Study On Stability Analysis And Quantized Control For Networked Control Systems

The closed-loop control systems where the plant,sensor,controller and actuator are connected through shared network are called networked control systems(NCSs). Compared with the traditional point-to-point control systems,the advantages of NCSs lie on their high diagnostic capacity,easy installation and maintenance,low prices,few wires,high reliability,increased system agility,etc.Furthermore,by using NCSs,we can share the network resources and control the remote plant.Today,NCSs have a widely application in aerospace,equipment manufacturers,industrial process control,remote medical treatment and some dangerous and special environments.In recent years,the analysis and synthesis for NCSs have been absorbed considerable attention in the fields of engineering and control.Some important journals,such as IEEE Systems Magazine,IEEE Trans.Automatic Control and Proceedings of the IEEE,had published some special issues on the topic of NCSs in the past several years,which is also an important issue in some international proceedings.However,the insertion of the network in the control systems brings some new challenging problems,these problems do not exist in the point-to-point control systems, which include:i) network-induced delay.The network nodes(sensor,controller, actuator and plant) may be far away from each other,therefore,the transmission time of the signal through the network can not be omitted.Generally speaking,the network-induced delay is composed of three parts,transmission time from sensor to controller,the computation time in the controller and transmission time from controller to actuator,ii) Packet dropout.Because of the unreliability of the network, signal may be lost in the process of transmission.The packet dropout can degrade the control performance of the NCSs.iii) Wrong packet sequence.In the process of transmission,the packets may be out of their original order because of choosing different route.That is,the packet which is sent out earlier may arrive at the destination later,iv) Due to the limited transmission capacity of the network,the big packet may be disassembled into several small packets before they are transmitted to the next node.And the small packets also meet the problems(i-iii) in the process of transmission,therefore,the integrity of the packet can not be guaranteed when assembled the small packets together,v) Data quantization.Because of the limited communication capacity of the network and the usage of the digital devices, the packet can not be transmitted without data quantization.Therefore,the effect of the quantization on the performance of the networked control systems should be considered.Furthermore,the asynchronous of clock and multi-rate sampling also make the analysis and control of NCSs complicated.Most of the problems referred above do not exist in the traditional point-to-point control systems,and some well established analysis methods in the traditional control systems will lose their effect in the networked control systems.Therefore,how to establish the NCSs model which can reflect the main characters of the network and propose some new analysis method to handle these problems are a hard task.To solve the problems mentioned above,many kinds of NCSs models and analysis methods have been proposed in the past years.However,limited by the system model or analysis technology,the researchers make some assumptions in their papers, which include:the networked delay is less than one sampling period,the networked delay only exists in the forward network or in the backward network,there are only networked delay or packet dropout in the network,etc.These assumptions do not always hold in the practical systems,which limit the application of the obtained result severely.Furthermore,there are some assumptions which exist in most of the publications,for example,assume that all the networked delay smaller than a given bound and there is no quantization in the data transmission.Therefore,further research is still needed for the analysis and synthesis of networked control systems.In the NCSs model used in this paper,most of the above mentioned assumptions can be removed.In Chapter 2,we firstly propose new type of Lyapunov functional, by using the convexity of matrix function,the conservatism caused by enlargingη(t) to its upper boundηM can be avoided.Based on this method,we also investigate the stability,stabilization and Hoo control of the networked control systems.The given examples illustrate the less conservativeness of the proposed method.The following problems exist commonly in the published references,which are solved in Chapter 3.1.In the published references,the authors often assume that all the networked delay is smaller than a given bound.However,as is known,because of the unreliability of the network,the delay can larger than the given bound.In this case,the obtained criteria in these references can not judge the stability of the NCSs.Therefore,new type of NCSs model and analysis methods are needed to solve this problem.2.In the existing NCSs model and analysis method,only the variable range of the delay is utilized,the stochastic property of the delay has not caused enough attention. In Chapter 3,besides the variable range of the delay,we also utilize the information of value distribution of it.Firstly,we divide the whole variable range of the delay into two subintervals and assume that the probability of the delay in different intervals are known a prior.The value distribution of the delay can reflect the quality of the network conditions rather than the variable range of it,detailed explain can be seen in Chapter 3.By using the value distribution of the delay,we build new type of networked control systems.By using new Lyapunov functional and analysis method,we can obtain the sufficient condition for the mean square stability of the NCSs,which are shown in terms of linear matrix inequalities and can be easily solved by the LMI toolbox in Matlab.Different from the existing results,the solvability of our Conditions rely not only on the variation range of the delay,but also on the value distribution of it.Through the analysis of this paper,we can also conclude that if Prob{η(t) >ηM}=0,the large delay has no effect on the mean square stability performance of NCSs.From the above analysis,we can conclude that the maximum allowable bound of the delay appearing with a low probability has little effect on the system performance.Therefore,what we really concerned is the maximum effectual delay bound of the delay,that is,the minimumηM which makes Pr ob {η(t) >ηM}= 0.The numerical example shows that by using our method,the maximum efficiency delay bound is much better than the existing results.In the networked control systems,quantization is inevitable from the following reasons.Firstly,controllers are usually implemented digitally,signals that take values in a continuous set need to be represented with finite precision to allow digital information precessing in finite time.Secondly,the limited capacity communication channel of the shared network can reflect the size of the signal.The effect of the quantization on the NCSs are much larger than the traditional control systems. However,up to now,when considering both effects of networked conditions and data quantization,the interrelated references are countable thus still needs further investigation.In this paper,we make a systemic study for the quantization problem in NCSs. Firstly,considering the networked delay and data quantization in both forward and backward network,we establish the networked control system.Based on the proposed model,we study the stability of the networked control systems and design the quantized controller to stabilize of the system.The obtained criteria are shown in terms of linear matrix inequality.When the information of the state can not be measured,we also investigate the observer based quantized output controller design for the NCSs in Captor 4.A separation lemma is proposed to separate the controller gain and observer gain into different equations,which makes the design problem more easier.In Captor 5,we consider the design problem of time-varying quantizer for NCSs. Firstly,considering the effect of data quantization and networked delay,we build the networked control system model.Based on this model,we study the quantized stabilization, quantized H_∞control of the NCSs.Furthermore,when the state information can not be measured,we also investigate the observer based quantized output feedback control and dynamic quantized output control problems.The numerical examples show that the obtained criteria can guarantee the stability of the NCSs.