基于特征模型的预测函数控制及应用研究
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摘要
在过去的几十年里,模型预测控制的研究越来越受到众多专家学者的重视,在大家的共同努力下,许多重要的研究成果不断出现。模型预测控制以其鲁棒性好,具有灵活的约束处理能力,综合控制质量较高,特别适合于处理具有输入输出约束、时滞时变特性、反向特性和变目标函数的工业过程等优点,受到工业界的广泛欢迎,应用成果层出不穷。预测函数控制作为第三代模型预测控制,在保持模型预测控制优点的同时,通过引入基函数的概念增强了输入控制量的规律性,提高了响应的快速性和准确性,可有效地减少算法的计算量。然而,与其它基于预测模型的模型预测控制一样,预测函数控制仍然存在一旦预测模型与实际被控过程出现不一致时,会出现控制性能下降的问题。尽管围绕模型失配问题展开了一系列的研究,如将神经网络模型、模糊模型引入预测函数控制作为预测模型,但这样做的结果使预测模型变得复杂,增加了在线计算工作量,预测函数控制原先所具有的算法简单、运算速度快的优点失去。
针对预测函数控制的模型失配问题,本文以保证预测函数控制所具有的算法简单、运算速度快的优点为研究出发点,同时减小模型失配以保证预测函数控制的控制性能不下降为前提,提出基于特征模型的预测函数控制控制方案。特征模型通常的形式是一个二阶慢时变的线性模型,它是根据被控对象动力学特征和控制性能的要求相结合建立起来的模型,特征模型的关键特点在于模型的形式简单、易于工程实现,而且在同样输入控制作用下,对象特征模型和实际对象在输出上是等价的。特征模型这一概念是由吴宏鑫院士结合自己多年的理论研究与工程实践而提炼出来。在本文中,作者对特征模型理论开展了进一步研究,一是总结出几种特征模型获取的方法,尤其是提出了基于测试法的特征模型获取方法,以及借助于Matlab的仿真分析法。这些方法可以方便地获取被控对象的特征模型,以及在已有高阶模型的基础上,实现模型降阶。二是为了避免特征模型时变参数计算问题,引入了参数区间的概念,将二阶慢时变的线性模型等效成一族二阶线性模型,从而保证特征模型引入预测函数控制后,传统预测函数控制所具有的算法简单、运算速度快等优点不丢失。仿真结果表明,新的算法明显地优于传统的预测函数控制算法。
由于参数区间的引入使基于新算法的特征多项式系数具有不确定性参数问题,为了便于进行稳定性分析,这里利用了多项式稳定性分析理论,找到了适合于的稳定性分析的方法----多项式稳定性分析理论。借助于DCS平台构建了与生产控制相吻合的实验环境进行了实验研究,实验研究进一步表明新算法比传统预测函数控制算法具有更好的控制性能。实验中采用的DCS为浙江中控JX-300X系统,控制程序采用JX-300X系统所提供的SCX语言编写,借助于JX-300X平台可以十分方便地把控制程序移植到工业生产实际中。
本文的主要工作概括如下:
1.对特征模型获取进行了研究,提出了一些特征模型获取的新方法,包括非线性系统的特征模型获取,尤其是利用测试法获取特征模型的方法,以及借助于Matlab的仿真分析法。引入了参数区间,从而使特征模型得以进一步简化。
2.提出了基于特征模型的预测函数控制算法。新算法可以克服传统预测函数控制算法在模型失配时的有效控制问题。借助于Matlab,对新算法与传统预测函数控制算法针对多种被控对象进行仿真研究,仿真结果表明,新算法明显优于传统预测函数控制算法。
3.给出了几种针对模型匹配与模型失配的预测函数控制系统的稳定性分析方法,尤其是引入了多项式稳定性分析方法来分析基于特征模型的预测函数控制算法系统的稳定性。
4.借助于DCS平台构建了与生产控制相吻合的实验环境进行了实验研究,实验研究进一步表明新算法比传统预测函数控制算法具有更好的控制性能。实验中采用的DCS为浙江中控JX-300X系统,控制程序采用JX-300X系统所提供的SCX语言编写,借助于JX-300X平台可以十分方便地把控制程序移植到工业生产实际中。
In the past few decade, the research of model predictive control has gained more and more attention among many experts. With everyone’s effort, many critical results are constantly spoken out. Model predictive control algorithm is obsessed of some advantages like good robustness, flexible ability of constraint solution, relatively higher comprehensive controlling quality, exclusively being adapted to industry process which has input-output constraint, time-delay and time-varying characteristic, reverse characteristic and variable target function, so it is widely accepted by industrial fields and practical results are emerging in an endless stream.
As the 3rd generation of model predict control, predictive functional control maintains the advantage of model predict control, meanwhile, it strengths regularity of input controlled quantity, improved the speediness and accurateness of response by introducing the concept of base functions, which can effectively decrease calculation quantity of algorithm. However, same as other model predict control, once predict model happens not in line with actual controlled process, it would meet with degrade of controlling performance. Although a series of model mismatch research have been carried out, for example, introducing neural networks model and fuzzy model into predictive function control, this kind of operation can only make predictive model becoming more complicated, increasing online calculation quantity and depriving of all the original merits of predictive functional control like easy algorithm and fast calculation.
Considering model mismatch problem of predictive functional control, this paper sets the assurance of predictive function control obsessing the strong points of easy algorithm and fast calculation as the starting line of research. Moreover, on the premise of decreasing model mismatch in order to assure maintaining the control characteristic of predictive functional control, this paper raises control scheme of predictive functional control on the basis of the characteristic model.
The usual form of the characteristic model is a second-order slow time- varying linear model, which is built up under the combined requirements of controlled object dynamic features and control feature. The main features of characteristic model is that it has simple model form and easily practiced, besides, under same input control, object characteristic model and practical object are equivalent.
The concept of characteristic model is abstracted by Hongxin Wu academician through his long years of theoretic research and project practice. This paper developed a further study on characteristic model theory, firstly, it concluded out several methods of acquiring characteristic models, especially the method on the basis of testing and emulation analysis with the help of Matlab. With these methods we can conveniently obtain characteristic model and realize model reduction. Secondly, in order to escape the calculation problem of time-varying parameters of characteristic model, this paper introduced in a concept of parameter zone and equivalent second-order slow time- varying to a cluster of second- order linear models thus it can assure when introducing characteristic model into predictive functional control, traditional predictive function control would not lose their advantages of easy and fast calculation. The result of simulation reflects that new algorithm is obviously better than traditional one. As the introduction of parameter zone leads characteristic polynomial parameter based on new algorithm having uncertainty parameter problem, in order to carrying out stability analysis, this paper utilized polynomial stability analysis theory to find out a method being good for stability analysis --- polynomial stability analysis theory. With the help of DCS platform, we did research under an experimental environment which fits to production control, experiment research further manifests that new algorithm has better controlling features over traditional one. The adopted DCS in experiment is from SUPCON JX-300X system, control program was made from SCX language provided by JX-300X, under the help of JX-300X platform we can quite easily plant control procedure into industrial production.
The main contents of this paper are like following:
1. Research on acquirement of characteristic model, introduction of some new methods of obtaining characteristic model, including the one of non-linear, especially taking advantage of testing method and simulation analysis method under the help of Matlab. The parameter zone is introduced to further simplify characteristic model.
2. Introduced predictive function control algorithm based on characteristic model. New algorithm can conquer the effective control problem when model mismatch happened. With the help of Matlab, we did simulation research on many kinds of controlled objects by traditional algorithm and new one, the simulation results shows that new algorithm is obviously better than traditional one.
3. Some methods analyzing on system stability of predictive function control algorithm , which model match and model mismatch, were given. Especially adopting polynomial stability analysis method to analyzing on system stability of predictive function control based on characteristic model algorithm.
4. Carried on research in a production control oriented experimental environment with the help of DCS platform, experimental research further presents that new algorithm obsesses better control features then traditional one. The adopted DCS in experiment is from SUPCON JX-300X system, control procedure was made from SCX language provided by JX-300X, under the help of JX-300X platform we can quite easily plant control procedure into industrial production.
针对预测函数控制的模型失配问题,本文以保证预测函数控制所具有的算法简单、运算速度快的优点为研究出发点,同时减小模型失配以保证预测函数控制的控制性能不下降为前提,提出基于特征模型的预测函数控制控制方案。特征模型通常的形式是一个二阶慢时变的线性模型,它是根据被控对象动力学特征和控制性能的要求相结合建立起来的模型,特征模型的关键特点在于模型的形式简单、易于工程实现,而且在同样输入控制作用下,对象特征模型和实际对象在输出上是等价的。特征模型这一概念是由吴宏鑫院士结合自己多年的理论研究与工程实践而提炼出来。在本文中,作者对特征模型理论开展了进一步研究,一是总结出几种特征模型获取的方法,尤其是提出了基于测试法的特征模型获取方法,以及借助于Matlab的仿真分析法。这些方法可以方便地获取被控对象的特征模型,以及在已有高阶模型的基础上,实现模型降阶。二是为了避免特征模型时变参数计算问题,引入了参数区间的概念,将二阶慢时变的线性模型等效成一族二阶线性模型,从而保证特征模型引入预测函数控制后,传统预测函数控制所具有的算法简单、运算速度快等优点不丢失。仿真结果表明,新的算法明显地优于传统的预测函数控制算法。
由于参数区间的引入使基于新算法的特征多项式系数具有不确定性参数问题,为了便于进行稳定性分析,这里利用了多项式稳定性分析理论,找到了适合于的稳定性分析的方法----多项式稳定性分析理论。借助于DCS平台构建了与生产控制相吻合的实验环境进行了实验研究,实验研究进一步表明新算法比传统预测函数控制算法具有更好的控制性能。实验中采用的DCS为浙江中控JX-300X系统,控制程序采用JX-300X系统所提供的SCX语言编写,借助于JX-300X平台可以十分方便地把控制程序移植到工业生产实际中。
本文的主要工作概括如下:
1.对特征模型获取进行了研究,提出了一些特征模型获取的新方法,包括非线性系统的特征模型获取,尤其是利用测试法获取特征模型的方法,以及借助于Matlab的仿真分析法。引入了参数区间,从而使特征模型得以进一步简化。
2.提出了基于特征模型的预测函数控制算法。新算法可以克服传统预测函数控制算法在模型失配时的有效控制问题。借助于Matlab,对新算法与传统预测函数控制算法针对多种被控对象进行仿真研究,仿真结果表明,新算法明显优于传统预测函数控制算法。
3.给出了几种针对模型匹配与模型失配的预测函数控制系统的稳定性分析方法,尤其是引入了多项式稳定性分析方法来分析基于特征模型的预测函数控制算法系统的稳定性。
4.借助于DCS平台构建了与生产控制相吻合的实验环境进行了实验研究,实验研究进一步表明新算法比传统预测函数控制算法具有更好的控制性能。实验中采用的DCS为浙江中控JX-300X系统,控制程序采用JX-300X系统所提供的SCX语言编写,借助于JX-300X平台可以十分方便地把控制程序移植到工业生产实际中。
In the past few decade, the research of model predictive control has gained more and more attention among many experts. With everyone’s effort, many critical results are constantly spoken out. Model predictive control algorithm is obsessed of some advantages like good robustness, flexible ability of constraint solution, relatively higher comprehensive controlling quality, exclusively being adapted to industry process which has input-output constraint, time-delay and time-varying characteristic, reverse characteristic and variable target function, so it is widely accepted by industrial fields and practical results are emerging in an endless stream.
As the 3rd generation of model predict control, predictive functional control maintains the advantage of model predict control, meanwhile, it strengths regularity of input controlled quantity, improved the speediness and accurateness of response by introducing the concept of base functions, which can effectively decrease calculation quantity of algorithm. However, same as other model predict control, once predict model happens not in line with actual controlled process, it would meet with degrade of controlling performance. Although a series of model mismatch research have been carried out, for example, introducing neural networks model and fuzzy model into predictive function control, this kind of operation can only make predictive model becoming more complicated, increasing online calculation quantity and depriving of all the original merits of predictive functional control like easy algorithm and fast calculation.
Considering model mismatch problem of predictive functional control, this paper sets the assurance of predictive function control obsessing the strong points of easy algorithm and fast calculation as the starting line of research. Moreover, on the premise of decreasing model mismatch in order to assure maintaining the control characteristic of predictive functional control, this paper raises control scheme of predictive functional control on the basis of the characteristic model.
The usual form of the characteristic model is a second-order slow time- varying linear model, which is built up under the combined requirements of controlled object dynamic features and control feature. The main features of characteristic model is that it has simple model form and easily practiced, besides, under same input control, object characteristic model and practical object are equivalent.
The concept of characteristic model is abstracted by Hongxin Wu academician through his long years of theoretic research and project practice. This paper developed a further study on characteristic model theory, firstly, it concluded out several methods of acquiring characteristic models, especially the method on the basis of testing and emulation analysis with the help of Matlab. With these methods we can conveniently obtain characteristic model and realize model reduction. Secondly, in order to escape the calculation problem of time-varying parameters of characteristic model, this paper introduced in a concept of parameter zone and equivalent second-order slow time- varying to a cluster of second- order linear models thus it can assure when introducing characteristic model into predictive functional control, traditional predictive function control would not lose their advantages of easy and fast calculation. The result of simulation reflects that new algorithm is obviously better than traditional one. As the introduction of parameter zone leads characteristic polynomial parameter based on new algorithm having uncertainty parameter problem, in order to carrying out stability analysis, this paper utilized polynomial stability analysis theory to find out a method being good for stability analysis --- polynomial stability analysis theory. With the help of DCS platform, we did research under an experimental environment which fits to production control, experiment research further manifests that new algorithm has better controlling features over traditional one. The adopted DCS in experiment is from SUPCON JX-300X system, control program was made from SCX language provided by JX-300X, under the help of JX-300X platform we can quite easily plant control procedure into industrial production.
The main contents of this paper are like following:
1. Research on acquirement of characteristic model, introduction of some new methods of obtaining characteristic model, including the one of non-linear, especially taking advantage of testing method and simulation analysis method under the help of Matlab. The parameter zone is introduced to further simplify characteristic model.
2. Introduced predictive function control algorithm based on characteristic model. New algorithm can conquer the effective control problem when model mismatch happened. With the help of Matlab, we did simulation research on many kinds of controlled objects by traditional algorithm and new one, the simulation results shows that new algorithm is obviously better than traditional one.
3. Some methods analyzing on system stability of predictive function control algorithm , which model match and model mismatch, were given. Especially adopting polynomial stability analysis method to analyzing on system stability of predictive function control based on characteristic model algorithm.
4. Carried on research in a production control oriented experimental environment with the help of DCS platform, experimental research further presents that new algorithm obsesses better control features then traditional one. The adopted DCS in experiment is from SUPCON JX-300X system, control procedure was made from SCX language provided by JX-300X, under the help of JX-300X platform we can quite easily plant control procedure into industrial production.
引文
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