| System identification plays a very significant role in the control theory and control science. In the modern industrial processes, most of controllers are designed based on the transfer function model, like PID controller, internal model controller (IMC), Smith predictor. Considering the needs of the controller design, the low order models are widely used in industrial processes since less parameters are beneficial to controller design, and the high-order system can be fitted efficiently by low-order model. Therefore the identification of low-order transfer function models, especially the low-order transfer function models with time delay, is crucial tool for us to fully understand the industrial process and realize the control and set-point tracking of industrial process. For control-oriented model identification in industrial engineering applications, this paper study some common industrial processes, like the first-order transfer function model with time delay, the second-order under-damped, critical damping, or damping transfer function model with time delay. The innovation research in the thesis as follows:(1) A step response identification method is proposed for common industrial processes with time delay from sampled data by developing a gradient searching approach to minimize the output prediction error. The essential point is that a step test is performed firstly to collect the input and output data. Based on constructing a transcendental equation set of the time domain expression of step response, a gradient-based algorithm is proposed to simplify the transcendental equations to polynomial equation realizing a least-squares fitting. The computation effort can be significantly reduced and the estimation precision is improved compared to the existing step identification methods based on using the time integral approach for model fitting. Five illustrative examples from recent references are used to show the effectiveness of the proposed method.(2) An auxiliary model is used in the algorithm to weaken the influence of noise. The convergence and consistency of the proposed algorithms are analyzed with a strict proof. By analyzing the convex of cost function under different excitation, a conclusion can be derived that the cost function has a larger convex domain under step excitation. Based on that conclusion, convergence and robustness analysis of the proposed methods are deduced with strict theoretical demonstration.(3) An attempt is performed by introducing an auxiliary function to realize the global optimization. The principle is transforming non-convex function optimization problem into a series of convex function optimization problems. By reducing auxiliary parameters gradually, the auxiliary function approaches the target function step by step. The algorithm is derived in detail for the first-order transfer model with time delay, along with the analysis of convergence and consistency. The illustrative examples demonstrate the performance of the proposed methods.In conclusion, in this paper, a step response identification method is proposed for common industrial processes with time delay from sampled data by developing a gradient searching approach to minimize the output prediction error. The illustrative examples from recent references demonstrate the good performance of the proposed methods in precision and robustness, while the computation effort can be significantly reduced compared to the existing step identification methods based on using the time integral approach for model fitting. Then an attempt is performed by introducing an auxiliary function to realize the global optimization, along with some illustrative examples and convergent analysis. Some conclusions are drawn in the end, together with the further research of the paper. |
