Discrete Control Simulation of Agitation Tank Based on Taylor Finite Difference

doi:10.16182/j.issn1004731x.joss.201803032

Abstract

Abstract: Zhang dynamics is used to solve the system equations of the agitation tank to get controllers. At the same time, Taylor finite difference method is used in the computer discrete control simulation for the agitator tank system. In addition, the convergence stability of Zhang dynamics applied to the agitation tank is proved through theoretical analysis. In order to achieve the draining purpose for the agitation tank, the computer discrete control simulation is conducted by means of MATLAB. For comparison, the computer simulation based on the neural network predictive controller is carried out. The comparative simulation results substantiate the effectiveness and high precision of the presented method. Moreover, compared with the ode45, Taylor finite difference method can decrease system functional evaluations and has easier software and hardware implementations.

Key words: Zhang dynamics, agitation tank, Taylor finite difference, discrete control

CLC Number:

TP391.9

Zhang Yunong, Ding Yaqiong, Li Le, Zhang Deyang, Qiu Binbin. Discrete Control Simulation of Agitation Tank Based on Taylor Finite Difference[J]. Journal of System Simulation, 2018, 30(3): 1023-1029.

References 18

[1]	肖洋轶, 石万凯, 刘敬, 等. 混砂车搅拌罐内混合过程的数值模拟[J]. 长安大学学报(自然科学版), 2014, 34(2): 120-126. Xiao Yangyi, Shi Wankai, Liu Jing, et al. Numerical simulation of mixing process in stirred tank of blender truck [J]. Journal of Chang’An University(Natural Science Edition), 2014, 34(2): 120-126.
[2]	晁冰, 程继夏. 中国清洁生产的发展进程及存在问题探讨 [J]. 绿色科技, 2013 (2): 141-143. Chao Bing, Cheng Jixia. Development process and existing problems of clean production in China[J]. Journal of Green Science and Technology, 2013(2): 141-143.
[3]	Bi J, Liu D, Zhan K.PID parameters optimization for liquid level control system based on genetic algorithm[J]. International Journal of Digital Content Technology and its Applications (S1975-9339), 2012, 6(1): 361-368.
[4]	Ge S S, Hang C C, Zhang T.Nonlinear adaptive control using neural networks and its application to CSTR systems[J]. Journal of Process Control (S0959-1524), 1999, 9(4): 313-323.
[5]	任竞尧, 邱俊乔, 王英, 等. 多输入多输出非线性系统ZG控制方法框架展望[J]. 大连大学学报, 2014, 35(6): 27-29. Ren Jingyao, Qiu Junqiao, Wang Ying, et al. Framework and outlook of ZG control method for multiple-input and multiple-output nonlinear systems [J]. Journal of Dalian University, 2014, 35(6): 27-29.
[6]	Zhang Y, Li M, Yin Y, et al.Controller design of nonlinear system for fully trackable and partially trackable paths by combining ZD and GD[C]// Proceedings of the 25th Chinese Control and Decision Conference, 2013: 209-214.
[7]	Zhang Y, Chen D, Yin Y, et al.ZG tracking control of Lu system with multiple inputs and with division-by-zero problem solved[C]// Proceedings of the 2014 IEEE Chinese Control Conference, 2014: 3477-3482.
[8]	Zhang Y, Chen J, Yu X, et al.ZG controllers of z2g0 and z2g1 types for tracking control of IPC mathematical model[C]// Proceedings of the 3rd IFAC International Intelligent Control and Automation Science Conference, 2013: 472-477.
[9]	Zhang Y, Yu X, Yin Y, et al.Singularity-conquering ZG controllers of z2g1 type for tracking control of the IPC system[J]. International Journal of Control (S0020-7179), 2014, 87(9): 1729-1746.
[10]	Zhang Y, Luo F, Yin Y, et al.Singularity-conquering ZG controller for output tracking of a class of nonlinear systems[C]// Proceedings of the 32nd Chinese Control Conference, 2013: 477-482.
[11]	Zhang Y, Liu J, Yin Y, et al.Zhang-gradient controllers of Z0G0, Z1G0 and Z1G1 types for output tracking of time-varying linear systems with control-singularity conquered finally[C]// Proceedings of the 10th International Neural Networks Conference, 2013: 533-540.
[12]	Hagan M T, Demuth H B, De Jesus O.An introduction to the use of neural networks in control systems[J]. International Journal of Robust and Nonlinear Control (S1049-8923), 2002, 12(11): 959-985.
[13]	孙彪, 孙秀霞. 一种新的趋近律离散滑模控制方法及仿真[J]. 系统仿真学报, 2010, 22(10): 2422-2425. Sun Biao, Sun Xiu-xia. New algorithm of reaching-law discrete-time sliding mode control and simulation [J]. Journal of System Simulation, 2010, 22(10): 2422-2425.
[14]	Zhang Y, Jin L, Guo D.Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization[J]. Journal of Computational and Applied Mathematics (S0337-0247), 2015, 273: 29-40.
[15]	董海峰, 孔文聪. 泰勒公式及其应用[J]. 课程教育研究, 2013 (30): 185-187. Dong Haifeng, Kong Wencong. Taylor’s formula and its application [J]. Course Education Research, 2013 (30): 185-187.
[16]	苗文静, 王昕. 关于泰勒公式及其应用的思考与讨论[J]. 哈尔滨师范大学自然科学学报, 2013, 29(5): 18-21.Miao Wenjing, Wang Xin. The thinking and discussion on the Taylor’s theorem and its application [J]. Natural Science Journal of Harbin Normal University, 2013, 29(5): 18-21.
[17]	Mathews J H, Fink K D.Numerical Methods Using MATLAB[M]. Englewood Cliffs: Prentice-Hall, 2004.
[18]	张雨浓, 杨逸文, 陈轲, 等. 梯度神经网络求解Sylvester方程之MATLAB仿真[J]. 系统仿真学报, 2009, 21(13): 4028-4031, 4037. Zhang Yunong, Yang Yiwen, Chen Ke, et al. MATLAB simulation of gradient-based neural network for Sylvester equation solving [J]. Journal of System Simulation, 2009, 21(13): 4028-4031, 4037.