基于时域的分数阶PID广义预测控制算法改进及其仿真研究
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摘要
PID调节器作为一种应用广泛的控制器,具有原理简单,适用面广等优势,但是,很多系统对象的模型比较复杂,传统的PID控制对时变,非线性系统不能达到控制要求。分数阶PID控制器较传统整数阶PID控制器增加了两个可调参数,使得其控制器的设计更加灵活,控制性能更加优良。广义预测控制(Generalized Predictive Control, GPC)采用多步输出预测,需要获取的大量的信息,需要在线对控制矩阵求逆和求解丢番图方程,实时性比较低,因此对广义预测控制算法进行改进具有重要意义。
本文分析了分数阶PID算法(FOPID)在工程实践中的应用,验证其优越性与实用性。在验证了FOPID控制算法优越性的基础上,并从已有学者研究出的PID算法和模型控制算法相结合推导出的各种新算法的过程中得到启发,提出算法的进一步改进,即FOPID-GPC算法,这种算法既具有FOPID算法的优点,稳定性好,又具有预测功能。文中给出了算法的具体推导过程,并以双容水箱液位控制系统和锅炉过热蒸汽控制系统两大典型系统为例,通过改进后的算法对这两个控制系统的数学模型进行仿真研究,在时域内讨论了FOPID-GPC控制器在参数的选择上对控制性能产生的影响,并通过Matlab仿真说明了FOPID-GPC算法比基本PID算法、GPC算法以及PIDGPC算法控制性能更好。本文尝试将改进算法应用于水箱液位控制系统以及锅炉过热蒸汽系统中,为探索新型控制算法在工程实践中的应用打下一定的理论基础。
As a widely used controller,the PID regulator has the advantages of simple principle,wide application range and so on,however,many models of the system's objects are complex,the traditional PID controller can not meet the control requirements that in controlling the nonlinear time variant system.Fractional order PID controller adds two adjustable parameters so that it is better than the traditional integer order PID controller, the controller design is more flexible,and it has more excellent control performance. Generalized predictive control (GPC) take multi step predictive output, and it needs to obtain a large mount of information, control the inverse matrix and compute the Diophantine equation, generalized predictive control has low realtime feature, so it is important to improve the generalized predictive control algorithm.
This paper analyzes the use of fractional PID algorithm (FOPID) in the application of engineering practice, and it verified the superiority and practicability of the algorithm,it get inspired On the base of verified the FOPID control algorithm superiority and from the scholars that had studied all sorts of new algorithm process derive by the combine of the PID algorithm and model control algorithm,the paper improve the algorithm that named FOPID-GPC algorithm, the algorithm has the advantage of good stability that containted by FOPID algorithm, and has forecast function. This paper shows the specific derivation process of the algorithm, and take ed two typical systems of the double tank water level control system and the boiler superheated steam control system as an example,it used the improved algorithm and the two mathematical model of control system simulation in time domain analysis,the select of FOPID-GPC controller parameters on control performance, through Matlab simulation illustrates the FOPID-GPC algorithm has better control performance than the basic PID algorithm, GPC algorithm and PIDGPC algorithm. This paper attempts to apply the improved algorithm in tank liquid level control system and the boiler superheated steam system, to explore a new control algorithm in the application of engineering practice to lay a theoretical foundation.
本文分析了分数阶PID算法(FOPID)在工程实践中的应用,验证其优越性与实用性。在验证了FOPID控制算法优越性的基础上,并从已有学者研究出的PID算法和模型控制算法相结合推导出的各种新算法的过程中得到启发,提出算法的进一步改进,即FOPID-GPC算法,这种算法既具有FOPID算法的优点,稳定性好,又具有预测功能。文中给出了算法的具体推导过程,并以双容水箱液位控制系统和锅炉过热蒸汽控制系统两大典型系统为例,通过改进后的算法对这两个控制系统的数学模型进行仿真研究,在时域内讨论了FOPID-GPC控制器在参数的选择上对控制性能产生的影响,并通过Matlab仿真说明了FOPID-GPC算法比基本PID算法、GPC算法以及PIDGPC算法控制性能更好。本文尝试将改进算法应用于水箱液位控制系统以及锅炉过热蒸汽系统中,为探索新型控制算法在工程实践中的应用打下一定的理论基础。
As a widely used controller,the PID regulator has the advantages of simple principle,wide application range and so on,however,many models of the system's objects are complex,the traditional PID controller can not meet the control requirements that in controlling the nonlinear time variant system.Fractional order PID controller adds two adjustable parameters so that it is better than the traditional integer order PID controller, the controller design is more flexible,and it has more excellent control performance. Generalized predictive control (GPC) take multi step predictive output, and it needs to obtain a large mount of information, control the inverse matrix and compute the Diophantine equation, generalized predictive control has low realtime feature, so it is important to improve the generalized predictive control algorithm.
This paper analyzes the use of fractional PID algorithm (FOPID) in the application of engineering practice, and it verified the superiority and practicability of the algorithm,it get inspired On the base of verified the FOPID control algorithm superiority and from the scholars that had studied all sorts of new algorithm process derive by the combine of the PID algorithm and model control algorithm,the paper improve the algorithm that named FOPID-GPC algorithm, the algorithm has the advantage of good stability that containted by FOPID algorithm, and has forecast function. This paper shows the specific derivation process of the algorithm, and take ed two typical systems of the double tank water level control system and the boiler superheated steam control system as an example,it used the improved algorithm and the two mathematical model of control system simulation in time domain analysis,the select of FOPID-GPC controller parameters on control performance, through Matlab simulation illustrates the FOPID-GPC algorithm has better control performance than the basic PID algorithm, GPC algorithm and PIDGPC algorithm. This paper attempts to apply the improved algorithm in tank liquid level control system and the boiler superheated steam system, to explore a new control algorithm in the application of engineering practice to lay a theoretical foundation.
引文
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