Eigenstructure Assignment In A Class Of Descriptor Second-order Systems Based On Displacement-acceleration Feedback

Descriptor system is a class of more general and extensive range of applications than normal systems.Research on descriptor systems has achieved some results,aerospace control,vibration control,robot control problems can be characterized by the control and design of second order dynamical systems.Therefore,this paper chooses the descriptor second order dynamical systems as the research object.With the requirement of high precision of practical engineering,the innovation of traditional eigenstructure allocation is becoming the focus of research.In the design of a descriptor second order dynamical system controller,the closed-loop system has desired characteristics through the optimization of the robust performance index.This paper uses the parametric method of eigenstructure assignment to control the descriptor second order system,and improves the response characteristics of the system.The main issues discussed in this paper are divided into the following two points:1)Establish the parametric expression for the feedback gain controller use the control law which is defined beforehand.2)Propose a new robust index that can improve the robustness of the closed-system.In view of the above problems,several aspects of innovate research have been carried out in this dissertation:First,the displacement-acceleration feedback information is used to solve the problem of eigenstructure assignment.Displacement-acceleration feedback control law is applied to a descriptor system,the dynamic order of the system can be changed,and the impulse response of the descriptor system can be eliminated.From the viewpoint of measurement,using accelerometer as sensor is favourable and more reliable than using position sensor to measure the dynamic response of structures.Acceleration is often easier to measure than displacement or velocity.At present,researchers have confirmed the importance of using position acceleration feedback in different engineering fields.Second,under the condition of the closed-loop eigenvalues is unknown,combined with the polynomial matrix right-coprime decomposition,a parametric method of eigenstructure assignment for descriptor second-order linear system is proposed.The parameterized expressions provide the degree of freedom of the system and can be used for the robustness design of the system.The algorithm is simple,effective,small in computation and accurate in solving process.It can be used in the design of controllers for descriptor second order dynamical systems.Third,a new robust performance index of descriptor second-order system to improve robustness is proposed.On the basis of the parametric method,the performance index can makesthe eigenvalues of the closed loop to be optimized with the desired regions,besides having the desired eigenvalues,but also hope that eigenvalues are insensitive to parameter perturbation.Different from the previous work,the optimization of the feedback gain matrix is increased,and the larger control input is prevented from being applied to the control system.