J. Cent. South Univ. (2014) 21: 978−986
DOI: 10.1007/s11771-014-2027-z
Guaranteed cost control of networked control systems under
limited communication capacity and variable sampling
LIU Ying-ying(刘英英)
1
, CHU Yun-kai(褚云凯)
2
, CHE Wei-wei(车伟伟)
3
1. School of Information Engineering, Shenyang University, Shenyang 110044, China;
2. Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China;
3. Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang University,
Shenyang 110044 China
© Central South University Press and Springer-Verlag Berlin Heidelberg 2014
Abstract: The problem of guaranteed cost control for the networked control systems (NCSs) with time-varying delays, time-varying
sampling intervals and signals quantization was investigated, wherein the physical plant was continuous-time one, and the control
input was discrete-time one. By using an input delay approach and a sector bound method, the network induced delays, quantization
parameter and sampling intervals were presented in one framework in the case of the state and the control input by quantized in a
logarithmic form. A novel Lyapunov function with discontinuity, which took full advantages of the NCS characteristic information,
was exploited. In addition, it was shown that Lyapunov function decreased at the jump instants. Furthermore, the Leibniz-Newton
formula and free-weighting matrix methods were used to obtain the guaranteed cost controller design conditions which were
dependent on the NCS characteristic information. A numerical example was used to illustrate the effectiveness of the proposed
methods.
Key words: networked control systems (NCSS); quantization; time-varying delays; time-varying sampling; guaranteed cost control
1 Introduction
In recent years, considerable attention has been paid
to networked control systems (NCSs). There are many
advantages of NCSs, such as their low cost, reduced
mass and power requirements, simple installation and
maintenance, and high reliability [1−2]. In network based
control loop, information between the controller and the
plant is exchanged through a network channel with
limited capacities, so signals have to be quantized at first.
The quantizers convert continuous signals into piecewise
continuous signals [3]. Therefore, the controller of NCSs
with quantizers is generally digital, and its model is
hybrid which simultaneously contains continuous signals
and discrete signals. In the digital controller design, to
improve the inter-sampling performance, the hybrid
model is generally built via a zero-order-hold (ZOH).
Recently, various approaches were applied in the field of
sampled-data control [4−7].
However, the introduction of the network also
brings about several disadvantages such as time-varying
network-induced delays, time-varying sampling intervals
or signal quantization, and theses disadvantages might be
main resources influencing the stability and the
performance degradation of the NCSs. Many results have
appeared on this topic [8−13]. For NCSs, it is important
to design a guaranteed cost controller such that the NCSs
are stable and satisfy a performance index. To the best of
the author’s knowledge, most of the existing literature
did not consider the case that time-varying delays, signal
quantization and time-varying sampling intervals
simultaneously exist in NCS, and their effects on NCS
guaranteed cost performance index. The guaranteed cost
control, as one of the fundamental problems for the
NCSs with these three characteristics, has not been fully
investigated and still remains challenging.
2 Problem formulation
An NCS with limited communication capacity
affected by logarithmic quantizers was considered, as
depicted in Fig. 1.
In the NCS, the state signals are continuous-time
and the control input signals are discrete-time. The plant
is a continuous-time linear time-invariant system whose
Foundation item: Project(61104106) supported by the National Natural Science Foundation of China; Project(201202156) supported by the Natural Science
Foundation of Liaoning Province, China; Project(LJQ2012100) supported by Program for Liaoning Excellent Talents in University
(LNET)
Received date: 2012−11−07; Accepted date: 2013−03−01
Corresponding author: LIU Ying-ying, PhD; Tel: +86−13700018158; E-mail: lyy3636@163.com