On intermittent control of time delay system with actuator saturation

With the development of science and industry, the rapid increase in time-delay systems has prompted more and more researchers to use intermittent control theory to analyze and synthesize the stability of the time-delay systems subject to actuator saturation and random perturbation. This note investigates the development status and research significance of time-delay systems, Intermittent control and actuator saturation, and that by method of Intermittent control analysis and discussion of the stability of time-delay systems with actuator saturation is of great theoretical significance and practical application value. Keywords-Intermittent control ;Time delay system;Actuator saturation I. A BRIEF INTRODUCTION TO TIME DELAY SYSTEM AND ITS RESEARCH SIGNIFICANCE Time delay is also called detention or time detention. The dynamic system with time delay exists extensively in the nature and all the engineering fields, such as power system, network control system, financial system, biological system, bio-medicine, environment, chemical process, mechanical process, neurotic network, building structure, aerospace industry and all kinds of production lines. They are all typical delay systems. Time delay system appeals to many experts and scholars because its application is very general and extensive. Zhang Wenfeng and Hu Haiyan carried out in 2001 parameter identification studies on the non-linear dynamic control system with feedback time delay[1]; Iv’anescu. Niculescu et al discussed extensively applied neutral time delay system (steam-pipe and water-pipe system and heat-exchanger system)[2], focusing on the consistent asymptotic stability of linear neutral system, and obtained the stability conditions of time delay dependence; Singh and Singhose studied the real-time shaping control and time delay control of flexible structures[3], referring to the real-time shaping and time delay filtering; Richard analyzed all sorts of models caused by time delay, stability and structural changes and briefly introduced some controlling methods, including sliding mode control and time delay control; he also discussed the structural use of time delay input under specific sliding conditions to realize the distributive time delay control of numbers and to process the time delay values of relevant information; Dong Xiaojuan carried out in 2010 an in-depth study on the random resonance of asymmetric dual stability system containing noise and time delay[4], discussing the influence of random force on the time delay dynamic system by means of functional differential equations. Time delay is caused by many factors, mainly including the parametric measuring delay in the system (the speed of measuring instruments), the speed of chemical reactions, the speed of data transmission by sensor, the correlation between long-pipe and belt transmission speed and the transmitted substance, etc. To sum up, time delay includes parametric measuring delay, launching delay, transmitting delay and processing delay. At present, it is not realistic to overcome or stifle all the time delays, therefore, it is utterly important to study the stability of time delay system and to make sure of the performance the system expects. The changing tendency of continuous time delay system is not only associated with the state of the current moment, but it also depends on the state of a certain moment or certain moments in the past, so the continuous time delay system is a infinite dimension system and the characteristic equation of the system is a transcendental equation and contains an infinite number of values. As for the discrete time delay system, the dimension of the system changes with the time delay changing tendency, taking on geometrical rules, which increases the difficulty of the stability analysis of the system. Therefore, studies on both continuous and discrete time delay systems are fairly challenging. In addition, it is of great value for the application of actual systems. II. THE CURRENT STATE OF TIME DELAY SYSTEM From the perspective of systematic theories, any controlling system with time delay will be influenced by the past state of the system, so when studying time delay controlling systems, we should not only consider the International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC 2015) © 2015. The authors Published by Atlantis Press 926 system’s current state. This is a direct reason of the fact that the solution of the time delay system’s state equation is absolutely different from those of ordinary differential equations. Therefore, new ways of thinking, perceptions and methods should be made use of when we discuss the stability and performance of this kind of controlling systems. Liu Hetao further studied in 1986 algebraic criteria of time delay system’s unconditional stability and transformed the unconditional stability into judging the characteristic values distribution of the matrix “A+B” in the time delay system as well as some additional conditions[5]. Liang Jiaxiu and Chen Siyang analyzed and put forward in 2001 the criteria of the unconditional stability of the third-order time delay deferential equation[6]. Jacovitti and Scarano carefully analyzed the delay estimation of the time delay controlling system by means of time discretion method[7]. Hu Haiyan and Wang Zaihua analyzed in 1999 the studies on strategies, systematic features and hot issues of dynamics of the non-linear delay dynamic system[8]. Time delay system can be divided into two categories: continuous time delay system and discrete time delay system. Their state equations can be shown as follows: ) ( ) ( ) (     t Bx t Ax t x  0   ) ( ) ( t t x    ] 0 , [ t     )) ( ( ) ( ) ( t d t Bx t Ax t x     , 0 ) (  t d ) ( ) ( t t x   , ] 0 )], ( [ max [ t t d    ) ( ) ( ) 1 (      k Bx k Ax k x , 0   , ) ( ) ( k k x   , ] 0 , [    k  )) ( ( ) ( ) 1 ( k d k Bx k Ax k x     , 0 ) (  k d , ) ( ) ( k k x   , ] 0 )], ( [ max [ k d k    ) ( ) ( ) ( ) ( ) ( 2 2 1 1 n n t x B t x B t x B t Ax t x              , 0 , , 2 1  n     ) ( ) ( t t x   , ] 0 ], [ max [ t 2 1 n    , , ,     wherein “(1)” shows the continuous time constant delay system, “(2)” shows the continuous time time-varying delay system, correspondingly, “(3)” shows the discrete time constant delay system, “(4)” shows the discrete time time-varying delay system. “(5)” shows a model of multiple delay continuous time system. At present, studies on time delay systems mainly includes system’s stability analysis, controller design,  H performance analysis,  H filter design, observer