Fault-tolerant control of delta operator systems with actuator saturation and effectiveness loss

This paper studies the problem of robust fault-tolerant control against the actuator effectiveness loss for delta operator systems with actuator saturation. Ellipsoids are used to estimate the domain of attraction for the delta operator systems with actuator saturation and effectiveness loss. Some invariance set conditions used for enlarging the domain of attraction are expressed by linear matrix inequalities. Discussions on system performance optimisation are presented in this paper, including reduction on computational complexity, expansion of the domain of attraction and disturbance rejection. Two numerical examples are given to illustrate the effectiveness of the developed techniques.     

Stability analysis for delta operator systems subject to state saturation

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method.     

Quantized stabilization of networked control systems with actuator saturation

In this paper, we investigate the problems of stabilization of networked control systems with quantization and actuator saturation via delta operator approach. The definition of the domain of attraction for delta operator systems is introduced to analyze the stochastic stability of the closed‐loop networked control systems. The quantizer is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a Bernoulli process. On the basis of the zoom strategy and Lyapunov theory in delta domain, sufficient conditions are given for the closed‐loop delta operator systems to be mean square stable, and the feedback controllers are designed to ensure the stability of networked control systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

一类非线性PID控制系统稳定性分析

针对一类由非线性增益函数与典型PID控制器级联组成的非线性系统,采用波波夫判据对此类闭环控制系统进行稳定性分析.分别确定了确保非线性PID,P,PI,PD闭环控制系统稳定的非线性增益的有效取值范围,为此类非线性控制系统的实际工程应用奠定了基础.     

可反馈线性化系统的鲁棒自适应容错控制设计

针对存在不确定执行器故障和未知不匹配干扰的可反馈线性化非线性系统, 提出一种鲁棒自适应容错控 制策略. 首先分别给出系统输入和扰动关于系统输出的相对阶, 针对两种相对阶之间的不同关系设计鲁棒控制器, 抑制干扰对系统输出的影响; 然后针对各故障情况分别设计容错控制器; 最后将各控制器进行融合得到一个综合 故障补偿控制器, 从而有效解决故障模式、类型、大小、时间和外界干扰等多重不确定性, 保证闭环系统稳定和渐近 输出跟踪性能. 仿真结果验证了所设计控制方案的可行性与有效性.     

Tracking control and disturbance rejection for nonlinear switched control systems with saturation effects

This article focuses on the concerns of a tracking control and active disturbance rejection for nonlinear switched systems described by Takagi–Sugeno fuzzy framework with state-dependent nonlinear perturbations, actuator saturations and disturbances. Especially, a nonlinear equivalent-input-disturbance technique is employed to guarantee that only the external disturbances are rejected while retaining the beneficial nonlinearity of the system. Notably, with the aid of the lifting technique, the modified repetitive control are accurately described by a continuous-discrete two-dimensional model is designed to improve the tracking precision. The fuzzy-membership-function-dependent piecewise Lyapunov–Krasovskii functional (LKF) by exploiting the knowledge of the membership functions are built to assure the exponential stability of the investigated system. Moreover, the controller and observer gains can be obtained as solutions to a set of strict linear matrix inequalities. Finally, an application example based on the cognitive radio model is given to verify the efficacy of the proposed control protocol.     

奇异线性系统在执行器饱和受限下不变集条件的改进

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.     

Control of periodic sampling systems subject to actuator saturation

In this paper, the control problem of linear systems with periodic sampling period subject to actuator saturation is considered via delta operator approach. Using periodic Lyapunov function, sufficient conditions of local stabilization for periodic sampling systems are given. By solving an optimization problem, we derive the periodic feedback control laws and the estimate of the domain of attraction. As the saturation function sat(·) belongs to the sector [0,1], sufficient conditions are derived by constructing saturation‐dependent Lyapunov functions to ensure that the periodic sampling system is globally asymptotically stable. A numerical example is given to illustrate the theoretical results proposed in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability analysis of a feedback system containing periodically varying parameters†

Stability analysis for a third-order feedback system with a periodically varying parameter is presented using a matrix method and approximating the time-varying parameter as piecewise constant over its period. The stability boundaries of such a system are predicted and compared with the boundaries determined by analogue computer simulation. Incidentally a method of generating similar matrices is brought out during this investigation.     

运用线性反馈分析设计饱和线性系统

给出了状态反馈控制饱和单输入系统以及动态输出反馈单输出饱和线性系统是全局渐近稳定还是区域渐近稳定的充分性条件,并在区域渐近稳定的情况下计算其不变吸引椭球.对于控制饱和系统,运用Ricatti方程迭代法设计控制器,以使所得椭球尽量大.仿真算例说明了所提出方法的有效性.     

Stabilization on null controllable region of delta operator systems subject to actuator saturation

This paper focuses on stabilization on null controllable region of delta operator systems subject to actuator saturation via constructing suitable controllers. Under a saturated linear feedback law, a set of stable equilibrium points is obtained for the delta operator system with actuator saturation. A comprehensive controller is given to show global stabilization of the delta operator system. Thereby, semi‐global stabilization of the delta operator system is also achieved. For higher‐order systems with no more than two unstable exponentially poles, a new feedback law is constructed to achieve semi‐global stabilization on the null controllable region. Finally, three examples are given to illustrate the effectiveness of the proposed techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantised feedback control for bilinear systems with actuator saturation

This paper is concerned with quantised feedback control problems for bilinear systems with actuator saturation. We propose two types of quantisers. For the first quantiser, quantised input and quantised state are considered. For the second quantiser, quantised control input is only investigated. A designed state feedback controller guarantees that the resulting closed-loop system is convergent to a small neighbourhood around the origin for every initial condition emanating from the large admissible domain. Sufficient conditions for feasibility are derived in terms of linear matrix inequalities. Several examples are presented to demonstrate the applicability of the proposed approach.     

Overall convergence rate of delta operator systems subject to actuator saturation

In this paper, overall convergence rate is considered for a delta operator system with actuator saturation. A saturation feedback law is presented for the delta operator system to obtain a desired overall convergence rate. Some properties on the overall convergence rate are revealed for time‐optimal actuator saturation delta operator systems. Limitations on the overall convergence rate are also investigated by proposed methods. An optimization problem is solved through a linear matrix inequality method to obtain the domain of attraction and overall convergence rate. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

Output regulation for linear delta operator systems subject to actuator saturation

In this paper, output regulation for linear delta operator systems subject to actuator saturation is investigated by state feedback. The relation between the regulatable regions and the null controllable region is described in this paper. A set of all initial conditions of a plant and a exosystem is called asymptotically regulatable region for which output regulation is possible. An asymptotically regulatable region is characterized according to a null controllable region of an anti‐stable subsystem of the plant. Feedback laws are constructed to solve the problems on output regulation. A numerical example is given to illustrate the effectiveness and potential for the developed techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults

This article investigates the stability analysis and control design of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults and saturation. It is assumed that the actuator faults of each subsystem are varying and governed by a Markovian process. The nonlinear term is located in a sector. First, sufficient conditions for stochastic stability of the underlying systems are established using a stochastic copositive Lyapunov function. Then, a family of reliable L₁‐gain controller is proposed for nonlinear positive Markovian jump systems with actuator faults and saturation in terms of a matrix decomposition technique. Under the designed controllers, the closed‐loop systems are positive and stochastically stable with an L₁‐gain performance. An optimization method is presented to estimate the maximum domain of attraction. Furthermore, the obtained results are developed for general Markovian jump systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.     

Low-and-high gain design technique for linear systems subject to input saturation —a direct method

The low-and-high gain design technique, which was initiated for a chain of integrators and completed for general linear asymptotically null controllable with bounded controls systems, was conceived for semi-global control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capacity and semi-global disturbance rejection. Although the low-and-high gain design technique, as initiated for a chain of integrators, is based on an explicit eigenstructure assignment algorithm, its full development is based on the solution of an algebraic Riccati equation (ARE) which is paramterized in an arbitrarily small scalar, called low gain, parameter. In this paper, we develop a new complete low-and-high gain design procedure which is based on an explicit eigenstructure assignment algorithm. The new design approach avoids the solution of the numerically stiff parametrized ARE. © 1997 by John Wiley & Sons, Ltd.     

A complete stability analysis for planar delta operator systems subject to state saturation

In this paper, stability analysis is investigated for planar delta operator systems subject to state saturation. General properties of limit trajectories are characterized for the planar delta operator systems subject to state saturation. A nontrivial limit trajectory only intersects with two pairs of opposite sides but not neighboring sides of a unit square. Hence, a relation is established between the present intersection of a trajectory with lines x₂ = ±1 and the next intersection. Necessary and sufficient conditions on global asymptotic stability are obtained for the planar delta operator systems with full and partial saturated state. Simulation results are given to show the effectiveness of the proposed methods.     

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.     

Analysis and design of delta operator systems with nested actuator saturation

In this paper, the problem of estimating the domain of attraction is considered for delta operator systems subject to nested actuator saturation. A set invariance condition is established for the delta operator system with nested actuator saturation in terms of auxiliary feedback matrices. Based on the set invariance condition, an optimisation approach is proposed to estimate the domain of attraction for the delta operator system. Thereby, the partial results of nested actuator saturation for both continuous-time systems and discrete-time systems are extended to delta operator system framework. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.