Parametric Eigenstructure Assignment For Linear Systems And Active Control Of Vibration

With the system getting increasing complex, the dimension is becoming higher and higher, which leads to the rapid increase of the work of system analysis and design--" dimension disaster ". It not only causes the heavy load of the computer, but also is difficult to satisfy the request for online real-time control. In the course of linear systems control design, there are two methods to solve this kind of problem, parallel computation and predigestion. This dissertation researches eigenstructure assignment method according to above two methods, and applies the research results to the vibration system in order to reduce the amplitude. So the research problems can be summarized as follows.1): How to decrease compute workload; improve compute speed of the feedback matrix?2): How to reduce the amplitude, while making eigenstructure assignment applied for vibration systems?To solve the above-mentioned problems, several aspects of research have been carried out in this dissertation, with the following ones to be innovative. First, the parallel parameter eigenstructure assignment method is designed. Comparing with the traditional eigenstructure assignment, this method cannot only parallel compute to improve the computational speed, but also reduce some limits. Meanwhile it also can assign partial poles, and make the application of eigenstructure assignment easier in the practice. The author also applied this method to the robust eigenstructure assignment, and proved it feasible through numerical simulation. Utilizing the particularity of the proportion damping system, a special parameterize eigenstructure assignment method is designed and analyzed in this dissertation. This method is to transform the proportion damping system into modal space to calculate, which needn't change two orders vibration systems into one order state equations. In the modal space, the eigenvector assignment and eigenvalue assignment are carried on separately. While eigenvalues are assigned accurately, the eigenvectors are expressed with parameter. The author also studied the application of the dominant modes parameterize method in the question of adverse eigenvalue, and discussed the dominant modes eigenstructure assignment with restriction.Second, the dominant mode eigenstructure assignment method is designed in order to decrease computation. In the vibration system, systematic displacement responses are mainly determined by the dominant mode. Therefore, only the dominant modes are optimized in the course of optimization, while other modes are neglected, thus the dominant mode eigenstructure assignment method can be achieved. Simulation proved that this method has better control results. The foundation of above-mentioned method is the dominant modes parameterize method designed in the paper. However, one thing has to be emphasized, that is this method has made all eigenvectors of the system changed.Third, the partial mode eigenstructure assignment method is designed. For further simplified calculation, only the dominant modes are optimized in the course of optimization while the other modes are not changed. This is partial mode eigenstructure assignment method. But simulation proves that the dominant mode eigenstructure assignment method has better control results than this method. The partial eigenstructure assignment method costs less energy. When the energy-cost is similar to quadratic optimal control, the control result is also similar to quadratic optimal control.