Stability Analysis And Stabilization Strategy Of Networked Control Systems

Feedback control systems wherein the control loops are closed through networks are called networked control systems (NCSs). Compared to the traditional control systems based on point-to-point structures, the primary advantages of the NCSs are reduced wiring, ease of installation, debug, maintainment and management, etc. In particular, with the popularity of the Internet and a variety of mobile communication devices access to the Internet, operators outside the site can achieve a lot of remote control functions through the NCSs without time and space limitation. However, due to the use of time-division multiplex-based data transport mechanism, the NCSs also bring some new problems, such as time-delay, packet dropout, clock syschronization and packet disorder, etc. These problems lead to the fact that the presupposition for the application of the traditional control theories—"synchronizing control, no delay sampling and actuation"’can not be met. In order to scientific analysis and synthesis of the NCSs, it is very important to improve and develop the existing control theories. In this paper, we study the stability analysis, controller design and robust control aspects for the networked control systems with time-varying and bounded delay and data packet dropout.In order to find out the typical features of the time-delay and data packet dropout, we analyze the compositions, causes, influencing factors of the network time-delay when information is transmitted between the adjacent nodes, and then further discuss the compositons of time-delay and packet dropout in the closed control loops. Two basic concepts of maximum delay bound (MDB) and maximum allowable delay bound (MADB) are proposed clearly, while the latter is an important criterion used to evaluate the conservativeness of the time-delay systems. On the basis of the discrete-time linear system theory, we analyze the examples of the NCSs with time-delay and data packet dropout and obtain the step response curves through MATLAB/Simulink simulation. According to the calculation and simulation results, we then qualitatively discuss the different impacts of transmission delay and data packet dropout on the control performance and it is pointed out that the former is more harmful than the latter.Assuming that the sensors are clock-driven and the controllers and actuators are event-driven, the NCSs with random and bounded transmission delay and data packet dropout are modeled as a class of continuous-time systems with time-delay through the introduction of the concept of input delay, and the LMI-based asympototic stability criteria and controller design algorithm are derived by Lyapunov-Krasovsii Theorem. The integral term produced during the calculation of Lyapunov functional derivative is eliminated by the introduction of some constrainted free weighting matrices instead of the free weighting matrix approach based on the zero equations like Newton-Leibniz formula or system state equation in the existing literatures, which increases the number of the free weighting matrices and reduces the conservativeness of the calculation results. In addition, this paper also improves the way that ignors a minor non-positive integral cross term of Lyapunov functional derivative existing in most of the similar literatures and uses reasonable upper bound technique, e.g., using the constrainted free weighting matrices to eliminate this term, so the system conservativeness is further reduced.Due to modeling error, noise and other factors, the model uncertainties widely exist in the control systems, therefore it is necessary to examine the robust control problem for the NCSs, the papameters of which vary within a certain range. Through Lyapunov-Krasovskii Theorem, the robust state-feedback asymptotic stability criteria and stabilization algorithm for the NCSs with random and bounded delay, data packet dropout and norm-bounded uncertainty are obtained. At the same time, not all of the states are measurable in most of the control svstems and the NCSs on the basis of the output-feedback controller are more common, so the robuse output-feedback stability and stabilization of the NCSs are also studied in this paper. In the existing literatures, the state-feedback asympototic stability contition is usually obtained firstly and then it is converted into the output-feedback one by the substitution of the output equation and this conclusion can not be changed into the LMI-based stabilization algorithm with less conservativeness. This paper takes a completely different approach. The output vectors are represented as the independent variables which are constrained by the output equation and then the LMI-based controller design algorithm is obtained which can be solved easily by the LMI toolbox in MATLAB. The above results take system stability as the design goal, but many systems need to meet certain performance standard in addition to stability, therefore the output-feedback H∞controller design method is presented for the NCSs with parameter uncertainties and external disturbance in this paper, which will allows the systems to reach certain disturbance suppression requirement.In order to further reduce system conservativeness, assumimg that the sensors and actuators are clock-driven and controllers are event-driven, the NCSs with random and bounded time-delay and data packet dropout are modeled as a class of discrete-time time-delay systems. By adding in a new sub-term with lower delay bound parameter to Lyapunov functional, the asymptotic stability condition and stabilization algorithm, wich are related with lower and upper time-delay bound independently, are obtained. The range of the input delay will be narrowed if the lower delay dound is greater than0, thus the conservativeness can be reduced conrrespondingly. In addition, for analysis and synthesis of the NCSs with time-delay and data packet dropout, the existing literatures simply combines the delay and packet dropout to the input delay and their different impacts on system performance are not disguished, which will leads to the conservative results certainly. In this paper, by analyzing the variation of the data packet dropout, it can be obtained that the number of the consecutive dropout is incremental with time. Then a new Lyapunov functioanl sub-term is constructed according to this characteristic and the asymptotic stability condition and stabilization algorithm wrhich are related with delay and packet dropout independently are derived. The simulation results show that the conservativeness is reduced significantly.