A Comparative Study of H ∞ Synthesis for Networked Control Systems Imam ARIFIN 1* , Bambang RIYANTO 1 arifin@ee.its.ac.id 1 Bandung Institute of Technology, Jalan Ganesa 10, Bandung 40132, Indonesia Abstract Two modeling methods of the Networked Control Systems are presented in this paper. The first method is NCS with 4 mode periodic controller, the second one is NCS with 2 mode controller. These methods are compared in this paper for their use in the NCS performance analysis. The analytic algorithms are presented for the solution of NCS controller design problem corresponding to each method. Finally, a comparative study on the computation and storage for the two methods is worked out. . 1. Introduction Networked Control Systems are control systems where spatially distributed controllers, sensors, actuators and other system components communicate over a band-limited network. The use of a network will lead to intermittent losses or delays of the communication information and may deteriorate the performance or cause instability [4],[7]. One of the important performance measure in modern control theory is H ∞ gain from disturbances to errors. This gain can be used to analyze the closed-loop robust stability of a networked control system. There are three approaches of H ∞ networked control systems. The goal of this paper is to study the performance of control system designed using each two approach and discuss their comparison. In the first approach, H ∞ control is designed for a system with a periodic sequencing under perfect communication (i.e. no loss) [1]. The limited communication constraint in control networks is taken into consideration in controller design by employing the notion of communication sequence. For a given communication sequence, the problem is formulated into a periodic control problem for which a direct LMI design method is developed. To obtain the optimal communication sequence, we use a heuristic search method and convex optimization. In the second approach, the message losses will be considered for H ∞ control design of network control system [2],[8],[9],[10]. However, one of the system will be viewed as a time invariant system (not a periodic one)[2]. In the third approach, H ∞ networked control design will be viewed as a periodic control problem with random switchings in the system matrices [3]. In this paper will only discuss the last two approach. We consider two aspects of remote control systems and formulate a synthesis problem of H ∞ type controllers : 1) the time sequencing of messages transmitted over a network that connects the plant and the controller, 2) the random losses of messages during their transmission over the channel. All of these methods will be cast in the form discrete time Markovian Jump Linear Systems(MJLSs) and LMI analysis and design formulation [5],[6]. Effect of packet loss and network delay on closed-loop system performance will be evaluated through simulation. From these analysis and simulation results, effective method to guarantee the stability and robustness of networked control systems is discussed. Finally, we point out that although a number of H ∞ control design of networked control system have appeared recently in the literature, a detailed investigation of each approach on stability and performance of the closed-loop system has not been studied yet. The rest of this paper is organized as follows. In section 2, formulation of two approaches of NCS is presented. Simulation results and comparison analysis are presented in Section 3. Conclusion of this paper is drawn in Section 4. . 2. Modeling Approach of Networked Control Systems Consider the remote control system depicted in figure 1. [3] Figure 1. Remote Control System State space equation of generalized plant G in the form discrete-time system : k k k k k k k k k k k w D x C y u D w D x C z u B w B Ax x 21 2 12 11 1 2 1 1 + = + + = + + = + (1) where n k x ℜ ∈ is the state, 1 m k w ℜ ∈ is the exogenous input, 2 m k u ℜ ∈ is the control input, 1 p k z ℜ ∈ is the controlled output, 2 p k y ℜ ∈ is the measurement output. Assume that (A, B 2 ) is controllable and (A, C 2 ) is observable. The plant is remotely controlled by the controller connected via a shared communication channel. It is assumed that there are multiple sensors and actuators communicating with the controller; however, as a result of the sequential nature of the channel, only one of them can transmit a message at any discrete-time instant. To meet this G K S1,k θ1,k S2,k θ2,k z y w u y ˆ v Proceedings of the International Conference on Electrical Engineering and Informatics Institut Teknologi Bandung, Indonesia June 17-19, 2007 D-02 ISBN 978-979-16338-0-2 710