The Research On Optimal And Guaranteed Cost Control Of The Delta Operator Systems

The discrete sampled systems have been developed rapidly with the development of computer technology. But when sampling rate is high, most traditional digital signal processing and control algorithms are inherently ill-conditioned. Considerable progress has been made by the use of Delta operator on ameliorating ill-conditioning problems. 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 sampled systems.We investigate the discrete time system which is described by S operator as follows.The problem of controller based on time domain performance index using 8 operator theory is discussed in this paper. Relation among S domain, Z domain and S domain is given. The process of design is showed by an example.The existing condition of optimal controller in the discrete time system described by S operator is discussed in this paper, in which the method of dynamic programming is used. The Riccati equation based on d operator is deduced and optimal controller of the discrete-time system described by S operator is designed.Existing a proper and real rational controller to the systems described by 8 operator is analyzed and proved. The controller makes the closed-loop systems internally stable and minimizes the H2 norm of the transfer matrix Tzw from w to z. Two Riccati formulae based on 8 operator is deduced. The H2 problems for continuous time systems, Z operator models and 8 operator models are investigated respectively.The guaranteed cost control problem of robust stabilization and robust performance for uncertain systems which is described by 8 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. A output feedback controller of the uncertain discrete time systemdescribed by 6 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.The poles of the closed loop systems is described by the Delta operator models in the specified stable region of the complex plane which makes the poles in the specified region when the sampling period is becoming shorter.