Smooth Dynamic System Structure Parameters And Identification Of Active Control Law Research

Parameter identification, a special technology developed along with the booming of digital signal processing and modern control theory in the1960s, is mainly applied into the subjects such as system fault diagnosis, finite element model modification and dynamic characteristic assessment. Yet as a significant technology, the theory of parameter identification is still not mature enough. In this case, we put our emphasis on the study of dynamic system’s parameter identification, which concretely includes the consideration of identification model and the construction of identification algorithms against the dynamic coefficients like mass, damping and stiffness as well as the active control rules like feedback gain and time delay.The principle job of parameter identification is the consideration of identification model, which is the premise of accurate characterization of dynamic systems. According to the numerous algorithms booming at present, the model can be divided into three parts, they are linear mode, nonlinear mode and active control mode respectively. In these modes, linear mode mainly adopts the state-space model in modern control theory so that it has unique mathematic expression and full grown theoretical support. But as to the other modes, they are still lack in general mathematic expressions.So we attempt to generalize the expression for the problem of system identification. Under the assumption of smooth constitutive function, the identification model can be described by a standard Kronecker product through Taylor expansion. Its linear degenerated form is the well-known state space function. And we adopt Orlov’s linear state feedback model for the expression of active control mode. Thereafter, the identification algorithms are all constructed based on these general modes.We firstly take the linear problem for research. As a preliminary solution, we utilize complete modal information to construct a self-contained identification algorithm. This algorithm makes full use of the eigenvector’s weighted orthogonality, that’s why it has advantages as high accuracy, good noise resistance and stable maintenance of the system’s original symmetry. As a further step, we put our emphasis on the nonlinear form, a more general identification mode than the linear one. Considering the maturity and broad applicability of the harmonic balance principle, we use it to deduce the coefficient’s balance equation by some combination theory in trigonometric functions and identify all the dynamic parameters by solving the equation. In addition, this algorithm can be degenerated to the classic impedance method in linear situation.Then, we look into the identification problem of active control rule in linear mode without time delay. The frequency response function is deeply studied together with some kind of linear algebra theory so that the identifiable condition as well as identification algorithm can be obtained. The conclusion of the identifiable condition is that the number of identifiable parameters is not larger than the minor one between the square of observable modal orders and the square of monitoring points. Particularly, when the control mode is priori known, the parameters are able to be identified just from local frequency response functions. In this case, the active control rule identification of a large structure would be easily carried out. Moreover, this algorithm can be applied directly into the identification of active control with time delay, but the identifiable condition becomes more complicated.For the identification of active control rule with time delay in nonlinear mode, the principle of harmonic balance method can also be applied. However, the coefficient’s balance equation in this case will change into complex exponential form thus the equation can’t be solved explicitly. So we construct an iteration algorithm based on least square method to substitute the process of the equation’s solution. It can be proved that this algorithm can assure uniqueness of the identified time delay on a given sufficient interval by special layout of exciting frequencies.For every algorithm discussed in this paper, the efficiency and stability are all demonstrated by corresponding numerical simulations. Besides, some experiments are also carried out so that the practicality of the algorithms is verified in reality.