Research Of Modal Computing Method Of Output Feedback Control Gain Matrix In Structural Pole Assignment

With the development of the science and technology, structure vibration control has been an important research field due to its urgent application need in actual engineering structures. Active vibration control has received considerable attention in recent years at homes and overseas because of its excellent advantages.This dissertation deals with the modal control method of the pole assignment of the discrete eigenvalue,the control for local vibration method and related issues in a more in-depth theory and research, mainly composed of two parts :1. The two pole assignment control method: state feedback control and output feedback control. In the structure of the state space, under two control methods, studying the relationship between the pole assignment and the controllability and observability of the vibration control system, i.e. the relationship between the complete the controllability and observability of the vibration control system and all the pole with corresponding eigenvector dispensability or some pole with corresponding eigenvector dispensability.2. Between the vibration control system and the assignment control of a part of eigenvalue and their eigenvector, study pole assignment in output feedback control. Through this, the method is got, which is simple, enforceable output feedback control gain matrix account method. Make the part vibration of the structure controlled that not influence vibration action of the other part, i.e. output feedback control gain matrix modal arithmetic. This is the main part of this research.The research work of this thesis consists of seven chapters:1) On the basis of reading extensive literatures, summarize the development of the modal control and the method application in some areas.2) In the state space, under original coordinate and modal coordinate; establish state space equation, base on space equation, and study the state space of the structure vibration analysis and control; the controllability and observability analysis of vibration system and the controllability and observability theory of the feedback control system.3) Researches on the state feedback and pole assignment in the state space of the vibration control system; relations between the pole assignment under the control of the state feedback and the controllability and observability of the vibration control system and the computational method of the output feedback control gain matrix which need to be researched.4) Researches on the output feedback and pole assignment in the state space of the vibration control system; relations between the pole assignment under the control of the output feedback and the controllability and observability of the vibration control system and the computational method of the output feedback control gain matrix which need to be researched.5) In the state space of the control system, the structural state equation under the modal coordinates is set up according to the structural finite element equation; choosing methods according to the eigenvalue and eigenvector which is controlled; researches on the method of assigning the poles under the output feedback control, using the open-loop system vector projecting method and the least energy distribution method; in the modal coordinates, researches on the modal computing methods of the output feedback gain matrix under the open-loop system eigenvector projecting method and the least energy distribution method.6) Take cantilever beam for example, based on Euler beam's finite element model and equation of the cantilever beam for applying Euler subjunctive to analyze and operate. In the state space of structural vibration control system, building the state space equation, analysis controllability and observability of control system and accounting modal's all eigenvalues and all eigenvectors, using method of output feedback control in pole assignment of vibration system. The deformation of a structure is caused mainly by the response of the lower modes, and the amplitude responses of higher modes are very small in contrast to the lower modes. So we mainly study the control of the lower modes. Firstly build finite element equation of structure and respective state space equation, compute some lower order modes. The goal is to control some lower modes and almost not to disturb the other modes. Secondly select control force distribution matrix B and sensor distribution matrix C and guarantee the system is controllable and observable. In order to keep the structure stable and protect from spill over, which means actuators and sensors are collocated, and request those actuators only generate translational force, which means only adding translational controls. Thirdly build state space equation under part of modal coordinates, Utilizing two important methods of modal computing method of output feedback control gain of projection method of open-loop system vectors of reassigned poles and minimum energy assignment to compute output feedback gains, and then apply the feedback gains to original state space equation of structure. From the control effects we obtain the results which we want. Under two control methods, the output feedback gains are computed by using original structural state space equation, four-order, six-order and eight-order state space equation of modal coordinates for first two eigenvalues assignment of original structure, respectively, and then apply those gains obtained under modal coordinates to original structural state space equation. Comparing the control effect of modal gains with one of original gain, it is verified that modal computing method is available.7) The research work of this thesis is summarized, and future work on passive/active vibration control with modal control is proposed.