Dynamic Optimal Setting Control Of Singular Systems Based On Disturbance Observer

A singular system is also known as a generalized system,a description system or a differential algebraic system.Compared with regular systems,it has a wider range of application and more accurate description for complex systems in practical engineering.Therefore,it is often used to model complex systems such as power grids,chemical processes,economic models and nuclear reactors.On one hand,the complexity of singular systems determines the difficulty of research.On the other hand,due to the widespread disturbances in various systems,the optimal control for singular systems has always been a hot topic.To this purpose,this paper mainly focuses on a class of singular systems with disturbances in practical production engineering.An optimal operational control for singular systems with disturbances is realized by combining a disturbance observer and a set points adjustment.Firstly,PID controllers are designed for the singular systems in the bottom loops,LMIs are used to solve the parameters of the bottom controller,and the Lyapunov stability theory is used to prove the stability of the system under the action of the controller.Secondly,the disturbance observer is designed in the upper layer(optimal setting layer)to estimate the value of the disturbance acting on the singular system,the Lyapunov stability theory is used to prove the stability of the system with the disturbance observer,and the set value is adjusted dynamically to make the system stable.It is proved that the output value of the system can accurately track the set value of the target.Finally,numerical simulations are carried out by using MATLAB,and the simulation results show the effectiveness of the two-level optimal setting control method.In summary,the three main works of this thesis are listed as follows:1?For linear singular systems with single type disturbances,a two-layer structure optimal operational control is studied based on disturbance observers.Firstly,PID controllers are designed at the bottom layer.For the disturbances acting on singular systems,a disturbance observer is designed to estimate the disturbances.On the basis of the fixed controller,a dynamic set points adjustment method is used to the singular system.It is verified that the output value of singular systems can track the target setting value.2?A two-layer optimal setting control method is studied for linear singular systems with non-single type disturbances(non-single type disturbances mainly include harmonic disturbances and norm bounded disturbances).Firstly,PID controllers are designed at the bottom layer.To satisfy the admissible conditions of singular system,the three unknown parameters of the PID controller are solved based on LMIs.Secondly,the disturbance observer is designed to estimate the disturbance,and then a dynamic set point adjustment method is combined to realize the tracking of the system output value under the condition that the bottom controller parameters of the singular system remain unchanged.3?The two-layer structure optimal setting control method is studied for nonlinear singular systems with single type disturbances.Firstly,the PID controller is designed at the bottom layer.Secondly,the disturbance observer is designed at the upper layer to estimate the single type disturbances,and the dynamic error is analyzed for nonlinear systems.Finally,the performance index can be minimized by dynamically adjusting the setting points.