具有多个反馈通道的不确定系统的网络预测控制资源-CSDN文库

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本文探讨了具有多个反馈通道的不确定网络控制系统的设计与稳定性分析问题。网络预测控制（NPC）方法是针对网络控制系统（NCS）中的分布式时延和数据包丢失问题而提出的。在控制器设计过程中，对时延和数据包丢失影响的建模是一个核心问题。对此，提出了足够的闭环NPC系统在分布式时延和数据包丢失情况下的稳定性条件，考虑了恒定和随机两种情况。文章使用了一个摆杆系统来验证所提出的方法，并且通过仿真和实验结果证明了该方法的有效性。知识点详细说明： 1. 网络控制系统（NCS）概念：NCS是一种利用网络来闭合控制回路的反馈控制系统。与传统非网络控制相比，NCS因其低成本、易维护和高效率等优点，受到越来越多的关注。 2. 网络控制系统面临的新问题：当网络被集成到控制回路中时，会引入一些传统控制系统没有的新问题。其中最突出的两个问题是时延和数据包丢失，这些问题可能会严重影响系统性能，甚至导致系统不稳定。 3. 分布式时延和数据包丢失的建模：为了解决NCS设计中的时延和数据包丢失问题，文章将这些问题的影响建模到闭环NCS中，并提出了相应的控制器设计方法以稳定NCS。 4. 观测器基础的网络预测控制（NPC）方法：为了补偿反馈通道中的分布式时延和数据包丢失，本文提出了基于观测器的NPC方法。这种方法通过观测器来预测系统未来状态，并基于这些预测来制定控制策略。 5. 稳定性条件：为了保证闭环系统的稳定性，文章提出了一组充分条件，这些条件适用于系统时延是恒定的或随机的情况。这些条件有助于确保即使在网络中存在不可预测的时延和数据丢失时，系统仍能保持稳定。 6. 摆杆系统实例：为了测试和验证所提出的NPC方法，文章使用了一个球与杆系统（ball-and-beam system）作为实验平台。摆杆系统是一个典型的教学用实验装置，用于演示和研究系统的动态行为以及控制策略。 7. 模拟与实验结果：通过将NPC方法应用于摆杆系统，文章展示了该方法在模拟和实验测试中的有效性。仿真与实验结果均表明，所提出的NPC方法能够有效地补偿网络时延和数据包丢失对系统性能的影响。 8. 控制方法综述：文章提到了多种处理NCS中时延和数据包丢失的方法，例如随机系统方法、最优控制方法、时延系统方法、切换系统方法、鲁棒控制方法等。这些方法试图在不同的框架下解决NCS中的控制问题，每种方法都有其独特的适用情景和优势。在网络预测控制的领域中，本文针对具有多个反馈通道的不确定系统的研究，为解决网络控制系统中数据传输的不确定性和时变性提供了新的思路和方法。这对于提高NCS的性能和可靠性具有重要的意义，并且为未来网络控制系统的深入研究和发展奠定了基础。

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5228 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 11, NOVEMBER 2013

Networked Predictive Control of Uncertain Systems

With Multiple Feedback Channels

Hongbo Song, Guo-Ping Liu, Fellow, IEEE, and Li Yu, Member, IEEE

Abstract—This paper studies the design and stability analysis

of uncertain networked control systems with multiple feedback

channels. An observer-based networked predictive control (NPC)

method is proposed to compensate for the distributed delays and

packet dropouts in the feedback channels. Sufﬁcient conditions are

presented for the closed-loop NPC system with distributed delays

and packet dropouts to be stable, both in constant and random

cases. A ball-and-beam system is employed to test the proposed

method. Both the simulation and experiment results demonstrate

the effectiveness of the method.

Index Terms—Delays, distributed, networked control systems

(NCSs), networked predictive control (NPC), observer-based

control, packet dropouts.

I. INTRODUCTION

NETWORKED control system (NCS) is a feedback con-

trol system whose control loops are closed via a network.

Compared with traditional non-NCSs, NCSs offer some attrac-

tive advantages such as low cost, easy maintenance, and high

efﬁciency. Therefore, NCSs have received increasing attention

in the last decade [1]–[4]. However, the insertion of a network

into the control loop will cause some new issues that traditional

control systems do not have. Among them, delay and packet

dropout are two issues that can severely degrade the system

performance or even cause instability and thus must be taken

into consideration in the controller design of NCSs [5]–[10].

Up to now, various methods have been presented to handle

the delay, t he packet dropout, or both of them in NCSs, such

as the stochastic system method [11], [12], the optimal control

method [13], [14], the time delay system method [15], [16], the

switched system method [17], [18], the r obust control method

[19], and so on. In this literature, the effects of the delay

and packet dropout were modeled into the closed-loop NCSs,

and the corresponding controller design methods were devel-

oped to stabilize the NCSs. As an alternative, [20] presented

Manuscript received February 26, 2012; revised July 20, 2012 and

September 9, 2012; accepted September 28, 2012. Date of publication

October 25, 2012; date of current version June 6, 2013. The work of H. Song

was supported by the National Natural Science Foundation of China under

Grant 61273116. The work of G.-P. Liu was supported in part by the Na-

tional Natural Science Foundation of China under Grant 60934006 and Grant

61273104. The work of Li Yu was supported by the National Natural Science

Foundation of China under Grant 61104063 and Grant 61273117.

H. Song is with the College of Information, Zhejiang University of Finance

and Economics, Hangzhou 310018, China (e-mail: di7ganshb@163.com).

G.-P. Liu is with the Faculty of Advanced Technology, University of Glam-

organ, Pontypridd CF37 1DL, U.K., and also with the CTGT Center, Harbin

Institute of Technology, Harbin 150001, China.

L. Yu is with the Department of Automation, Zhejiang University of Tech-

nology, Hangzhou 310023, China.

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TIE.2012.2225398

a networked predictive control (NPC) method that actively

compensates for the delay and packet dropout. The main feature

of NPC is to predict the future behavior of the system and to

take the corresponding control action according to the real-time

information of the delay and packet dropout. The NPC method

was shown to be effective in compensating for the delay and

packet dropout in NCSs [20].

Further studies on the NPC method were made in [21]–[30],

to name a few. For example, in [21] and [22], a state-space-

model-based NPC method was developed, which can deal

with multiple-input–multiple-output (MIMO) NCSs. In [25],

the problem of predictive control was studied for nonlinear

uncertain networked systems. In [26], an event-driven NPC

method was presented for single-input–single-output (SISO)

NCSs so that the synchronization problem can be avoided.

It should be pointed out that most of the existing results on

NPC considered SISO NCSs or considered MIMO NCSs but

assumed that the plant outputs are transmitted via one sensor

node. However, NCSs are distributed systems and are often in

large scale. Thus, the plant outputs may have to be transmitted

via separated sensor nodes, which make the NCSs with multiple

communication channels [1], [3]. In this case, the delays and

packet dropouts are distributed, and the former NPC methods

need to be modiﬁed to be implemented. Few results are con-

cerned with the NPC of systems with multiple communication

channels. In [31], the packet-based predictive control problem

was studied for NCSs with multiple feedback communication

channels. However, the stability analysis of the closed-loop

NCSs was not considered, and it is assumed that all the plant

states are measurable and that the system model is accurate.

Although the NPC method in [21] and [22] can deal with

the distributed delays and packet dropouts by using the queuing

method proposed in [32] and [33], i t will introduce some con-

servatism because it discards some of the useful real-time plant

outputs on purpose. Moreover, the plants in real world more or

less have uncertainty, but the system models in [21] and [22]

are considered to be time invariant. From both mathematical

and physical points of view, if we do not discard the useful

real-time data and use them for f eedback control instead, the

performance of the closed-loop NPC system will be improved

when the plant is an uncertain system. The above observations

motivate this paper on the NPC for uncertain systems with

multiple communication channels. However, this paper only

considers feedback channels and assumes forward channels to

be ideal for simplicity. Since forward channels and feedback

channels carry signals with different functions in NCSs, the

way of compensation in forward channels is different from the

one in feedback channels. Thus, it is much more difﬁcult to

SONG et al.: NPC OF UNCERTAIN SYSTEMS WITH MULTIPLE FEEDBACK CHANNELS 5229

Fig. 1. Structure of the OB-NPC system.

consider the design and stability analysis of NCSs with both

channels. Considering both channels will be an interesting and

challenging future work for the authors.

In this paper, an observer-based NPC (OB-NPC) method is

presented to control uncertain networked systems with multiple

feedback channels. The key point is an improved predictive

technique that is proposed to deal with the distributed delays

and packet dropouts. An algorithm is given to implement the

method. Sufﬁcient conditions are presented for the stability

analysis of the closed-loop NPC system, both in constant and

random cases. A ball-and-beam system is used to test the

performance of the proposed method, and both the simulation

and experiment results show the effectiveness.

II. D

ESIGN OF OB-NPC

A. Structure of the OB-NPC System

The structure of the OB-NPC system is shown in Fig. 1,

where the main parts are the output buffers (OBs), the receiver

buffer (RB), and the observer-based predictor (OBP). The OBs

are used to compensate for the distributed packet dropouts. The

objective of the RB is to handle the packet disorder problem.

The OBP is designed to compensate for the distributed delays

in the feedback channels. The forward channels are assumed to

be ideal so that the controller is just simply a local controller.

The main idea of NPC in the state-space model framework

was presented in [21] and [22], which is shown to be effective

in dealing with the NCSs with a single communication channel.

As for the case with multiple channels, the queuing method

in [32] and [33] can also make the NPC implementation in

[21] and [22] applicable by changing the distributed delays

into a single delay whose value is equal to the upper bound

of the delays. Obviously, this treatment will introduce some

conservatism because it discards some of the useful real-time

plant outputs on purpose. Moreover, when the delays vary in a

large bound and the system model uncertainty is large, the con-

servatism will degrade the system performance more seriously.

To overcome the problem, this paper will present an OB-NPC

method whose objective is to eliminate the conservatism and

improve the system performance.

Since the performance of the closed-loop NPC system highly

depends on the accuracy of the prediction, the basic idea is

to use all the real-time plant outputs that are available for the

OBP so that the prediction can be more accurate. Moreover, the

distributed packet dropouts and the packet disorder are another

two issues to be addressed. First, packet dropouts make some

data unavailable for the OBP. These data can be compensated

by using the OBs. Second, delays that are longer than one

sampling period may result in data disorder, i.e., old data may

arrive at the OBP before new data. Thus, some data may be

omitted by the OBP based on the standard principle of using

the most recent data. In addition, the updating procedure of

the observer becomes complicated with data disorder. These

problems can be handled by introducing the RB and a logic

scheme to determine whether new data arrive or not.

In Fig. 1, the plant is described by the following uncertain

linear discrete-time state-space model:



x(k +1)=(A +ΔA)x(k)+(B +ΔB)u(k)

y(k)=Cx(k)

(1)

where x ∈ R

,y∈ R

, and u ∈ R

are the state, output, and

input vectors of the plant, respectively, and A, B, and C are

the nominal values for the system matrices with appropriate

dimensions. ΔA and ΔB are system uncertainties, and it is

assumed that (A +ΔA) and (B +ΔB) belong to a convex

bounded polyhedral domain described by q vertices as



Ω(λ)



Ω(λ)=



i=1



i=1

=1;λ

≥ 0



(2)

where Ω

=(A

),i=1, 2,...,q.

The observer-based predictor is designed based on the fol-

lowing standard state observer:

ˆx(k+1|k)=Aˆx(k|k−1)+Bu(k)+L(y(k)−C ˆx(k|k−1)) (3)

where ˆx(k +1|k) is the prediction of x(k +1) based on the

observer state ˆx(k|k − 1) and plant output y(k), and L is

the observer gain matrix, which can be designed by standard

methods such as the Lyapunov method. The state feedback

controller is of the following form:

u(k)=−K ˆx(k|•) − K

r(k) (4)

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