An improved Backstepping technique using sliding mode control for transient stability enhancement and voltage regulation of SMIB power system

The problem of transient stability and voltage regulation for a single machine infinite bus (SMIB) system is addressed in this paper. An improved Backstepping design method for transient stability enhancement and voltage regulation of power systems is discussed beginning with the classical Backstepping to designing the nonlinear excitation control of synchronous generator. Then a more refined version of this technique will be suggested incorporating the sliding mode control to enhance voltage regulation and transient stability. The proposed method is based on a standard third-order model of a synchronous generator connected to the grid (SMIB system). It is basically implemented on the excitation side of the synchronous generator and compared to the classical Backstepping controller as well as the conventional controllers which are the automatic voltage regulator and the power system stabiliser. Simulation results prove the effectiveness of the proposed method which ameliorates to a great extent the transient stability compared to the other methods.     

Nonlinear variable structure excitation and steam valving controllers for power system stability

A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper. On the basis of the classical dynamic equations of a generator, excitation control and steam valving control are simultaneously considered. Design of these controllers combines the differential geometry theory with the variable structure controlling theory. The mathematical model in the form of ＂an affine nonlinear system＂ is set up for the control design of a large-scale power plant. The dynamic performance of the nonlinear variable structure controllers proposed for a single machine connected to an infinite bus power system is simulated. Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.     

Stabilizing low complexity feedback control of constrained piecewise affine systems

Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin.This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction.     

Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

Min-max model predictive control (MPC) is one of the control techniques capable of robustly stabilize uncertain nonlinear systems subject to constraints. In this paper we extend existing results on robust stability of min-max MPC to the case of systems with uncertainties which depend on the state and the input and not necessarily decaying, i.e. state and input dependent bounded uncertainties. This allows us to consider both plant uncertainties and external disturbances in a less conservative way.It is shown that the input-to-state practical stability (ISpS) notion is suitable to analyze the stability of worst-case based controllers. Thus, we provide Lyapunov-like sufficient conditions for ISpS. Based on this, it is proved that if the terminal cost is an ISpS-Lyapunov function then the optimal cost is also an ISpS-Lyapunov function for the system controlled by the min-max MPC and hence, the controlled system is ISpS. Moreover, we show that if the system controlled by the terminal control law locally admits certain stability margin, then the system controlled by the min-max MPC retains the stability margin in the feasibility region.     

Observer‐based controller for constrained uncertain stochastic nonlinear discrete‐time systems

In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Stability,positive invariance and design of constrained regulators for networked control systems

In this article, the stability analysis, the positive invariance of polyhedral sets and the design of state-feedback regulators for networked control systems (NCS) with bounded transmission delays, constant and unknown or time-varying, are investigated. The dynamics of the NCS is described by autoregressive-moving-average (ARMA) models. Contrary to former approaches based on quadratic Lyapunov functions, in this article polyhedral Lyapunov functions are used for both stability and positive invariance analysis and state-feedback synthesis. Then, based on the property that the exponential of a matrix can be expressed as a weighted sum of its constituent matrices, it is proven that the problems of determination of stability margins or the design of stabilising controllers can be reduced to linear programming optimisation problems. The use of ARMA models allows the development of methods for the design of state-feedback controllers satisfying state constraints or convergence rate specifications defined on the NCS state space and not on the state of an augmented state space representation.     

Distributed Periodic Event-Triggered Optimal Control of DC Microgrids Based on Virtual Incremental Cost

This article presents a distributed periodic eventtriggered(PET)optimal control scheme to achieve generation cost minimization and average bus voltage regulation in DC microgrids.In order to accommodate the generation constraints of the distributed generators(DGs),a virtual incremental cost is firstly designed,based on which an optimality condition is derived to facilitate the control design.To meet the discrete-time(DT)nature of modern control systems,the optimal controller is directly developed in the DT domain.Afterward,to reduce the communication requirement among the controllers,a distributed event-triggered mechanism is introduced for the DT optimal controller.The event-triggered condition is detected periodically and therefore naturally avoids the Zeno phenomenon.The closed-loop system stability is proved by the Lyapunov synthesis for switched systems.The generation cost minimization and average bus voltage regulation are obtained at the equilibrium point.Finally,switch-level microgrid simulations validate the performance of the proposed optimal controller.     

Decentralized receding horizon control for large scale dynamically decoupled systems

We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

Nonlinear generalization of scaled ℋ︁∞ control: global robustification against nonlinearly bounded uncertainties

This paper proposes a novel approach to the problem of ??₂ disturbance attenuation with global stability for nonlinear uncertain systems by placing great emphasis on seamless integration of linear and nonlinear controllers. This paper develops a new concept of state‐dependent scaling adapted to dynamic uncertainties and nonlinear‐gain bounded uncertainties that do not necessarily have finite linear‐gain, which is a key advance from previous scaling techniques. The proposed formulation of designing global nonlinear controllers is not only a natural extension of linear robust control, but also the approach renders the nonlinear controller identical with the linear control at the equilibrium. This paper particularly focuses on scaled ??^∞ control which is widely accepted as a powerful methodology in linear robust control, and extends it nonlinearly. If the nonlinear system belongs to a generalized class of triangular systems allowing for unmodelled dynamics, the effect of the disturbance can be attenuated to an arbitrarily small level with global asymptotic stability by partial‐state feedback control. A procedure of designing such controllers is described in the form of recursive selection of state‐dependent scaling factors. Copyright © 2004 John Wiley & Sons, Ltd.     

Distributed tracking control of uncertain mechanical systems with velocity constraints

This paper considers the leader‐following control problem of multiple mechanical systems with uncertainty and velocity constraints. So as to deal with the velocity constraints, a reduction procedure is applied to transform the model of each system to a cascaded system. With the aid of the cascade structure of each system and the properties of linear time‐varying systems, distributed robust feedback controllers are proposed such that the state of each follower system asymptotically converges to the state of a leader system with the aid of neighbors' information. So as to reduce the cost of the communication between systems, an event‐triggered leader‐following control problem is also considered, and event‐triggered distributed controllers are proposed. As an application of the proposed results, formation control of wheeled mobile robots is considered, and distributed controllers are obtained with the aid of the results in Theorems 1 and 2. Simulation results show the effectiveness of the proposed results. Copyright © 2017 John Wiley & Sons, Ltd.     

Estimation of the asymptotic stability region of uncertain systemswith bounded sliding mode controllers

In this note, the problem of estimating the asymptotic stability region (ASR) of uncertain systems with bounded sliding mode controllers is considered. To simplify the problem the authors use a state transformation and choose a suitable Lyapunov function for the transformed control system. Using the Lyapunov function the authors estimate the ASR and show the exponential stability of the closed-loop control system in the region. Also, by an example the authors show that for a certain class of uncertain dynamical systems with bounded sliding mode controllers their method gives a more improved estimate of the ASR     

含结构参数扰动的线性连续系统的鲁棒约束方差控制

考虑含结构参数扰动的线性连续随机系统的鲁棒约束方差控制设计问题,即寻找状态反 馈控制器,使受扰系统不仅具有期望的稳定裕度,而且其每个状态分量的稳态方差不大于各 自预先给定的上界.给出了具有这种性能的鲁棒控制器的存在条件及解析表达式,并以数值 例子说明文中设计方法的直接性与有效性.     

Leader-following control of multiple nonholonomic systems over directed communication graphs

This paper considers the leader-following control problem of multiple nonlinear systems with directed communication topology and a leader. If the state of each system is measurable, distributed state feedback controllers are proposed using neighbours’ state information with the aid of Lyapunov techniques and properties of Laplacian matrix for time-invariant communication graph and time-varying communication graph. It is shown that the state of each system exponentially converges to the state of a leader. If the state of each system is not measurable, distributed observer-based output feedback control laws are proposed. As an application of the proposed results, formation control of wheeled mobile robots is studied. The simulation results show the effectiveness of the proposed results.     

High-frequency nonlinear vibrational control

This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. (1986) investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace     

Smart control techniques for design of TCSC and PSS for stability enhancement of dynamical power system

This paper deals with the simultaneous application of thyristor controlled series capacitor based damping controller and power system stabilizer for stability improvement of dynamic power system. The adaptive neuro-fuzzy inference system and Levenberg–Marquardt artificial neural network algorithm are used to develop the control strategy for thyristor controlled series capacitor based damping controller and power system stabilizer. The power system stabilizer generates appropriate supplementary control signal to an excitation system of synchronous generator to damp the frequency oscillations and improves the performance of the power system dynamic. The performance of power system affected due to the system configuration and load variation. In order to achieve the appreciable damping, the series capacitor is suggested in addition to the power system stabilizer. Nonlinear simulations of single machine infinite bus system are carried out using the individual application of power system stabilizer and simultaneous application of power system stabilizer and thyristor controlled series capacitor. The comparison analysis between conventional and smart control strategies based controllers is demonstrated. Single machine infinite bus system is tested under various operating conditions and disturbances to show the effectiveness of proposed control schemes.     

Efficient algorithms for online tracking of set points in robust model predictive control

This paper presents some computationally efficient algorithms for online tracking of set points in robust model predictive control context subject to state and input constraints. The nonlinear systems are represented by a linear model along with an additive nonlinear term which is locally Lipschitz. As an unstructured uncertainty, this term is replaced in the robust stability constraint by its Lipschitz coefficient. A scheduled control technique is employed to transfer the system to desired set points, given online, by designing local robust model predictive controllers. This scheme includes estimating the regions of feasibility and stability of the related equilibriums and online switching among the local controllers. The proposed optimisation problems for calculating the regions of feasibility and stability are defined as linear matrix inequalities that can be solved in polynomial time. The effectiveness of the proposed algorithms is illustrated by an example.     

Design of Adaptive Block Backstepping Controllers with Perturbations Estimation for Nonlinear State‐Delayed Systems in Semi‐Strict Feedback Form

This paper is an extended study of an existing block backstepping control scheme designed for a class of perturbed multi‐input systems with multiple time‐varying delays to solve regulation problems, where the time‐varying delays must be linear with state variables. A new control scheme is proposed in this research where all the unknown multiple time‐varying delay terms in the dynamic equations can be nonlinear state functions in non‐strict feedback form, and the upper bounds of the time‐delays as well as their derivatives need not to be known in advance. Another improvement is to further alleviate the problem of “explosion of complexity,” i.e., to reduce the number of time derivatives of virtual inputs that the designers have to compute in the design of controllers. This is done by utilizing an existent derivative estimation algorithm to estimate the perturbations in the designing of proposed controllers. Adaptive mechanisms are also embedded in the controllers so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are demonstrated to verify the merits and feasibility of the proposed control scheme.     

具有短时延的网络控制系统的一种鲁棒控制方法

针对具有短时延的网络控制系统, 本文提出了一种基于鲁棒控制的方法来解决该类系统的稳定化控制问题. 考虑状态反馈控制律, 将闭环网络控制系统描述为一个离散时间线性不确定系统模型, 其中的不确定部分反映了时延的时变特性对系统动态的影响. 得到了该闭环网络控制系统的渐近稳定性条件, 且该条件建立了闭环网络控制系统稳定性与两个时延参数, 即允许时延上界和允许时延变换范围, 之间的定量关系. 进一步的, 还给出了稳定化反馈控制器的设计步骤. 最后通过一个示例验证了本文所提出方法的有效性.