Reconfigurable control of Hammerstein systems after actuator failures: stability,tracking, and performance

A new method for the reconfigurable control of stable Hammerstein systems with sector-bounded static nonlinear input characteristics subject to actuator failures is described. It aims at the recovery of the nominal stability, setpoint tracking, disturbance rejection and performance properties by the reconfigured closed-loop system. This article extends the virtual actuator from linear systems to Hammerstein systems and provides sufficient linear matrix inequality conditions for closed-loop stability, and a corresponding synthesis algorithm. It is shown that the approach is robust against uncertainties of the static input nonlinearity in a small-gain sense, and universal in a certain sense. Feasible setpoints for the reconfigured closed-loop system are characterised, and infeasible setpoints are projected to feasible ones. An extension guarantees minimum performance loss. The method is successfully experimentally evaluated using a system of interconnected tanks.     

A two‐step predictive control design for input saturated Hammerstein systems

The two‐step model predictive control is designed for input saturated Hammerstein systems. It first applies the unconstrained linear dynamic subsystem to get the desired intermediate variable, and then obtains the actual control action by solving nonlinear algebraic equation group and desaturation. The stability of the closed‐loop system is analysed and its domain of attraction is designed applying semi‐global stabilization techniques. The stability conclusions are illustrated with an example. Copyright © 2006 John Wiley & Sons, Ltd.     

ON THE STABILITY OF OUTPUT FEEDBACK PREDICTIVE CONTROL FOR SYSTEMS WITH INPUT NONLINEARITY

For input saturated Hammerstein systems, a two‐step output feedback predictive control (TSOFPC) scheme is adopted. A receding horizon state observer is chosen, the gain matrix of which has a form similar to the linear control law. Through application of Lyapunov's stability theory, the closed‐loop stability for this kind of system is analyzed. The intermediate variable may or may not be available in real applications, and these two cases are considered separately in this paper. Furthermore, the domain of attraction for this kind of system is discussed, and we prove that it can be tuned to be arbitrarily large if the system matrix is semi‐stable. The stability results are validated by means of an example simulation.     

确定性Hammerstein模型的自适应控制算法及其全局收敛性

本文对广义的Hammerstein模型描述的一类非线性系统,提出一种复合的自适应控制算 法.在适当的条件下,证明了这类非线性系统的稳定性和算法的全局收敛性.本文提出的算 法可以适用于开环不稳定且具有"非最小相位"特性的系统.     

Adaptive control of stochastic Hammerstein–Wiener nonlinear systems with measurement noise

This paper deals with the adaptive control of a class of stochastic Hammerstein–Wiener nonlinear systems with measurement noise. Despite the fundamental progress achieved so far, a general theory framework about adaptive control of Hammerstein–Wiener models is still absent. Such situation is mainly due to the lack of an appropriate parameterisation model. To this end, this paper presents a novel parameterisation model that is to replace unmeasurable internal variables with their estimations. Then, the adaptive control algorithm to be applied is derived on the basis of self-tuning control. In addition, due to the use of the internal variable estimations, the stability and convergence properties are different from the self-tuning control. Our aim, in theoretical analysis, is to discover what limitations are in using the estimations instead of the true values in a control algorithm. Representative numerical examples are given and the simulation results verify the theoretical analysis.     

Adaptive finite‐time stabilization of nonlinearly parameterized systems subject to mismatching disturbances

This paper gives a first try to the finite‐time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer–based control method. Then, based on the disturbance observer–based control, backstepping technique, finite‐time adaptive control, and Lyapunov stability theory, a composite adaptive state‐feedback controller is strictly designed and analyzed, which guarantees the closed‐loop system to be practically finite‐time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme.     

约束Hammerstein系统输出反馈非线性预测控制

针对具有状态、输入和中间变量约束的Hammerstein系统,采用两步法控制策略,给出一种新的可保证闭环系统指数稳定的输出反馈非线性模型预测控制算法.基于Hammerstein系统的特殊结构,结合状态观测器给出无约束线性环节的输出反馈最优控制律,通过滚动优化一有限时域的约束优化问题计算实际控制量.给出保证闭环系统指数稳定的充分条件.以工业双环管聚丙烯装置牌号切换控制为例进行仿真,仿真结果验证该算法的有效性和实用性.     

NLFXLMS and THF‐NLFXLMS Algorithms for Wiener‐Hammerstein Nonlinear Active Noise Control

Nonlinear Filtered‐X LMS (NLFXLMS) is an indirect adaptive control algorithm for nonlinear active noise control (NANC) system. The algorithm has been developed for both Hammerstein and Wiener secondary paths where the nonlinearity is represented by scaled error function (SEF) and tangential hyperbolic function (THF). NLFXLMS algorithm is limited in practical application because the degree of nonlinearity has to be known in advance. This limitation leads to the development of the THF‐NLFXLMS algorithm where the degree of nonlinearity is estimated by modelling the secondary path. In this work, the NLFXLMS and THF‐NLFXLMS are extended to Wiener‐Hammerstein system. The performance of the proposed Wiener‐Hammerstein THF‐NLFXLMS is compared with NLFXLMS algorithm which is considered as the benchmark and second order Volterra algorithm of comparable computational complexity. Simulation results show that the THF‐NLFXLMS has a similar performance to NLFXLMS and outperforms the second order Volterra algorithm as the system becomes more nonlinear.     

非线性HAMMERSTEIN系统的预测控制及其pH过程应用

本文基于非线性离散Hammerstein模型,开发了一种非线性Hammerstein系统预测控制(Non-Linear Hammerstein Predic- tive Control,NLHPC)算法。遵循预测控制策略,该算法利用Hammerstein模型进行输出预测。理论分析结果表明,该算法不仅具有好的稳定性和鲁棒性,而且其自身具有积分作用。在一台工业PC机上实现了该NLHPC算法,并用于具有强非线性的酸碱中和过程实验装置pH值的控制。实验结果表明NLHPC有着比工业界常用的非线性PID控制(nonlinear PID,NL-PID)更好的控制性能。     

Adaptive Control Scheme for Large‐Scale Interconnected Systems Described by Hammerstein Models

This paper proposes an adaptive algorithm for the online control of discrete‐time large‐scale nonlinear systems, which reduces the noise effects acting on the system output (regulation problem) and allows the system output to keep track of a time‐varying trajectory (tracking problem). We consider a large‐scale nonlinear system that can be decomposed into single‐input single‐output (SISO) interconnected nonlinear subsystems with known structure variables (orders, delays) and unknown time‐varying parameters. Each interconnected subsystem is described by block‐oriented models, specifically a discrete‐time Hammerstein model. Parameter adaptation is performed using a recursive parametric estimation algorithm based on the adjustable model method and the least squares techniques. Simulation results of an interconnected petroleum process are provided to demonstrate the effectiveness of the developed control scheme.     

一种新型非线性Hammerstein系统动态矩阵控制算法

将动态矩阵控制策略(DMC)推广到由一个非线性静态多项式函数和一个线性动态阶跃响应环节组成的非线性Ham-merstein系统,详细地给出了该新型非线性Hammerstein系统动态矩阵控制算法(NLH-DMC).把NLH-DMC应用于一套强非线性pH中和过程,给定值跟踪和抗干扰仿真结果表明,NLH-DMC比线性DMC(LDMC)和过程控制领域常用的非线性PID(NL-PID)具有更好的控制性能.进一步的仿真实验证实,NLH-DMC不仅具有良好的控制响应,而且在存在较大模型误差时仍具有很好的稳定性及鲁棒性.     

Design of a nonlinear controller based on a piecewise-linear Hammerstein model

This paper presents a nonlinear controller, which can be used to control single-input single-output nonlinear systems that can be approximated in terms of Hammerstein models. The proposed nonlinear controller is based on the principles of a classic linear pole placement controller and the piecewise-linear Hammerstein model. The controller can be used to control processes with highly nonlinear or even discontinuous static functions, while keeping simple controller structure and a very low computational burden.     

约束Hammerstein系统非线性预测控制及在聚丙烯牌号切换中的仿真研究

对状态和输入受约束的Hammerstein系统, 提出一种新的可保证闭环指数稳定的非线性模型预测控制策略. 基于线性子系统镇定的最优控制律, 滚动预测非线性代数方程的解算误差, 继而在线优化计算满足约束的预测控制量. 进一步, 得到闭环系统指数稳定的解算误差上界. 从而闭环系统不仅满足约束而且对解算误差具有鲁棒性. 最后以工业聚丙烯牌号切换控制为例, 仿真验证本文算法的有效性.     

具有Hammerstein形式的非线性系统广义预测控制

本文提出了具有Ｈａｍｍｅｒｓｔｅｉｎ形式的非线性系统广义预测控制方法，分析了当控制水平等于１时闭环系统的稳定性，同时还提出了使用线性估计器的非线性自适应广义预测控制算法。仿真结果表明了算法的有效性。     

Distance‐based undirected formations of single‐integrator and double‐integrator modeled agents in n‐dimensional space

We study the local asymptotic stability of undirected formations of single‐integrator and double‐integrator modeled agents based on interagent distance control. First, we show that n‐dimensional undirected formations of single‐integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double‐integrator modeled agents in n‐dimensional space is achieved under a gradient‐like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.     

An impulsive‐switched‐system approach to aperiodic sampled‐data systems with time‐delay control

This paper devotes to the stability of aperiodic sampled‐data systems with time‐delay control, where the delays can impose a positive effect on the stability of the systems. The systems are modeled as impulsive switched systems with fixed switching laws. A novel separation theorem is presented to determine the Schur property of a matrix product and then used to obtain a less conservative stability criterion for the impulsive switched systems with fixed switching laws. By the separation theorem and a loop‐functional approach, some new stability and stabilization criteria for aperiodic sampled‐data systems with time‐delay control are provided in terms of linear matrix inequalities. Finally, the stability and stabilization results are tested on some classical numerical examples to illustrate the efficiency of the proposed method.     

Sampled‐data control of networked nonlinear systems with variable delays and drops

This paper investigates the stabilization problem of the nonlinear networked control systems (NCSs) with drops and variable delays. The NCS is modeled as a sampled‐data system. For such a sampled‐data NCS, the stability properties are studied for delay that can be both shorter and longer than one sampling period, respectively. The exponential stability conditions are derived in terms of the parameters of the plant and time delay. On the other hand, a model‐based control scheme based on an approximate discrete‐time model of the plant is presented to guarantee the stability of the closed‐loop system subject to variable time delays and packet losses. The performance of the proposed control schemes are examined through numerical simulations of an automated rendezvous and docking of spacecraft system. Moreover, the simulations show that by employing the model‐based controller, a higher closed‐loop control performance can be achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilization of networked control systems with nonuniform random sampling periods

In this paper, a new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network‐induced delays. The plant is a continuous‐time system, which is sampled by time‐varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed‐loop networked control systems with both packets dropout and network‐induced delays are presented in terms of linear matrix inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques. Copyright © 2010 John Wiley & Sons, Ltd.