State‐limiting PID controller for a class of nonlinear systems with constant uncertainties

Proportional Integral Derivative (PID) controllers still represent the core control method for achieving output regulation of either linear or nonlinear systems in the majority of industrial applications. However, conventional PID control cannot guarantee specific state constraint requirements for the plant, when the system introduces uncertainties. In this paper, a novel nonlinear PID control that achieves output regulation and guarantees a desired state limitation below a given value for a wide class of nonlinear systems with constant uncertainties is proposed. Using nonlinear ultimate boundedness theory, it is shown that the proposed state‐limiting PID (sl‐PID) control maintains a given bound for the desired system states at all times, ie, even during transients, whereas an analytic method for selecting the controller gains is also presented to ensure closed‐loop system stability and convergence at the desired equilibrium. Two nonlinear engineering examples that include an electric motor and a dc/dc converter are investigated using the conventional PID and the proposed sl‐PID to validate the superiority of the proposed controller in achieving the desired output regulation with a given bounded state requirement.     

Reliable decentralized PID controller synthesis for two-channel MIMO processes

Reliable stabilization and regulation of two-channel decentralized multi-input multi-output (MIMO) control systems is considered. The system has integral-action due to using proportional + integral + derivative (PID) controllers. Closed-loop stability and asymptotic tracking of step-input references are achieved at each output channel when all controllers are operational. Stability is maintained when one of the controllers fails completely and is set to zero. Controller synthesis procedures are proposed for stable MIMO plants and for several unstable MIMO plant classes that admit PID controllers. These synthesis procedures are applied to various examples of process systems to illustrate the design methodology.     

具有时变时滞和多包丢失的网络控制系统量化H∞控制

研究了具有时变时滞与多数据包丢失的网络控制系统(networked control systems,NCSs)的量化H∞控制问题.同时考虑传感器-控制器间的测量通道及控制器-执行器间的控制通道的多数据包丢失,并将其用满足Bernoulli分布的随机变量来表示.控制输入信号和测量输出信号分别在传感器和控制器两侧进行对数量化,量化误差描述为扇区有界不确定性.利用Lyapunov理论和线性矩阵不等式方法,得到了使得闭环NCSs满足一定H∞性能指标的均方意义下指数稳定充分条件,并给出了基于观测器的时滞相关控制器设计方法.最后,通过实例证明了该方法的有效性.     

线性不确定系统信息受限下的远程跟踪

研究了信息受限下一类线性不确定系统的跟踪调节问题. 假定由高阶微分方程产生的参考信号与受控系统(不确定线性系统)通过有限容量信道相连. 针对该信号设计了具体的编码方式, 并在受控系统端重构了该参考信号, 进而依据此重构信号设计了跟踪控制器, 最终到达了跟踪目标. 最后数值例子验证了本文结论的有效性.     

Acceleration amplitude-phase regulation for electro-hydraulic servo shaking table based on LMS adaptive filtering algorithm

Electro-hydraulic servo shaking table usually requires good control performance for acceleration replication. The poles of the electro-hydraulic servo shaking table are placed by three-variable control method using pole placement theory. The system frequency band is thus extended and the system stability is also enhanced. The phase delay and amplitude attenuation phenomenon occurs in electro-hydraulic servo shaking table corresponding to an acceleration sinusoidal input. The method for phase delay and amplitude attenuation elimination based on LMS adaptive filtering algorithm is proposed here. The task is accomplished by adjusting the weights using LMS adaptive filtering algorithm when there exits phase delay and amplitude attenuation between the input and its corresponding acceleration response. The reference input is weighted in such a way that it makes the system output track the input efficiently. The weighted input signal is inputted to the control system such that the output phase delay and amplitude attenuation are all cancelled. The above concept is used as a basis for the development of amplitude-phase regulation (APR) algorithm. The method does not need to estimate the system model and has good real-time performance. Experimental results demonstrate the efficiency and validity of the proposed APR control scheme.     

基于极值搜索算法的一类多输入多输出非仿射型非线性系统输出跟踪控制

针对一类状态不可测的多输入多输出非仿射型非线性系统, 提出了基于极值搜索算法的输出跟踪控制方法. 此方法无需设计系统状态观测器, 仅利用系统的输出量和极值搜索向量形成控制律. 应用平均化理论分析平均化系统的稳定性, 然后利用奇异值扰动方法, 证明了所提出的控制方法可以保证闭环系统的稳定性和输出跟踪误差的收敛性. 仿真结果验证了本文方法的有效性.     

Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems

This paper deals with global output regulation with nonlinear exosystems for a class of uncertain nonlinear output feedback systems. The circle criterion is exploited for the internal model design to accommodate the nonlinearities in the exosystems, and the explicit conditions are given for the exosystems such that the proposed internal model design can be applied. The uncertainties of the output feedback systems are in the form of unknown constant parameters, and adaptive control techniques are used to ensure the global stability of the proposed control design for output regulation.     

基于强化学习的部分线性离散时间系统的最优输出调节

针对同时具有线性外部干扰与非线性不确定性下的离散时间部分线性系统的最优输出调节问题, 提出了仅利用在线数据的基于强化学习的数据驱动控制方法. 首先, 该问题可拆分为一个受约束的静态优化问题和一个动态规划问题, 第一个问题可以解出调节器方程的解. 第二个问题可以确定出控制器的最优反馈增益. 然后, 运用小增益定理证明了存在非线性不确定性离散时间部分线性系统的最优输出调节问题的稳定性. 针对传统的控制方法需要准确的系统模型参数用来解决这两个优化问题, 提出了一种数据驱动离线策略更新算法, 该算法仅使用在线数据找到动态规划问题的解. 然后, 基于动态规划问题的解, 利用在线数据为静态优化问题提供了最优解. 最后, 仿真结果验证了该方法的有效性.     

具有 iISS 逆动态的非线性系统的输出反馈调节

研究了具有积分输入状态稳定 (Integral input-to-state stability, iISS)逆动态和未知控制方向的更一般的非线性系统的输出反馈调节问题. 利用自适应反推的方法, 所设计的输出反馈控制器使得闭环系统的输出调节到原点, 并且闭环系统的其他信号有界.     

Robust model predictive control under redundant channel transmission with applications in networked DC motor systems

In networked systems, intermittent failures in data transmission are usually inevitable due to the limited bandwidth of the communication channel, and an effective countermeasure is to add redundance so as to improve the reliability of the communication service. This paper is concerned with the model predictive control (MPC) problem by using static output feedback for a class of polytopic uncertain systems with redundant channels under both input and output constraints. By utilizing the min–max control approach combined with stochastic analysis, sufficient conditions are established to guarantee the feasibility of the designed MPC scheme that ensures the robust stability of the closed‐loop system. In terms of the solution to an auxiliary optimization problem, an easy‐to‐implement MPC algorithm is proposed to obtain the desired sub‐optimal control sequence as well as the upper bound of the quadratic cost function. Finally, to illustrate its effectiveness, the proposed design method is applied to control a networked direct current motor system. Copyright © 2016 John Wiley & Sons, Ltd.     

Output Feedback Regulation of Stochastic Nonlinear Systems With Stochastic iISS Inverse Dynamics

This paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: 1) Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) using Lyapunov function in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is first introduced, two important properties of SiISS are obtained: (i) SiISS is strictly weaker than SISS using Lyapunov function; (ii) SiISS is stronger than the minimum-phase property. However, only under the minimum-phase assumption, there is no dynamic output feedback control law for global stabilization in probability. 2) Almost sure boundedness, a reasonable and stronger concept than boundedness in probability, is introduced. The purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed-loop control system. 3) Some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed-loop system are established. 4) A unifying framework is proposed to design a dynamic output feedback control law, which drives the states to the origin almost surely while maintaining all the closed-loop signals bounded almost surely.      

Output feedback guaranteed cost control of networked linear systems with random packet losses

This article is concerned with the output feedback guaranteed cost control problem for a class of networked control systems (NCSs) with both packet losses and network-induced delays. The packet-loss processes in the forward channel and the backward channel are modelled as two Markov chains. The dynamic output feedback controllers are considered, and the closed-loop NCS is modelled as a discrete-time Markovian system with two modes and unit time delay. By using a properly constructed Lyapunov function and the state transformation technique, a sufficient condition is derived for the closed-loop NCS to be mean-square exponentially stable and ensure a decay rate that can be tuned according to the packet loss situations in the networks. Moreover, design procedures for the guaranteed cost controllers are also presented based on the obtained stability condition and guaranteed cost performance result. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.     

基于自适应分布式滤波观测器的多智能体系统编队控制

本文考虑了全局指令系统输出信息受到信道扰动情况下线性多智能体系统的编队控制问题.首先,基于协作式输出调节理论框架对线性多智能体系统的编队控制问题进行数学建模.其次,针对受到信道扰动的全局指令系统输出信息,提出了一类基于受扰输出的自适应分布式滤波观测器,在降低网络信息交换量的同时消除扰动的影响.最后,设计了输出反馈确定等价控制律,解决了线性多智能体系统的分布式编队控制问题.给出了数值仿真结果检验控制性能.     

丢包扰动环境下基于强化学习的最优输出调节

针对存在线性外部干扰和状态反馈过程中发生丢包的网络控制系统的跟踪控制问题,采用输出调节的思想,提出基于离轨策略强化学习的数据驱动最优输出调节控制方法,实现仅利用在线数据即可求解控制策略.首先,对系统状态在网络传输过程存在丢包的情况,利用史密斯预估器重构系统的状态;然后基于输出调节控制框架,提出一种基于离轨策略强化学习的数据驱动最优控制算法,在系统状态发生丢包时仅利用在线数据计算反馈增益,在求解反馈增益过程中找到与求解输出调节问题的联系;接着基于求解反馈增益过程中得到的与输出调节问题中求解调节器方程相关的参数,计算前馈增益的无模型解;最后,通过仿真结果验证所提出方法的有效性.     

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

This paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.     

A unifying framework for global regulation via nonlinear output feedback: from ISS to iISS

This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable inverse dynamics, subject to possibly unknown control direction. The contribution of the paper is two-fold. Firstly, we consider the problem of global regulation, instead of global asymptotic stabilization (GAS), for systems with generalized dynamic uncertainties. It is shown by an elementary example that GAS is not solvable using conventional smooth output feedback. Secondly, we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system. Using our framework, most of the known classes of output feedback form systems are broadened in several directions: unmeasured states and unknown parameters can appear nonlinearly, restrictive matching and growth assumptions are removed, the dynamic uncertainty satisfies the weaker condition of Sontag's integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded.     

Global output regulation for strict‐feedback nonlinear systems with mismatched nonvanishing disturbances

This paper concerns the problem of global output regulation for a class of strict‐feedback nonlinear systems subject to mismatched nonvanishing disturbances. A composite control scheme is developed using a nonlinear disturbance observer‐based control approach. A novel idea is that the disturbance estimation is introduced into the design of virtual control laws in each step. Global stability analysis for the closed‐loop system is presented by the direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in the presence of mismatched nonvanishing disturbances without the requirement of solving any partial differential equations involved with the traditional output regulation theory. An application design example of a single‐machine infinite‐bus system with static var compensator is presented with simulation results to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Passivity-based control for a DC/DC high-gain transformerless boost converter

In this work, an adaptive passivity-based controller for a DC-DC high-gain transformerlessdouble-inductor boost converter is fully detailed. The proposed current-mode control scheme results in two feedback loops, a current controller for tracking the inductor current considering damping injection and energy shaping, and a voltage loop composed by a proportional-integral action to guarantee output voltage regulation. Furthermore, a parametric uncertainty estimator using immersion-invariance approach is designed to improve the robustness of the current loop. As a result, a multi-loop adaptive nonlinear energy-based controller, which ensures regional asymptotic stability via Lyapunov analysis is accomplished. In addition, considering practical conditions, real-time numerical simulations, using a 1 kW case-study converter, are carried out in order to assess the effectiveness of the proposed control scheme. Results for output voltage regulation, current tracking, and parametric uncertainty estimation under input voltage and load step changes are shown.     

Observer-based controller design for networked control systems with sensor quantisation and random communication delay

This article addresses the study of observer-based controller design for network-based control systems in the presence of output quantisation and random communication delay simultaneously. In the communication channel, the output measurement are quantised before transmission, and two kinds of network-induced delays are taken into account simultaneously: (i) random delay from sensor to controller and (ii) random delay from controller to actuator. These two types of random delays are modelled as two independent Bernoulli distributed white sequences. The observer-based controller is synthesised to stabilise the networked closed-loop system in the sense of stochastic stability. Sufficient conditions for the existence of the controller are provided by stochastic Lyapunov method. An illustrative numerical example is employed to demonstrate the applicability and flexibility of the proposed design strategy.     

Design and implementation of a neuro-adaptive backstepping controller for buck converter fed PMDC-motor

A neuro-adaptive backstepping control (NABSC) method using single-layer Chebyshev polynomial based neural network is proposed for the angular velocity tracking in buck converter fed permanent magnet dc (PMDC)-motor. Owing to their universal approximation property, neural networks have been utilized for approximating the unknown nonlinear profile of instantaneous load torque. The inherent computational complexity of the neural network based adaptive scheme has been circumvented through the use of orthogonal Chebyshev polynomials as basis functions. A detailed stability and transient performance analysis has been conducted using Lyapunov stability criteria. The proposed control scheme is shown to yield a superior output performance with enhanced robustness for wide variations in load torque and set-point changes, compared to existing conventional approaches based on adaptive backstepping. The theoretical propositions are verified on an experimental prototype using dSPACE, Control Desk DS1103 setup with an embedded TM320F240 Digital Signal Processor proving its applicability to real-time electrical systems. The efficiency of the proposed strategy is quantified using performance measures and are evaluated against the conventional adaptive backstepping control (ABSC) methodology. Ultimately, this investigation confirms the effectiveness of the proposed control scheme in achieving an enhanced output transient performance while faithfully realizing its control objective in the event of abrupt and uncertain load variations.