基于时域的分数阶PID动态矩阵控制算法研究及其应用
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摘要
模型预测控制(Model Predictive Control, MPC)是继经典控制理论和现代控制理论之后出现的一类基于模型的先进控制算法,在工业控制过程中得到广泛应用。它通过实验手段获取系统的模型,其基本思想为“模型预测——反馈校正——滚动优化”,通过系统的二次性能指标获取最优控制量。它的典型算法有三大类：模型算法控制(Model Algorithmic Control, MAC)、动态矩阵控制(Dynamic Matrix Control, DMC)、广义预测控制(Generalized Predictive Control, GPC).本文以DMC的状态空间描述为基础,主要对PID动态矩阵控制算法进行改进和研究。
相对于传统的整数阶控制,分数阶控制是一种很好的概括和补充,它使传统的控制理论更具鲁棒性,使控制系统的静态和动态特性能够得到很好的改善,并且分数阶控制器可以在频域内进行设计。因此,本文在分析分数阶PID算法和动态矩阵控制算法的基础上,推导了分数阶PID动态矩阵控制算法(Fractional-order PID Dynamic Matrix Control, FOPIDDMC).该算法既具有分数阶PID算法的优点,结构简单,参数调节方便,又具有预测功能。在时域内分析了分数阶PIDDMC控制器的参数选择对控制性能的影响,给出参数选取范围。通过仿真说明了分数阶PIDDMC算法比基本DMC算法和PIDDMC算法具有更好的控制性能。
目前,应用于EPA控制系统和电厂过热汽温系统的控制算法还是以传统PID算法为主,本文将改进的FOPIDDMC算法应用在EPA控制系统和过热汽温系统中,并在时域内分析了参数选择对系统控制性能的影响,为今后的工程实践打下基础。
此外,大多数工业过程被控对象都有延迟特性,因为网络引入的通信延迟能导致系统性能退化甚至不稳定。针对这种网络控制系统中的延迟,本文分析了导致时延的原因,并引入时间标记的PIDDMC算法(Time-stamped PID Dynamic Matrix Control, TSPIDDMC),建立随同时间标记的通信延迟模型。通过时间标记测量网络延迟,在线校正系统的阶跃响应系数和控制系数,并给出了算法的推导过程。仿真实验证明,针对文章所研究的延迟,这种新算法能得到比PIDDMC算法更好的控制性能,改进了网络控制系统的可靠性。
Model predictive control is a type of advanced control algorithms based on model after the typical control algorithm and the modern control algorithm. It has been widely used in industrial process control. The models in this algorithm are gained through experimental methods. The main ideas of the algorithm are "model predicting—feedback revising—rolling optimizing". By calculating the quadratic performance index of the system, the optimal control variable will be got. The typical algorithms of model predictive control are model algorithmic control (MAC), dynamic matrix control (DMC), generalized predictive control (GPC). In this paper, base on State Space description of DMC, our discussions mainly focus on improving and researching PIDDMC algorithm.
The factional-order control is supplement and summary to the traditional integer-order control theory. It makes the traditional control theory better in simulation and robustness and makes the static and dynamic performs of the control system can be improved. What's more, the fractional-order controller can be designed within the frequency domain. Base on analyzing the two control algorithm, this paper derives Fractional-order PID Dynamic Matrix Control (FOPIDDMC) algorithm. This algorithm has not only the advantage of the fractional-order PID, which is reliable in operation and convenient in regulating parameters, but also the prediction function. Simulation results show that this algorithm is better than basic DMC algorithm and PIDDMC algorithm in many performances.
At present, the algorithm applied in EPA control system and superheated temperature system of power plants is mainly traditional PID algorithm. In this paper, the improved FOPIDDMC algorithm is applied in EPA control system. The influence of FOPIDDMC controller parameter tuning on system performance is investigated in time domain, which lays a good foundation for future engineering practice.
Most industrial processes have characteristic of time delay. The communication delay introduced by the networks can lead to performance degradation and even instability. To address network-induced delays, a time-stamped PID dynamic matrix control (TSPIDDMC) algorithm which uses a communication delay model to improve reliability over network control systems is proposed. The network-induced delays are measured by a time-stamp method, based on which the step response coefficients and control coefficients ate corrected in each sampling period and the algorithm derivation is given. Simulative validation of this new algorithm resulted in improved performance and stability over PIDDMC control.
相对于传统的整数阶控制,分数阶控制是一种很好的概括和补充,它使传统的控制理论更具鲁棒性,使控制系统的静态和动态特性能够得到很好的改善,并且分数阶控制器可以在频域内进行设计。因此,本文在分析分数阶PID算法和动态矩阵控制算法的基础上,推导了分数阶PID动态矩阵控制算法(Fractional-order PID Dynamic Matrix Control, FOPIDDMC).该算法既具有分数阶PID算法的优点,结构简单,参数调节方便,又具有预测功能。在时域内分析了分数阶PIDDMC控制器的参数选择对控制性能的影响,给出参数选取范围。通过仿真说明了分数阶PIDDMC算法比基本DMC算法和PIDDMC算法具有更好的控制性能。
目前,应用于EPA控制系统和电厂过热汽温系统的控制算法还是以传统PID算法为主,本文将改进的FOPIDDMC算法应用在EPA控制系统和过热汽温系统中,并在时域内分析了参数选择对系统控制性能的影响,为今后的工程实践打下基础。
此外,大多数工业过程被控对象都有延迟特性,因为网络引入的通信延迟能导致系统性能退化甚至不稳定。针对这种网络控制系统中的延迟,本文分析了导致时延的原因,并引入时间标记的PIDDMC算法(Time-stamped PID Dynamic Matrix Control, TSPIDDMC),建立随同时间标记的通信延迟模型。通过时间标记测量网络延迟,在线校正系统的阶跃响应系数和控制系数,并给出了算法的推导过程。仿真实验证明,针对文章所研究的延迟,这种新算法能得到比PIDDMC算法更好的控制性能,改进了网络控制系统的可靠性。
Model predictive control is a type of advanced control algorithms based on model after the typical control algorithm and the modern control algorithm. It has been widely used in industrial process control. The models in this algorithm are gained through experimental methods. The main ideas of the algorithm are "model predicting—feedback revising—rolling optimizing". By calculating the quadratic performance index of the system, the optimal control variable will be got. The typical algorithms of model predictive control are model algorithmic control (MAC), dynamic matrix control (DMC), generalized predictive control (GPC). In this paper, base on State Space description of DMC, our discussions mainly focus on improving and researching PIDDMC algorithm.
The factional-order control is supplement and summary to the traditional integer-order control theory. It makes the traditional control theory better in simulation and robustness and makes the static and dynamic performs of the control system can be improved. What's more, the fractional-order controller can be designed within the frequency domain. Base on analyzing the two control algorithm, this paper derives Fractional-order PID Dynamic Matrix Control (FOPIDDMC) algorithm. This algorithm has not only the advantage of the fractional-order PID, which is reliable in operation and convenient in regulating parameters, but also the prediction function. Simulation results show that this algorithm is better than basic DMC algorithm and PIDDMC algorithm in many performances.
At present, the algorithm applied in EPA control system and superheated temperature system of power plants is mainly traditional PID algorithm. In this paper, the improved FOPIDDMC algorithm is applied in EPA control system. The influence of FOPIDDMC controller parameter tuning on system performance is investigated in time domain, which lays a good foundation for future engineering practice.
Most industrial processes have characteristic of time delay. The communication delay introduced by the networks can lead to performance degradation and even instability. To address network-induced delays, a time-stamped PID dynamic matrix control (TSPIDDMC) algorithm which uses a communication delay model to improve reliability over network control systems is proposed. The network-induced delays are measured by a time-stamp method, based on which the step response coefficients and control coefficients ate corrected in each sampling period and the algorithm derivation is given. Simulative validation of this new algorithm resulted in improved performance and stability over PIDDMC control.
引文
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[3]A.Oustaloup, X.Motreau, M.Nouillant. The CRONE suspension[J]. Control Engineering Practice,1996,4(8):1101-1108.
[4]Matignon. Stability results for fractional differential equations with applications to control processing[C]. Computational Engineering in Systems and Application Muticonference. Lille:IMACS IEEE-SMC,1996,963-968.
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[6]Podlubny I. Fractional-order systems and PIλDμ controllers[J]. IEEE Transactions on Automatic Control,1999,44(1):208-214.
[7]Valerio D, Sa'da Costa J. Time-domain implementation of fractional order controllers[J]. IEEE Proceedings:Control Theory and Applications,2005,152(5):539-552.
[8]Zhao, C., Xue, D.,&Chen, Y.Q.. A fractional order PID tuning algorithm for a class of fractional order plants[J]. Proc.of the IEEE ICMA,2005,216-221.
[9]朱呈祥,邹云.分数阶控制研究综述[J].控制与决策,2009,24(2)：162-169.
[10]Kalman, R. E.. Contributions to the theory of optimal control[J]. Bulletin de la Societe Mathematique de Mexicana,1960,5:102-119.
[11]Kalman, R. E.. A new approach to linear filtering and prediction problems[J]. Transactions of ASME, Journal of Basic Engineering,1960,87:35-45.
[12]Propoi, A. I.. Use of linear programming methods for synthesizing sampled-data automatic systems[J]. Automatic Remote Control,1963,24 (7):837-844.
[13]Lee, E. B., Markus, L.. Foundations of optimal control theory[M]. New York:Wiley,1967.
[14]Richalet, J., Rault, A., Testud, J. L., Pagon, J.. Model predictive heuristic control: applications of industrial processes[J]. Automatica,1978,5:413-428.
[15]Rouhani, R., Mehra, R. K.. Model algorithmic control (MAC)[J]. Basic Theoretical Properties[J]. Automatica,1982,4:401-414.
[16]Culter, C.R.. Ramaker, B.L.. Dynamic matrix control-a computer control algorithm[J]. AIChE National Meeting, Houston, TX, April,1979.
[17]Clark, D. W., Mohtadi, C, Tuffs, P. S.. Generalized predictive control[J]. Automatic,1987, 23(2):137-160.
[18]Lelic M A, Zarrop M B. Generalized Pole Placement Self-running Controller[J]. Int J Control,1987,46(2):547-568.
[19]Mills, P. M., Zomaya, A. Y., Tade, M. O.. Adaptive model-based control using neural networks[J]. International Journal of Control,1994,60(6):1163-1192.
[20]Najim, K., Rusnak, A., Meszaros, A.. Constrained long-range predictive control based on artificial neural networks[J]. International Journal of System Science,1997, 28(2):1211-1226.
[21]张海龙.基于神经网络的智能预测控制理论研究[D].大庆石油学院,2009.
[22]李志斌.一种基于RBF神经网络预测模型的DMC预测控制[J].科学技术与工程,2010,10(7)：1644-1647,1651.
[23]Abonyi, J., Nagy, L., Szeifert, F.. Fuzzy model-based predictive control by instantaneous linearization[J]. Fuzzy Sets and System,2001,120(1):109-122.
[24]Liu, B., Shen, Q., Su, H. Y., Chu, J.. A nonlinear predictive control algorithm based on fuzzy on-line modeling and discrete optimization[A]. Proceedings of the IEEE International Conference on Systems, Man and Cybernetics,2003,816-822.
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