多通道约束下的网络控制系统的最优跟踪性能

本文针对双通道约束下的线性时不变网络控制系统的随机信号跟踪性能极限问题进行了研究.网络通信包含通信噪声和通信带宽两种信道因素.被控系统考虑是非最小相位和不稳定系统,并且系统包含多个不同的非最小相位零点和多个不同的不稳定极点.对上行通道和下行通道都存在通信带宽约束及高斯白噪声影响的情形,从频域角度,通过采用双自由度控制器和尤拉参数化方法,获得了此类网络控制系统的最优可达的跟踪性能.研究结果表明网络控制系统的跟踪性能极限完全由被控对象的结构特征(非最小相位零点、不稳定极点以及被控对象的系统增益),参考输入信号和网络特性(高斯白噪声的统计特征、通信信道带宽)所决定.最后,仿真结果检证了所得结果的正确性.     

Best Tracking Performance of Networked Control Systems Based on Communication Constraints

The best tracking problem for a single‐input‐single‐output (SISO) networked control system with communication constraints is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The communication constraints under consideration are finite bandwidth and networked induced‐delay. Explicit expressions of the minimal tracking error have been obtained for networked control systems with or without communication constraints. It is shown that the best tracking performance dependents on the nonminimum phase zeros, and unstable poles of the given plant, as well as the bandwidth and networked induced‐delay. It is also shown that, if the constraints of the communication channel do not exist, the best tracking performance reduces to the existing tracking performance of the control system without communication constraints. The result shows how the bandwidth and networked induced‐delay of a communication channel may fundamentally constrain a control system's tracking capability. Some typical examples are given to illustrate the theoretical results.     

Regulation performance limitation of networked time-delay systems with incomplete information

In this paper, the regulation performance limitation of networked time-delay systems is studied. The communication network is mainly affected by parameters such as packet dropouts, encoding-decoding, interference signal, and channel noises. Non-minimum phase zeros, unstable poles, and time delay are all considered for a given plant. The corresponding regulation performance expression is derived using coprime factorization and spectral decomposition techniques in the frequency domain. The results indicate that the regulation performance of the system is related to the inherent characteristics of the given plant, including non-minimum phase zeros, unstable poles, and time delay. Additionally, network communication parameters such as white Gaussian noise, packet dropouts, encoding-decoding, and external interference signals all affect the regulation performance of networked time-delay systems. Finally, some simulation examples are provided to demonstrate the effectiveness of the theory.     

基于丢包和带宽限制网络化系统稳定性分析

基于数据包丢失和网络带宽限制研究了网络化系统稳定性问题.通信网络的特征通过数据包丢失、带宽和加性白噪声来体现.采用频域的方法得到了网络化系统稳定所需信噪比的最小(极限)值.该最小(极限)值说明了网络化系统稳定所需信噪比是由通信网络通道的丢包率、带宽、系统的不稳定极点的位置和非最小相位零点的位置决定.研究结果进一步揭示网络化系统稳定所需信噪比的最小(极限)值与系统本质特征(非最小相位零点的位置和不稳定极点的位置)和通信网络参数(数据包丢失和带宽)的关系.仿真结果说明该理论的正确性.     

Optimal tracking performance of MIMO control systems with communication constraints and a code scheme

This paper investigates the issue of the optimal tracking performance for multiple-input multiple-output linear time-invariant continuous-time systems with power constrained. An H₂ criterion of the error signal and the signal of the input channel are used as a measure for the tracking performance. A code scheme is introduced as a means of integrating controller and channel design to obtain the optimal tracking performance. It is shown that the optimal tracking performance index consists of two parts, one depends on the non-minimum phase zeros and zero direction of the given plant, as well as the reference input signal, while the other depends on the unstable poles and pole direction of the given plant, as well as on the bandwidth and additive white noise of a communication channel. It is also shown that when the communication does not exist, the optimal tracking performance reduces to the existing normal tracking performance of the control system. The results show how the optimal tracking performance is limited by the bandwidth and additive white noise of the communication channel. A typical example is given to illustrate the theoretical results.     

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.     

Optimal regulation performance of discrete time-delay systems based on quantization and input energy constraints

In this paper, we study the optimal regulation problem of networked control systems and propose a new performance index for a given discrete time-delay system. The regulation performance of the controlled plant is investigated by considering the effects of various constraints on the communication channel such as quantization, bandwidth, and packet dropouts using frequency domain methods and two-degree-of-freedom control techniques. The results show that the regulation performance is not only related to the location and direction of the non-minimum phase zeros and unstable poles of a given system but also related to the internal time delay of the controlled plant. Packet dropouts, quantization, and bandwidth limitations can also negatively affect the optimal performance. In addition, the trade-off of the input energy constraint can also make the optimal regulation performance suffer. Finally, the reliability of this innovative result is illustrated by some simulation examples.     

An Optimal Tracking Performance of MIMO NCS with Quantization and Bandwidth Constraints

This paper presents an optimal tracking performance of multiple‐input multiple‐output (MIMO) networked control systems (NCSs) with quantization and bandwidth constraints. In this study, we simultaneously consider the encoding‐decoding, quantization and bandwidth of communication channel. The optimal tracking performance of NCSs is obtained by spectral factorization technique and partial fraction. The obtained results demonstrate that the optimal tracking performance is influenced by the nonminimum phase zeros and unstable poles as well as their directions for a given plant. In addition, it is shown that characteristics of reference signal, encoding‐decoding, quantization, and bandwidth of communication channel are also closely related to tracking performance. Finally, the efficiency of proposed tracking performance is verified by typical examples.     

多通道网络化系统跟踪性能极限

本文基于白噪声和编码影响研究多通道网络化系统跟踪性能极限.网络化系统的跟踪性能指标是通过跟踪误差的能量来定义的,采用谱分解技术和范数矩阵理论得到多通道网络化系统跟踪性能极限的下界表达式.研究结果显示了对象的固有特性(非最小相位零点、零点方向、不稳定极点和极点方向)和多通道的编码器及白噪声决定网络化系统跟踪性能极限;同时也说明了多通道网络是如何影响系统跟踪性能极限.仿真结果验证了该结论的正确性.     

非最小相位系统的扩展Laguerre基函数迭代学习控制

针对非最小相位系统的跟踪问题,提出了一种新的基函数迭代学习控制算法.该算法利用新型的非因果Laguerre扩展基函数逼近系统逆传递函数,设计最优迭代学习律使系统输入收敛到系统的稳定逆,保证了控制性能.算法不依赖于系统的先验模型,仅需以基函数信号作为系统输入进行模型辨识,减少了模型不确定性的影响.通过对单连杆柔性机械臂这样的典型非最小相位系统跟踪问题的仿真,验证了该方法的良好效果.     

多变量离散系统随机信号跟踪性能极限

研究线性时不变、多变量、离散系统对随机信号的跟踪性能极限问题, 所考虑的随机参考输入信号为布朗运动序列. 研究结果表明此类系统的跟 踪性能极限完全由被控对象的结构特征和参考输入的统计特征决定, 其中, 结构特征指被控对象的非最小相位零点和不稳定极点的位置和方向. 作为特殊情形, 本文给出了参考输入为一致随机信号以及被控对象仅含有单个非最小相位零点和单个不稳定极点时系统跟踪性能极限问题的解. 最后, 给出了两自由度补偿器跟踪系统对随机信号的跟踪性能极限.     

A robust sliding-mode output tracking control for a class of relative degree zero and non-minimum phase plants: A chemical process application

A well-known robust observer-based sliding-mode output tracking control developed for strictly proper, minimum phase systems is extended to the control of relative degree zero, MIMO non-minimum phase plants. By assuming that the class of uncertainty is limited to an appropriate sub-space of the actuator range-space, a sliding-mode tracking control for non-minimum phase systems is posed. By introducing some dynamics, in the form of a plant output filter, relative degree zero plants are proved to be robustly controllable. The design of the linear components of the tracking control and the observer gains is posed in an H ₂-framework. The control law is exemplified on the control of a highly non-linear, benzene producing, large scale chemical process.     

Virtual Reference Feedback Tuning for non-minimum phase plants

Model reference control design methods fail when the plant has one or more non-minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods, where the plant is typically unknown. In this paper, we extend the Virtual Reference Feedback Tuning method to non-minimum phase plants. This extension is based on the idea proposed in Lecchini and Gevers (2002) for Iterative Feedback Tuning. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non-minimum phase zeros.     

Optimal tracking and two-channel disturbance rejection under control energy constraint

In this paper, the optimal tracking problem under control energy constraint is studied. The disturbance in the upstream channel and down channel is adequately considered. Some new results are derived and it is shown that the performance limitation is tightly dependent on the non-minimum phase zeros and the unstable poles. In addition, the performance limitation, which is greater than that of the disturbance only in the down channel, depends on other new non-minimum phase zeros. Finally, the example explains and validates the conclusion.     

A dynamic feedback control strategy for control loops with time-varying delay

Dynamic systems of nth order with time-varying delay in the control loop are examined in this paper. The infinite-dimensional pure delay problem is approximated using a jth-order Padé approximation. Although the approximation provides a well-matched finite-dimensional configuration, it poses a new challenge in terms of unstable internal dynamics for the resulted non-minimum phase system. Such a non-minimum phase characteristic limits the closed-loop system bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the unstable internal dynamics of the system is captured and a new dynamic compensator is proposed to stabilise it in a systematic framework. A dynamic controller is developed, which provides the overall system stability against unmatched perturbation and meets the desired tracking error dynamics. The proposed approach is then applied to fuelling control in gasoline engines addressing the varying transport delay of the oxygen-sensor measurement in the exhaust. The developed methodology is finally validated on a Ford F-150 SI lean-burn engine model with large time-varying delay in the control loop.     

非线性非最小相位系统的控制研究综述

非线性非最小相位系统是指具有不稳定零动态或内部动态的非线性系统, 其本身固有的非最小相位特性限制了许多常规非线性控制方法(如反推控制、反馈线性化、滑模控制等)的直接应用. 因此, 非最小相位系统的控制比最小相位系统要困难得多, 是控制理论与工程应用中具有挑战性的课题之一. 本文综述了目前非线性非最小相位系统的研究成果, 着重介绍了非最小相位系统的成因、特性、 理想内模求解等问题, 并对其镇定、轨迹跟踪及路径跟踪等控制方法进行了分析比较. 最后, 讨论了非线性非最小相位系统研究领域中尚存在的问题, 并对其未来发展方向进行了展望.     

Optimal tracking performance of MIMO discrete‐time systems with communication constraints

The optimal tracking problem for multiple‐input multiple‐output linear‐time‐invariant discrete‐time systems with communication constraints in the feedback path is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The objective is to obtain an optimal tracking performance, attainable by all possible stabilizing compensators. It is shown that the optimal tracking performance consists of two parts, one depends on the nonminimum phase zeros and zero direction of the given plant, as well as the reference input signal direction, and the other depends on the nonminimum phase zeros, unstable poles, and pole direction of the given plant, as well as the bandwidth and additive white Gaussian noise of the communication channel. It is also shown that, if the constraint of the communication channel does not exist, the optimal tracking performance reduces to the existing tracking performance of the control system without communication constraints. A typical example is given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Output tracking for nonlinear non-minimum phase systems with output delay and application to an F-16 jet fighter

In this article, output tracking for a class of nonlinear non-minimum phase systems with output delay is considered. By applying the first-order Padé approximation technique to deal with the time-delay function, the original control problem is reduced to the output-tracking problem of a new non-minimum phase system without delay. The bounded tracking profiles of the unstable internal dynamics in the new system are generated by using the nonlinear inversion-based method, and a complete sliding mode control scheme is proposed to stabilise the output-tracking error as well as the internal dynamics. Moreover, the proposed control scheme is applied to solve the flight-path angle tracking problem of an F-16 jet fighter.     

编解码和时延约束下的网络化控制系统最优跟踪性能

本文研究了具有丢包、时延、编解码等通信资源受限下多输入多输出离散时间网络控制系统的最优跟踪性能. 基于频域方法, 采用二元随机过程来模拟数据包丢失, 并假设信道噪声是加性高斯白噪声(AWGN), 推导了在丢包、信道噪声、时延和编解码影响下的跟踪性能极限. 采用单参数补偿器(SDOF), 利用互质分解、Youla参数化等工具得到了编解码和时延约束下的网络控制系统最优跟踪性能的显式表达式. 结果表明, 跟踪性能与对象的固有特性(非最小相位零点与不稳定极点的位置和方向)、时延、丢包率和AWGN 功率谱密度密切相关.     

Performance Limitation of Networked Systems with Network‐Induced Delay and Packet‐Dropout Constraints

In this paper, we deeply investigate the tracking performance limitation of single‐input single‐output (SISO) networked systems with packet dropouts and network‐induced delay constrains, where the power of the tracking error is adopted to measure of the performance and is minimized by searching through all stabilizing one‐parameter controllers, with/without considering the channel input power. Moreover, the explicit expressions of the tracking performance limitation are obtained by applying the spectral factorization technique. Theoretical analysis shows that the tracking performance limitation is closely dependent on non‐minimum phase zeros, unstable poles of a given plant, the characteristics of the reference signals, network‐induced delay and packet dropouts probability of communication channel. Finally, some typical examples and simulations are conducted to illustrate the theoretical results.