在不同情况下，通过引入动态补偿器的概念，设计了奇异模型跟踪系统的切换函数，得到了在切换面上实现跟踪的条件，然后利用趋近律方法设计了变结构控制，以保证在切换面外的运动在有限时间到达切换面，通过滑动运动实现跟踪，最后讨论了参数模型为正常系统的线性定常奇异系统的跟踪问题。     

Observer‐based adaptive neural control for a class of nonlinear singular systems

The problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.     

Certainty equivalence in nonlinear output regulation with unmeasured error

In this article, we consider a nonlinear output regulation problem in which the controlled output and the measured output are not the same. It is assumed that the controlled plant has a single control input, and that it can be transformed into Gauthier–Kupka's observability canonical form. Then, it is shown that a design based on certainty equivalence is effective for determining a controller that solves the given problem.     

Global nonlinear output regulation: Convergence-based controller design

In this paper we present output-feedback controllers solving the global output regulation problem for a class of nonlinear systems. The proposed controllers are based on the notion of convergent systems. The presented solution extends well-established results on the linear output regulation problem and the local nonlinear output regulation problem to the global case. For Lur’e systems, which are not necessarily in the output-feedback form, the proposed controllers can be found by solving the regulator equations and certain linear matrix inequalities. For systems in the output-feedback form with uncertain parameters and uncertain nonlinearities we provide a robust regulator that does not rely on the minimum phaseness assumption on the system, which is crucial in the previous regulator designs for output-feedback systems. The results are illustrated by examples.     

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.     

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.     

Output Regulation Of A Class Of Singular Nonlinear Systems With The Normal Output Feedback Controller

Existing results for output regulation of singular nonlinear systems via normal output feedback control require the normalizability assumption. In this paper, we will show that, for a large class of singular nonlinear systems, it is possible to construct a normal output feedback control to solve the regulation problem without the normalizability assumption. The major result is illustrated by an example.     

Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.     

Practical Output Regulation of Uncertain Strict‐Feedback Form Systems

In this paper, an output feedback control is proposed to solve the practical output regulation problem of a class of nonlinear systems. In the first step of the design procedure, two sets of coordinate transformations are used to convert the output regulation problem of the system in the strict‐feedback form into the regulation problem of the transformed system in the uncertain normal form. Then, for the resulting system, a state feedback in the cast of nested sliding mode control is designed. Finally, by using the nonlinear separation principle, the output feedback controller is achieved by substituting the estimated states, resulting from the high‐gain observer, instead of real states. It can be shown that the states of the closed‐loop system are ultimately bounded. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Singular PDEs and the assignment of zero dynamics in nonlinear systems

The present research work aims at the development of a systematic method to arbitrarily assign the zero dynamics of a nonlinear system by constructing the requisite synthetic output maps. The minimum-phase synthetic output maps constructed can be made statically equivalent to the original output maps, and therefore, they could be directly used for nonminimum-phase compensation purposes. Specifically, the mathematical formulation of the problem is realized via a system of first-order nonlinear singular PDEs and a rather general set of necessary and sufficient conditions for solvability is derived. The solution to the above system of singular PDEs can be proven to be locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package. The minimum-phase synthetic output maps that induce the prescribed zero dynamics for the original nonlinear system can be computed on the basis of the solution of the aforementioned system of singular PDEs. Moreover, static equivalence to the original output map can be readily established by a simple algebraic construction.     

经输出动态反馈的非线性奇异系统输出调节问题

讨论非线性奇异系统的输出调节问题,在没有可正常化的假设条件下,给出了降阶的 正常状态空间的输出动态反馈控制器的设计,并导出了这种控制器存在的充分必要条件.     

磁悬浮系统的精确积分流形控制设计

基于非性磁悬浮系统的奇异摄动特点,研究了一种精确几何积分流形控制方法,使磁悬浮系统的稳态流形能够无误差地跟踪给定设计流形。将复杂奇异摄动磁悬浮系统按照不同时间尺度分解为降阶系统和边界层,以线性降阶系统设计流形为例,推算出稳定慢控制的具体形式并说明参数稳定范围,结合稳定边界层的快控制,最终推算出磁悬浮系统的复合控制规律。仿真和实验均证明该控制算法能够保证降价系统的流形无误差地跟踪给定的设计流形。利用该算法能够使磁悬浮系统无误差地跟踪任意给定的设计流形,从而提高磁悬浮系统的动态特性。输出流形与设计流形的一致性还可以用来简化系统模型,降低磁悬浮车辆系统动力学分析的复杂程度。     

奇异系统的输出跟踪在化学反应器中的应用

稳定逆定理在非线性奇异系统中有着非常重要的应用。在微分几何理论的基础上,提出一种非线性奇异系统的稳定逆控制方法。计算出能够映射出期望输出轨迹的参考状态、参考代数变量和参考输入轨迹,并将其作为前馈控制器,然后引入反馈控制达到期望的状态轨迹稳定和输出轨迹跟踪。该方法在气液两相反应器这样一类广泛存在于化工过程中的反应模型中的应用,验证了该方法的有效性。     

Speed tracking control of PM synchronous motor by internal model design

In this article, we consider a speed tracking and load torque disturbance rejection problem of PM synchronous motor by internal model design. The problem is first formulated as a global robust output regulation problem of a special class of multivariable systems. Then the output regulation problem is further converted into a global stabilisation problem of an augmented system composed of the original plant and an internal model. As the augmented system does not take any known special form, we have developed a specific tool to deal with the stabilisation problem. In particular, a generalised changing supply function technique applicable to non-input-to-state stable (ISS) systems is developed. This technique, in conjunction with a particular nonlinear internal model, leads to an effective solution to the problem.     

Admissibility and static output‐feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions

This paper presents a necessary and sufficient condition for discrete‐time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output‐feedback stabilization problem for discrete‐time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defective statistics about modes transitions are studied by considering the uncertain transition probabilities and partially unknown transition probabilities situations account in a composite way. The closed‐loop system is represented in an augmented form, in which input and gain‐output matrices are separated. By virtue of the system augmentation, a sufficient condition for the existence of desired controllers is established. An extension to mode‐independent static output‐feed stabilization is provided as well. Copyright © 2013 John Wiley & Sons, Ltd.     

Characteristic locus method robustness improvement through optimal static normalizing pre‐compensation

Controlled systems designed by using the characteristic locus method can be very sensitive to small perturbations in the plant input and output at the frequencies where the plant transfer matrix is far from normal. In order to improve the closed‐loop system robustness, previous work proposes the design of a dynamic normalizing pre‐compensator followed by the design of a commutative controller for the pre‐compensated plant. The restriction on its structure and the need for approximation by a stable rational transfer matrix were among the limitations of the dynamic pre‐compensator. This paper shows that it suffices to design a static pre‐compensator that makes the pre‐compensated plant as closely as possible to a normal matrix in a frequency band containing the crossover frequency. The pre‐compensator is found by solving an optimization problem, whose solution is obtained directly by computing either a singular value decomposition of a real matrix or the spectral decomposition of a symmetric matrix, depending on whether normalization is to be achieved in one or more frequencies. Numerical examples illustrate the theoretical results of the paper. Copyright © 2009 John Wiley & Sons, Ltd.