Robust Eigenstructure Assignment In A Class Of Matrix Second-order Systems Based On Displacement-plus-acceleration Feedback

The purpose of this paper is mainly study the control law of second-order systems, Typically, The results are applied to improve the dynamic response characteristics of the mass-spring-dashpots system.Robot control, vibration control and structural dynamics can be attributed to the control and design of matrix second-order systems. With the rapid increase of the actual engineering workload, the analysis and design of the linear system is becoming more and more complex,so that traditional eigenstructure assignment method can not meet the needs of social life and modern industry with high precision and high efficiency control requirements.In the course of second-order dynamic systems control design,The best way to solve this problem is to continuously innovate the control law and the robust design index.Based on the eigenstructure assignment problem, the research problems can be summarized as follows:1) Establish the parametric expression for the feedback gain matrices use the control law which is defined beforehand.2) Propose a new robust index that can improve the robustness of the closed-system.Based on the above ideas,several aspects of research have been carried out in this dissertation, with the following ones to be innovative:First, the displacement-plus-acceleration feedbacks information is used to solve the problem of eigenstructure assignment. It is well-known that, with the rapid development of sensor technology,accelerations have been commonly obtained through the use of accelerometers.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 and singular value decomposition(SVD),a parametric method of eigenstructure assignment for second-order linear system is proposed.The algorithm can utilize the degrees-of-freedom to improve the robustness of the closed-system.it can reduce the workload of the design of system even the algorithm is simple and does not contain ‘go back’procedures.In order to Maintain the accuracy of the original system model,The main advantage of the described approach is that the problem is tackled in the second-order form.The algorithm can also improves the efficiency of the dynamic system and convenient for the design and implementation of the controller.Finally, a new robust performance index and robust pole assignment algorithm is proposed. On the basis of the parametric method,The performance index can makes the eigenvalues of the closed loop to be optimized with the desired regions,besides having the desired eigenvalues, but also hope that eigenvalues by perturbation parameter changes as small as possible,that is the closed-loop system characteristic value regarding the 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.