| With the development of technology,new high-strength materials have been used, and work environment have become more and more complex even harsh. All these lead to the vibration problems becoming acute. Vibration problems are prevalent not only in the aerospace, machinery, but also in building and other departments in the civil engineering, nuclear engineering, land and water transport, and in almost all the engineering fields. Therefore the vibration control problems of structure have become a serious problem to be solved right now. The so-called vibration control is that using certain means to make the vibration characteristics of the controlled objects meet people'requirements, according to the nature of the controlled objects, work environment and control requirements, (usually refers to the vibration suppression).There are two mainly methods of vibration control: passive control and active control. Passive control doesn't need extra energy from the outside system, so it is also named source free control. Because it's easy to achieve, economy and reliability, and making perfect in many Occasions as well as simple devices, it has been widely used in the engineering field. But with the development of technology and the requests of people to the products'vibration characteristics become higher, its shortcomings emerge gradually. This method is difficult to meet people's needs. However, active control has more potential advantages, such as good effect, strong adaptability and so on. All these make it become a new approach naturally. As far as now, any technology of passive control in vibration fields all has the corresponding methods of active control. However, the latter has more advantages and characters which the former doesn't have.Active control has been used widely in vibration field, which include open-loop system and closed-loop system. Open-loop control also named program control. The control law of this system's controller is pre-set according to the requirements that have nothing to do with the vibration states of the controlled objects. While the controller of the closed-loop system works according to the feedback information of the vibration states of the controlled objects. So it also named feedback control and is one of the most widely used types of control. Feedback is an important concept in control field. For example, if the output signals (known as the feedback signal) of the controlled objects first are operated by the controller (feedback element) and then return to the input of the system, we are saying that the system for closed-loop system. Feedback control has two advantages: first, it can amend the system that is interfered by the outside interference. Second, it can reduce the sensitivity of closed-loop system characteristics on the system's parameters changes.There are two types of feedback control: state feedback control and output feedback control. The former uses state variables as the feedback signals,which need all the information of the state variables. The latter was also named part state feedback control, namely, using the output variables as the feedback signals. One prominent advantage of the output feedback is that it's easy to implement. However, facts have proved that state feedback has better characteristics compared with output feedback. Moreover, with the development of the Observer Theory and Kalman Filtering Theory, state feedback implementation problem has been basically solved. Therefore, generally speaking, state feedback has greater applicability.In active vibration control applications, there are three popular models: State-space description, transfer function description and weight function description. In engineering, according to the difference characteristic between continuous control and discrete control, they will be presented for continuous and time discrete mathematical description. This article is based on state-space description. State-space description reflects the system's internal relations, thereby, determines the system's internal structure. It not only can determine all the internal state of system's sport, but also could be convenient to deal with the initial conditions.As the basic knowledge to solve the problem of closed-loop control system, this paper first introduce the study situation of the structural vibration control and the basic knowledge of modern control theory. Then introduce the conclusions and the method to get state feedback gain vector of the traditional single-input system. Finally, using modal control methods as well as pole allocation methods of closed-loop system, a new method for computing the feedback gain vector is presented. Because the modal equations are used to develop the modal control gains, the tedious mathematical manipulation for deducing the gain vector can be avoid. The results expressed by matrix are more intuitive than traditional method, and also more easily implemented on computers.Chapter IV bases on the gain vector expression that has been obtained in the previous chapter. First, we deduced the sensitivity analysis expression of the modal gain vector for the specified eigenvalues. And by comparing the first-order approximation and the exact value of the gain vector, we can say that the new method is validity. Second, chapter IV gives a fast method to get the approximate value of the sensitivity. The numerical example shows the validity of this method.Finally, we gave gain vector a small change, and then we solved the eigenvalues changes in turn by using the sensitivity expressions. On the one hand, when we only require the system's stability but without overshoot and transient process or when the system energy is limited, this method can provide a basis for how to select the expected eigenvalues. Thereby we can avoid the blindness. On the other hand, there are always uncertain factors in the structural engineering practices, such as the inaccuracy of the measurement, errors in manufacture and installation, or failure of some components, etc. Although in most cases errors or uncertainty are small, but if these errors and uncertainty happen together, they will produce large errors in structural analysis, especially in multicomponent system. The method given in section III of this chapter, can predict the errors of the expected eigenvalues according to the small errors of the gain vector.The numerical examples show the validity of the methods and theories of this paper. The results of this paper have an important application value for optimal design and robustness analysis of the closed-loop control system. |
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