Test Signals Ananlysis And Study For Multivariable System Identification

The fundamental problem in all kinds of predictive control is how to choose an appropriate functional model which reflects the characteristic of the control system. The primary method to acquire a valuable functional model in the current industry is system identification. And the key to obtain a worthful result of correct identification is choosing rightly recognizable test signals. In this dissertation, some problems of test signals of system identification are intersively studied and discussed. The main results can be summarized as follows:(1) The statistical properties of least squares method are analyzed. For the unbiasedness and consistency of least-squares estimator, the sufficient and necessary condition is proposed. Then the relationship between disturbance and identification result is discussed.(2) From the definition of identifiablility, the input signal is persistently exciting of order 2n is the sufficient condition but not the neccessary condition of a process. It can be the neccessary condition when the least squares method is taken as the main identificaition method.(3) A design method of pseudo random binary sequence (PRBS) for multivariable system is proposed. To the multivariable system whose stable time of each variable is different from each other, it shortens the length of test signal after we make the improvement. The white noise generalized binary noise is proposed. This signal has the same properties as white noise. And it is easy to create. It can be used as test signal in system identification.(4) A multifrequency binary sequence (MBS) whose frequency is concentrated on both high frequency band and low frequency band is proposed. For multivariable system which is made up of some high frequency variables and low frequency variables, this method can improve identification accuracy. (5) Aim at the multivariable system which has constrains on both inputs and outputs, the design methods for test signals are proposed both in steady state and dynamics system. This method can improve signal-to-noise ratio. To the closed-loop dynamic process constrained system, divided the process into steady stage and dynamic stage, and test signals are designed for the both stages.(6) Based on asymptotic theory (ASYM), a design method for the test signals of multivariable system is proposed. For the four fundamental problemsof identifucation, such as test signal design for control, model structure selection, model order and parameter estimation, four steps are used. This method has preferable identification accuracy and stable numerical value. At the same time, it is easy to handle. The industry system with color noise can be identificate use this method.