Research On System Identification And Their Application In Control

System identification can identify the mathematical model by input and output data, while accurate mathematical model system is the premise of the traditional control theory, Therefore the accuracy of system identification will greatly affect the quality of control. With the development of the system identification,data-driven control gradually attract academic attention,utilizing input-output data to identify a suitable controller is the feature of the data-driven control.Subspace predictive control and virtual reference feedback control are typical data-driven control methods. Under the framework of system identification theory, this thesis propose several novel identification methods aiming at the common linear and nonlinear system model, at the same time the paper conduct deep discussion and research according to subspace predictive control and virtual reference feedback control.The main work of the thesis is as follows.For linear regression models, the conventional least squares estimation under the colored noise can’t get unbiased estimates of unknown parameters,the paper get an unbiased estimate through proposing a separable iterative recursive identification algorithm. Considering an unknown bounded noise sequence for the linear regression model,a novel least squares algorithm with dead zone is proposed to deal the noise.The simulation results show that the algorithm has better convergence. Aiming at the identification of linear system with measurement noise of input and output signals,a new filtering method is raised to deal it. The simulation result shows the effectiveness of the algorithm.Finally for the problem of the model structure inspection of closed-loop identification of linear systems, the bound of uncertainty of model parameters and the cross-correlation function are contructed according to the asymptotic variance matrix product of unknown parameters under the prediction error identification method. The optimal input filter is derived from the perspective of optimizing. The simulation results show the effectiveness of the algorithm.For nonlinear system identification, unknown weights regarding the input observational data is added to the affine linear function of direct weighting method, therefore there are two types of unknown weights playing the role of approximating the original nonlinear system in the identification algorithm, Also convergence of the proposed algorithm is proved by simulation. For direct weighting method,the second part choose the probability of estimation error border less than a specified threshold for the norm of approximation error, the unknown weights were derived by an explicit expression. Finally, simulation examples demonstrate the effectiveness of the proposed algorithm.Aiming at virtual reference feedback tuning control(VRFT),two controllers is designed through input and output data under unknown system model,at the same time the given desired closed-loop transfer function and the sensitivity function is taking into account.The controller parameters is derived by iterative least identification based on optimization. The simulation results show the effectiveness of the proposed method. The asymptotic variance matrix expression vector of unknown parameters can be derived from the probability of statistical significance in statistics according to virtual reference feedback tuning control. This matrix can be used as the basis of the optimal filter design, it can also test accuracy of the controller.For random state-space model with fault, subspace identification method is used to indicate future output data by past and present input- output observational data.Then the transfer function between fault and residual error can be established. Based on this relationship, an optimization problem with constraints can be obtained by solving the fault estimate. The control input and output variables constraints are added to the quadratic cost function of predictive control. The process of fast gradient optimization algorithm theory is according to the structural characteristics of constrained optimization problems.The control input can be derived from optimizing the the quadratic cost function. Meanwhile for the form of affine linear control input, affine constraints of control variables is added to the quadratic cost function,the affine item and gain item of control input can be solved by an optimization problem. Simulation results show effectiveness of the proposed method.