Modeling, Stability And Control Of Networked Control Systems

One of the main features of modern control systems is the data transmission via networks. Automatic control technology is involved with communication network more and more. Various real-time networks such as field-bus are extensively applied into industrial control engineering. The networked control system structure will prevail in the future, whose sensors, controllers and actuators are all connected via networks. With the impact of network circumstance, many issues emerged inevitably, such as network induced transmission delay, multi-channel transmission brought by the limited bandwidth, data packet dropouts from the failed communication, the asynchronous clock among network nodes etc. These problems not only depress the performance of normally designed control systems, but also destroy the system stability. After analyzing the disadvantages brought by network, this paper investigated the modeling, stability anaysis and control law synthesiss of networked control systems. The related theories and methods include Lyapunov stability theory, delay system theory, switched system theory and impulsive system theory. First of all, this paper analyzed detailedly the effects brought by the network and presented many methods to cope with the harmful factors. Though the analysis is basically qualitative, it will help model networked control systems. The transmission delay is the most apparent disadvantage from the network connectivity. A large amount of materials studied the constant transmission delay, yet seldom considered the time varying ones. To supply this gap, we modeled the networked control systems with time varying transmission delays and obtained some results. First we established the linear discrete interval system model with time varying delays for networked control systems. Then the robust stability of this model was studied via discrete Lyapunov stability theory and matrix inequality methods. Otherwise this paper established nonlinear networked control systems model with time varying delays and investigated its exponential stability problem. The stability condition is obtained in simple matrix inequalities by applying the Jacobin matrices. The data packet dropouts event is also one of the most important phenomena arising from network connectivity. This paper described the networked control systems with data packet dropouts by applying the switched system model in both continuous and discrete cases. Equivalent impulsive system models (including both impulsive differential system and impulsive difference system) were then presented for the first time. So we can study the networked control systems based on these impulsive systems. We extended the stability results of switched systems with respect to dwell-time to these impulsive systems. The asymptotic stability condition of equivalent impulsive system models was then obtained. Note that the physical meaning of the stability condition is obvious. Our conclusion fits the reality very well. On the other hand, the robust stabilization problem was discussed by applying linear matrix inequalities and the stability condition of impulsive difference systems was obtained. The models and methods are all created for the first time. Furthermore, the guaranteed cost control problem of networked control systems with data dropouts was investigated in this paper. The continuous case is difficult because time varying matrices cannot be expressed directly. As a result we only discussed a special case, the guaranteed cost control problem of a class of parametric uncertain impulsive differential systems. The existence condition and design method of the guaranteed cost control law were obtained from linear matrix inequalities technology. In the discrete case, we also got the existence condition and design method of the guaranteed cost control by applying the results of robust stabilization for networked control systems with data dropouts. We described uncertain networked control systems with a class of uncertain switched system models. The robust control problem with H∞performance bound was studied for these systems. The design method of the state feedback control law was obtained. Main results are represented by some LMIs. This paper presented the networked impulsive control systems (NICSs) for the first time. A scalar named data dropouts over N steps (DRNS) was defined to quantify the ratio of data dropouts in the network. The relationship between DRNS and the asymptotic stability of NICSs was discussed. Considering the effect of network-induced delay, we construct a state predictor based on the system model parameters. Then the predicted state data was obtained from this predictor with the delayed feedback state data. Control outputs were calculated from the predicted state data. A necessary and sufficient condition for the asymptotic stability of this system was acquired further.