Optimization Design Of Networked Control Systems Based On LMI Technique

In modern industrial systems, sensors, controllers and actuators are often connected over a network medium, which are called networked control systems (NCSs). Compared with the traditional control systems having point to point structure, advantages of NCSs include resource sharing, good fault-tolerant and fault detection ability, less wiring and easy maintenance, high reliability, etc.Although the introduction of NCSs may lead to many advantages when compared with the traditional control systems, inserting network into control systems will also introduce new challenges for the analysis and design of control systems, such as network-induced time delay, packet dropout, packet disordering, multi-packet transmission, communication constraints, time-varying sampling period, etc. The existing results mainly focus on such problems as stability analysis, controller design, etc. for NCSs with time delay and packet dropout. By designing the controllers appropriately and adopting new methods to compensate the negative influences of time delay and packet dropout, th H∞performance of NCSs may be optimized, however, such problems are not taken into full consideration.This thesis, based on previous works of others, taking time delay and packet dropout in NCSs into full consideration, proposes an active varying sampling period method to make full use of network bandwidth, compared with the constant sampling period based methods, the proposed method can both ensure the sufficient use of network bandwidth and reduce the possibility of network congestion. A delay switching method is proposed to deal with network-induced time delay, and it is proved theoretically to be less conservative than the parameter uncertainty-based method; a both delay switching and parameter uncertainty-based method is also proposed, which method may reduce the high computational complexity of the delay switching method and introduce less conservativeness than the parameter uncertainty-based method. The prediction control-based method is improved to compensate the negative influences of packet dropout, and the improved method may reduce the negative influences of prediction errors; a linear estimation-based approach and a multiple communication channels sharing-based method are proposed to overcome the negative influences of time delay and packet dropout, compared with the methods without compensation, the proposed methods may improve the performance of systems greatly; the problems of H∞output tracking performance optimization and controller design for NCSs are studied, the designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The details of this thesis are as follows.Chapters 1-2 first summarize and analyze the development and main research methods in networked control systems. Preliminaries about the considered problems are also given.Chapter 3 investigates the problems of stability analysis and H∞controller design for NCSs with passive time-varying sampling period and active time-varying sampling period. For NCSs with passive time-varying sampling period, the cases that time delay is longer than a sampling period and the number of consecutive packet dropout is larger than one are taken into consideration, and we also take the case that actuator receives two or more than two control inputs during a sampling period into consideration, which are seldom considered in the literature. The active varying sampling period method is proposed to make full use of network bandwidth, the main idea of this method is that the sensor should shorten the sampling period when the network is idle and improve the performance of control systems correspondingly, when the network is occupied by the most users, the sensor should enlarge the sampling period to reduce the number of packets transmitted through the network and reduce the possibility of network congestion correspondingly. For NCSs with passive time-varying and active time-varying sampling periods, the system models are presented firstly, then by defining appropriate Lyapunov functions and combining multi-objective optimization method, linear matrix inequality approach, free-weighting matrix method and Jensen inequality method, this chapter presents the sufficient conditions and controller design ensuring the asymptotic stability of systems. The simulation examples illustrate the less conservativeness and reduced computational complexity (which is achieved by adopting the Jensen inequality) of the proposed design methods.In Chapter 4, the delay switching-based method and the both delay switching and parameter uncertainty-based method are proposed to deal with stochastic time-varying delay of NCSs. Considering that the existing parameter uncertainty-based method may lead to much conservativeness, this chapter proposes the delay switching method to deal with network-induced time delay, and it is proved theoretically to be less conservative than the parameter uncertainty-based method. Considering that the delay switching method may lead to the increase of computational complexity, the both delay switching and parameter uncertainty method is proposed, which method may reduce the high computational complexity of the delay switching method and introduce less conservativeness than the parameter uncertainty-based method. Since the active varying sampling period method proposed in Chapter 3 can not avoid the frequent switching of sampling periods, this chapter proposes an improved active varying sampling period method, which can both ensure the sufficient use of network bandwidth and avoid frequent switching of sampling period.Chapter 5 investigates the H∞performance optimization and state feedback controller design for linear time-invariant systems, the prediction control-based method and the linear estimation-based approach are proposed to overcome the negative influences of time delay and packet dropout. For the prediction-based compensation method, the actual time delay is taken into full consideration when determining which control input should be used:if the transmission time delay of a control input is smaller than a predefined deadline, it should be used directly, otherwise, the predicted control input should be used, then the negative influences of prediction errors may be reduced effectively. A linear estimation-based time delay and packet dropout compensation method is proposed, compared with the prediction-based method, since it is unnecessary to predict the control inputs p-step-ahead and transmit the predicted control inputs to the actuator, the proposed linear estimation-based method may reduce the network load. Based on the proposed compensation methods, two new system models are presented, and the problem of H∞controller design is discussed by using LMI-based method. The simulation examples illustrate the merits of the proposed compensation methods.Chapter 6 proposes the multiple communication channels sharing-based method to compensate the negative influences of time delay and packet dropout, and H∞performance optimization and controller design are also studied. Compared with the single communication channel-based method, the sharing of the idle communication channels may compensate the negative influences of time delay and packet dropout without leading to the increase of the cost of hardware. Compared with the prediction-based method or the estimation-based method, the proposed multiple communication channels sharing-based method can avoid the negative influences of prediction error or estimation error. By defining appropriate Lyapunov functions and using LMI-based method, H∞controller design and performance optimization are studied. The merit of the proposed controller design methods lies in their less conservativeness, which is achieved by avoiding the utilization of bounding inequalities for cross products of vectors, and the simulation examples illustrate the less conservatism of the proposed methods.Chapter 7 studies the problems of H∞output tracking performance optimization and controller design for discretized networked control systems with time delay and packet dropout. For NCSs with constant sampling period, H∞output tracking performance optimization and controller design are presented by using LMI-based method and discrete Jensen inequality. For NCSs with time-varying sampling period, a multi-objective optimization method is proposed to optimize H∞output tracking performance of systems, and output tracking controller design is presented correspondingly. Since the discrete Jensen inequality is adopted for H∞output tracking controller design, the proposed design methods may introduce less computational complexity than the free weighting matrix-based method. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances, which has also been illustrated by numerical examples.Finally, the results of the dissertation are summarized and further research topics are pointed out.