Research On Robust Control Of Generalized Delta Operator System With Uncertain Derivative Term

In the past,the problems of the discretized continuous system encountered were solved by the classical translation operator,but the use of this method to solve the discrete problem has the disadvantages that cannot be ignored.In order to deal with the instability problem caused by the classical translation operator,the control field has proposed the Delta operator method.In the traditional control system,the parameters of the system must be accurate,but when we solve practical problems,the control system does not match the theory and reality because of digital error and modeling error,so the system can hardly be set accurate parameters and any parameter changes will seriously affect the stability of the system.Therefore,it is necessary to consider these effects caused by actual unknown factors and how to keep the system stable in the controller design of the system.At present,the research on the singular system has gradually tended towards the study of the generalized Delta operator subsystem whose derivative items contain uncertainties.While considering that the derivative term contains uncertainty,in order to make the system always maintain a certain degree of stability,it is usually considered to introduce a controller whose derivative term is uncertain to adjust.Therefore,how to achieve the desired performance index while considering the controller becomes one of the problems to be solved urgently.To solve the proposed system stability problem,this paper does the following work:(1)Because of the fundamental importance of the system's allowable control in the practical application of generalized delta systems,this paper will discuss the admissibility performance of derivative systems with uncertainties in the derivative term using the Delta operator correlation theory and the LMI method,and derive the derivative term.Uncertain conditions for robust admissibility of Delta operator systems and derivation of derivative controllers.Using Matlab simulation to experiment,the simulation diagram shows that the derivative term contains an uncertain generalized Delta operator subsystem that remains stable under the controller.(2)Using the Delta operator correlation theory and LMI method to derive the sufficient and necessary conditions of robust(39)? control performance under the admissibility performance condition of the singular derivative system with known derivative term,the controller is further introduced based on this.Using Matlab simulationexperiment,the simulation diagram shows that the derivative term uncertain generalized Delta operator subsystem is stable under the controller.Finally,the simulation results show that the closed-loop system has robust admissibility performance and robust(39)? control performance.Comparing the closed-loop system state response image in the simulation diagram,the proportional derivative state feedback controller can better control the derivative generalized Delta operator subsystem.