Elsevier

Automatica

Volume 57, July 2015, Pages 85-92
Automatica

Brief paper
Output tracking control of networked control systems via delay compensation controllers

https://doi.org/10.1016/j.automatica.2015.04.006Get rights and content

Abstract

In this paper, the problem of networked output tracking control is investigated by considering the delay compensations in both the feedback and forward channels in networked control systems. The delayed output measurements are treated as a special output disturbance, and the feedback channel delay is compensated with the aid of an extended functional observer. For the delay in the forward channel, the buffer and packet-based delay compensation approaches are presented, respectively. Then, the stability analysis is performed for the networked closed-loop systems. Finally, a servo motor control system is used to demonstrate the effectiveness of the proposed new design scheme.

Introduction

With the growth in computing and networking abilities, more and more networks (e.g., the Internet) have been implemented in distributed control systems, which results in the so-called networked control systems (NCSs). Compared with the traditional feedback control systems, NCSs have advantages in terms of low cost, weight and power requirements reduction, simplicity in installation and maintenance, as well as easy resource sharing, and so on. NCSs receive more and more attention in recent years, research topics on NCSs include modeling, stability analysis, control and filtering design, see for example,  Qiu, Feng, and Gao (2010), Vesely, Rosinova, and Quang (2013), Mkondweni and Tzoneva (2014), Yue, Tian, Zhang, and Peng (2009), Xia, Shang, Chen, and Liu (2009), Imer, Yuksel, and Basar (2006), Gao, Liu, and Lam (2009), Zhao, Liu, and Rees (2009a), Zhang, Lam, and Xia (2011), Zhang and Xia (2011), Xia, Fu, and Liu (2011), and the references therein.

Although the network makes it convenient to control large distributed systems, the introduction of limited-capacity network channels into control systems also brings many undesired problems. Among all the problems, the data dropout and the network communication delay are known to be two of the main causes for the performance deterioration or even the instability of the NCSs. Recently, various methods have been presented to handle these two issues or both of them in NCSs, and many control approaches have been established. To mention a few, sampled-data system approaches (Hu et al., 2007, Sun et al., 2010), stochastic system approaches (Luan et al., 2011, Nilsson et al., 1998), optimal control method (Hu and Zhu, 2003, Lian et al., 2003), time delay system method (Gao et al., 2008, Yue et al., 2005), switched system method (Donkers et al., 2011, Sun et al., 2010), robust control method (Zhang & Yu, 2009), and so on.

It is worth mentioning that, in the aforementioned works, the system simply passively accepts the presence of the network communication delay and data dropout, to actively compensate for them, networked predictive control (NPC) strategies are recently proposed in  Liu, Mu, Rees, and Chai (2006). The main feature of NPC is to predict the future control inputs of the system and take the corresponding control action according to the current network condition, then the network communication delay and data dropout can be actively compensated. Further studies on NPC methods were made in  Liu, Xia, Chen, Rees, and Hu (2007a), Liu, Xia, Chen, Rees, and Hu (2007b), Zhao, Liu, and Rees (2009b), Wang, Liu, Wang, Wang, and Rees (2009), Wang, Liu, Wang, Rees, and Zhao (2010), Zhang, Xia, and Shi (2013b), Zhang, Shi, and Xia (2013a), Guo and Li (2010). For example, in  Zhao et al., 2008a, Zhao et al., 2008b, some NPC approaches are proposed for networked Hammerstein-type systems. In  Liu et al., 2007a, Liu et al., 2007b, the state space model based NPC methods was developed for NCSs with feedback channel delay and both forward and feedback channel delays, respectively. In  Pin and Parisini (2011), the NPC approach was developed for uncertain constrained nonlinear systems. In  Hu, Liu, and Rees (2007), an event-driven NPC method was presented for single input single output (SISO) NCSs.

It should be pointed out that, in most of the existing NPC methods, the predicted control inputs are computed based on the delayed state/output measurements (Guo and Li, 2010, Zhang et al., 2013a, Zhang et al., 2013b, Zhao et al., 2011, Zhao et al., 2009b), which indicates the existing NPC methods are only effective in compensating for the delay in the forward channel of the NCSs, and how to compensate the feedback channel delay is important and interesting. In this paper, we consider the output tracking control problem of NCSs with delay compensations in both the feedback and forward channels. By viewing the delayed output measurement as a special output “disturbance”, the feedback channel delay can be compensated with the aid of the proposed extended functional observer. The main contributions of this paper lie in:

  • 1.

    the delay compensation strategies are proposed to actively compensate the network communication delay in the feedback and forward channels, respectively; and

  • 2.

    the networked output tracking controllers with delay compensation are designed and the stability analysis is performed for the networked closed-loop systems.

Finally, simulation results on a servo motor control system are given to illustrate the effectiveness of the proposed techniques.

Section snippets

Problem formulation

The NCSs structure considered in this paper is shown in Fig. 1, {x(k+1)=Ax(k)+Bu(k)y(k)=Cx(k) where x(k)Rn is the state vector, u(k)Rm is the control input vector, y(k)Rq is the system output vector, r(k) is a bounded reference input, and has constant steady-state value. A, B and C are known constant system matrices with appropriate dimensions. In addition, the following assumptions are made for system (1).

Assumption 1

The pair (A,B) is stabilizable, the pair (A,C) is detectable, and [AInBC0]  is of

Delay compensation in feedback channel

In this section, we consider the delay compensation problem in the feedback channel. As is shown in Fig. 1, the observer is located at the controller side, and there exists network communication delay τk in the feedback channel, thus, at instant k, the corresponding output signal received by the observer is yτ(k)y(kτk) rather than y(k). If the system state is not available for the system, we need to introduce an observer to estimate the state. The common and traditional observer is given as xˆ

Delay compensation in forward channel

In the previous section, the network communication delay in the feedback channel is compensated by regarding the delayed measurement as an output “disturbance”, and the extended functional observer is proposed to accurately estimate the system state and disturbance. Obviously, if the system state can be estimated accurately, the impact of the network communication delay in the feedback channel can be eliminated effectively, and the state estimate applied into the controller will be more

Stability analysis

In this section, motivated by  Guo and Li (2010), we will perform the stability analysis of the networked closed-loop system.

Theorem 3

Suppose that   Assumption 1, Assumption 2, Assumption 3   are satisfied. System   (1)   with u(k)=u(k|kd̄) is BIBO stable if there exist matrix L̄, and controller gain K in   (15)   such that MĀL̄C̄ and A+BK are Schur, respectively.

Proof

According to system (1), and after some iterations, it can be shown that x(k+d̄)=Ad̄x(k)+j=1d̄Ad̄jBu(k+j1).

Define the state prediction

Numerical example

In order to verify the effectiveness of the proposed method, a servo motor control system that consists of a DC motor, load plate, speed, and angle sensors is considered. The model of the motor control plant at sampling period 0.04 s was identified as (Liu et al., 2007b) G(z1)=A(z1)B(z1)=0.05409z2+0.115z3+0.0001z411.12z10.213z2+0.335z3 which can also be written in state-space form (1) with the following system matrices A=[1.120.2130.335100010],B=[100],C=[0.05410.1150.0001].

According

Conclusions

In this paper, a networked output tracking control approach has been developed with consideration of delay compensation in both forward and feedback channels. Both control design and stability analysis problems have been investigated. The extended functional observer is proposed to compensate the feedback channel delay by viewing the delayed measurement as a disturbance, and the buffer- and packet-based approaches are presented to compensate the forward channel delay. Finally, a DC-motor system

Acknowledgments

The authors wish to thank the associate editor and referees for their very constructive comments and suggestions, which have helped improve the presentation of the paper.

Jinhui Zhang was born in Hebei Province, China, in 1982. He received the B.S. degree in Mathematics and Applied Mathematics and the M.S. degree in Applied Mathematics from Hebei University of Science and Technology, Shijiazhuang, China, in 2004 and 2007, respectively, and the Ph.D. degree in Control Science and Engineering from Beijing Institute of Technology, Beijing, China, in 2011. He was a Research Associate in the Department of Mechanical Engineering, University of Hong Kong, Hong Kong,

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    Jinhui Zhang was born in Hebei Province, China, in 1982. He received the B.S. degree in Mathematics and Applied Mathematics and the M.S. degree in Applied Mathematics from Hebei University of Science and Technology, Shijiazhuang, China, in 2004 and 2007, respectively, and the Ph.D. degree in Control Science and Engineering from Beijing Institute of Technology, Beijing, China, in 2011. He was a Research Associate in the Department of Mechanical Engineering, University of Hong Kong, Hong Kong, from February 2010 to May 2010, a Senior Research Associate in the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, from December 2010 to March 2011, and a Visiting Fellow with the School of Computing, Engineering & Mathematics, University of Western Sydney, Sydney, Australia, from February 2013 to May 2013. He joined Beijing University of Chemical Technology in March 2011, where he is currently an Associate Professor. His research interests include networked control systems, robust control/filter theory, disturbance rejection control.

    Yujuan Lin was born in Guangdong Province, China, in 1990. She received the B.E. degree in Automation from Beijing University of Chemical Technology, Beijing, China, in 2008. She is currently pursing the M.E. degree in Control Science and Engineering at the same university. Her current research interests include networked control systems, robust control and disturbance rejection control.

    Peng Shi received the B.Sc. degree in Mathematics from Harbin Institute of Technology, China; the M.E. degree in Systems Engineering from Harbin Engineering University, China; the Ph.D. degree in Electrical Engineering from the University of Newcastle, Australia; the Ph.D. degree in Mathematics from the University of South Australia; and the D.Sc. degree from the University of Glamorgan, UK.

    He was a lecturer at the University of South Australia; a Senior Scientist in the Defence Science and Technology Organisation, Australia; and a Professor at the University of Glamorgan, UK. Now, he is a Professor at the University of Adelaide, and Victoria University, Australia. His research interests include system and control theory, computational intelligence, and operational research. He is a Fellow of the Institute of Electrical and Electronic Engineers, the Institution of Engineering and Technology, and the Institute of Mathematics and its Applications. He has been in the editorial board of a number of journals, including Automatica; IEEE Transactions on Automatic Control; IEEE Transactions on Cybernetics; IEEE Transactions on Fuzzy Systems; IEEE Transactions on Circuits and Systems-I; and IEEE Access.

    This work was partially supported by the National Natural Science Foundation of China   61473024 and 61403018, the Australian Research Council (DP140102180, LP140100471, LE150100079), and the 111 Project (B12018). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor James Lam under the direction of Editor Ian R. Petersen.

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