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The Prediction Control Based on the Improved Grey Dynamic Model

Author: XiongWei
Tutor: DaiWenZhan
School: Zhejiang University of Technology
Course: Control Theory and Control Engineering
Keywords: GM (1,1) Verhulst Time- delay plant non-linear system
CLC: N941.5
Type: Master's thesis
Year: 2011
Downloads: 141
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Abstract


The Grey Prediction Control based on the grey dynamic model, is one of the effective method for the complex uncertain system control. In the paper, based on the improved grey dynamic model, a novel grey prediction control which combines the self-organizing fuzzy control is put forward.1. The research of enhancing grey prediction model precision.It is shown by study that the factors affecting grey prediction model primarily are the smooth degree of primarily date sequence, the background value and the initial value of grey model. In order to increase grey model precision, the research is conducted separately:(1) Based on function arc cot(.)transformation, the method of enhancing smooth degree of data is proposed. It has been proved in theory that the sequence after arc cot(.) transformation can not only meet the conditions of modeling GM(1,1), but the smooth degree of discrete sequence after been transformed by arc cot(.) transformation is much better than that after been transformed by other transformations.(2) An algorithm that based on the optimal value of background is put forward. The method is applied to build a classical non-equidistance model relating the titanium alloy color and its temperature. The practical application shows the effectiveness of the proposed method.(3) Enhancing grey prediction model precision from two aspects. Firstly, It has been proved that the discrete-time sequence transformed by cot(.)α(α> 0)can meet the condition of modeling GM(1,1), moreover, the smooth degree of discrete-time sequence transformed by cot(.)α(α> 0)is better than that of discrete-time sequence transformed by other functions. Then, the background value is rebuilt by optimization, which fatherly enhances the precision of grey prediction model. 2. The research of enhancing grey Verhulst prediction model precision.It is shown by study that the factors affecting grey prediction Verhulst model primarily are the background value and model structure parameterα. In order to increase grey Verhulst model precision, the research is conducted separately:(1) Firstly, the cause of grey Verhulst model’s inaccuracy is analyzed. Secondly, the background value is rebuilt by using original data sequence. Thirdly, model structure parameterαis obtained by optimization,which based on the principle about information overlap of grey system. Finally, the improved-grey Verhulst modeling is applied for building the model of national production of crude oil and results show its effectiveness.(2) An unequal interval grey Verhulst model based on rebuilt- background value is proposed. Based on the study of background value, it is proved that the former method of constructing background value is a main cause of model’s inaccuracy. So a novel approach for reconstructing background value is put forward by integrating.The approach is applied in unequal interval grey Verhulst modeling and simulation result show it is of very high precision.3. The research of predictive control based on improved grey prediction model.(1) For large time- delay plant, the algorithm of self-turning grey fuzzy predictive controller based on arc cot(.) transformation is presented. The dynamic response of system is divided into several control areas based on both current error and the change of error, and the different predictive length is given for different area. The output of fuzzy controller dependents on the sum of current error and predictive error.(2) Self-adjusting PID controller based on GM (1, 1) Model and BP neural network is proposed for nonlinear system with time delay. The step-varying fourth order Runge-Kutta and GM(1,1)grey model are introduced for predictive model, and three parameters of PID controller are erected by BP neural network self-learning,Δu is adjusted by error function e ( k + d)for the system output to trace input value. Simulation result shows its effectiveness.

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