Analysis And Optimization The System Which Based On The Signal Quantization And Delta Operator

With the develop of NCS and information transmission, information flow become very large. in order to decrease information flow,the the signal quantization in the area of signal processing and control is more and more popular .There will be quantization error introduced by the signal under the quantized,therefore,the study of quantification is very useful. The discrete sampling system has been developing rapidly for the progress of the computer technique, but Most traditional digital signal processing and control algorithms are inevitablely ill-conditioned when applied in situations in which data are sampled at high rate. Delta transformation is a new discrete method. In a high speed sampling system, the discrete model described by using delta operator will drive to the continuous model with the sampling frequency increasing,and its conclusion is similar to that of the continuous model. So it solves the problem that the the numerical instability of shift operator discrete model.The feedback control theory of Delta operator has become a frontier subject in current control field. It is of great theoretical and practical significance for practical control systems,especially for high speed sampling systems.We study the diserete time system described by Delta operator and quantization in following aspects.From the definition of Delta operator, revealed the relations between the Delta domain ,S domain and Z domain. Then analyzed the controllability of the discrete systems under the Delta operator, concluded that its controllability is the same as traditional description. In view of the network control system exists random time delays,using Delta operator for discrete, the existence condition of theoptimal control laws for the networked control system in Delta operator domain can obtained by using a dynamic programming approach. Then, designed the optimum feedback controllers of the discrete system based on Delta operator. We also compared and verificated the discrete NCS model which described using Delta operator will drive to the continuous model in high speed sampling system.The guaranteed cost control problem of robust stabilization and robust performance for uncertain systems which is described by Delta operator is discussed in this paper. The condition of existing guaranteed cost controller is analyzed and proved in which the method of linear matrix inequality(LMI) is used. An output feedback controller of the uncertain discrete time system described by operator is designed,which guarantees the system is quadratic stabilization. An upper bound of the closed loop performance statistic given by the index of quadratic performance is found for all admissible parameter uncertainties.In the quantization control system, a joint controller is designed so that the unstable system can be stabilized by using a linear control inside the linear region and a quantized control outside the region. We analyzed the performance index of a stable system, got stable process of system through simulation. In addition, through analyzing the performance of quantization system, we revealed the relations between the existence of quadratic guaranteed cost matrix and quadratic stability of the system.