Controller Design of Output Feedback MIMO Networked Control Systems with Multiple Packet Transmission

MIMO (mult-input multi-output) networked control systems (NCSs) with multiple packet transmission is considered. The network-induced delay is assumed to be time-varying and less than one sampling period. Suppose the data of sensor node is part of system outputs and is transferred with static scheduling strategy, then the NCS is modeled as uncertain periodic system. The uncertain periodic system theory is used for the stability sufficient condition. Then a control design approach is presented via bilinear matrix inequalities (BMIs) method. The simulation result shows the effectiveness of the proposed approach. Introduction Control systems that sensors, controller and actuators are connected over a network medium are usually called networked control systems. There are many advantages in NCSs such as low cost, simple installation and maintenance, and high reliability etc. Thus, increasing research interests have been paid to the study of the stability and controller design of NCSs. By decomposing network-induced delay into fixed one and varying parts, the NCSs were modeled as parameter-uncertain systems and controller design methods based on delay dependent stability conditions were presented in [1] and [2]. [3] designed the stochastic optimal controllers for networked control systems with network-induced delay longer than a sampling period. All works mentioned above discussed the case of single-packet transmission of NCSs. However, especially in distributed NCSs, sensors are spread over wide area. For this case, the sampled data is transmitted in multiple packets and may not arrive to controller simultaneously. Then, multiple packet transmission NCSs should be considered. As for the problem of multiple packet transmission, [4] presented the model of NCSs and then discussed the system stability. [5] presented the discretized model of MIMO NCS with multiple time delays, and the closed-loop NCS model only included a standard controller designed without considering the time delay effect a priori. [6] modeled the NCS with multiple packet transmission as switching system, then proposed a controller design method to realize H∞ performance. [7] derived the model of NCS with multiple packet transmission and packet dropout, the presented the stability condition and state feedback controller design method. This paper presents a model of observer-based output feedback NCS with multiple packet transmission. The stability and observer-based output feedback controller design are also presented by using matrix inequalities method. Finally an example is give to illustrate the effectiveness of the proposed method. Applied Mechanics and Materials Vols. 16-19 (2009) pp 935-940 Online available since 2009/Oct/12 at www.scientific.net © (2009) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.16-19.935 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 130.203.136.75, Pennsylvania State University, University Park, United States of America-04/06/14,13:18:00) Modeling of NCS Throughout this paper, we assume that the sensors are clock-driven, the controller and actuators are event-driven (realized via zero-order holder). The control and the actuators will be updated until the new packet arrives. Denote T as the length of sampling period. The overall network-induced delay (the sum of sensor-controller delay and controller-actuator delay) is less than T. The controlled system with out network is expressed as ( ) ( ) ( ) ( ) ( ) t t t t t       x Ax Bu y Cx (1) where ( ) n t R x , ( ) p t R u , ( ) m t R y , A, B, C are constant matrices of appropriate dimensions. Only system outputs y(t) can be measured by different sensors, and every sensor node transfer its sampling data independently. At every sampling instant, only one sensor node can get the right to transfer data, and static scheduling strategy is used to decide which sensor data should be transmitted, that is, the transfer order is fixed a priori. Once the controller receives sensor data, control signal is calculated, lumped into one packet and transmitted to actuators by broadcasting mode so that all actuators can receive control signal simultaneously. Thus, the MIMO NCS with multiple packet transmission can be illustrated by Fig.1. acuator plant sensor 1 controller sc  ca  1 y u network r y sensor r Fig.1 An output feedback MIMO NCS with multiple packet transmission Considering the network-induced delay, discretize Eq.1 with sampling period T, we get 1 1 ( ) k k k k k k           x Gx H DFE u DFEu y Cx (2) where , , , , G H D F E can be obtained by the method proposed in [8]. Within one sampling period, only one output of the controlled plant, i.e. , k i i k y C x can arrive to controller, where i C is the i th row of C . In order to obtain feedback control law, we introduce a set of state observers to reconstruct plant states: 1 , ˆ ˆ ˆ ( ) k k k i k i i k y      x Gx Hu L C x (3) where i L is feedback gain matrix corresponding to , k i y . 936 e-Engineering & Digital Enterprise Technology VII