字典序多目标非线性预测控制的研究
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摘要
作为一类较为成熟的计算机控制算法,基于线性模型的预测控制已经在许多领域得到了成功应用。近年来,随着工业控制要求的不断提高,非线性预测控制的理论价值与实际应用前景逐渐显现,使之成为控制理论研究的热点之一。
目前,有两个阻碍非线性预测控制实际应用的理论问题:算法的计算量一般较大,难以满足实际工程中在线优化对计算速度的要求;在目前的非线性预测控制研究中,往往将多目标控制问题转换为单目标控制问题,以便求解,缺乏对实际工程中常见的有约束、多目标控制问题的研究,难以满足工业控制的需求。为解决上述理论问题,推动非线性预测控制的实际应用,本文对字典序多目标非线性预测控制器的框架结构、快速算法等内容进行了研究,主要的工作成果如下:
(1)作为工作基础,首先研究了线性系统的多目标预测控制器:以多温区空间晶体生长炉为对象,采用遗传算法作为优化方法,引入阶梯式控制策略,设计了阶梯式多变量预测控制器,并进行了仿真研究。基于字典序方法,研究了模块多变量控制器的框架结构、主控量选择策略、不同形式控制约束与控制目标的处理;在此基础上,设计了模块多变量模型算法控制器,并以Shell标准控制问题为对象进行了仿真研究。
(2)针对模块多变量预测控制器,研究了非线性预测控制的快速算法:分析了一步快速非线性预测控制算法的误差来源,得出了解析的误差表达式,并提出了校正方法;通过以多个一步预测代替多步预测,提出了基于参考轨迹的阶梯式快速非线性预测算法,能解析求解多步预测控制律,同时可保持较小的计算量;以水箱液位控制系统为对象,对这两种算法进行的仿真和实验控制研究,验证了算法的有效性,特别是在模型失配时的性能。
(3)研究了模块多变量非线性预测控制器的框架结构,对控制目标的处理和控制输入的选择进行了讨论,并以一步快速非线性预测控制为具体算法,实现了模块多变量非线性预测控制器。以水箱液位控制系统为对象的仿真实验验证了控制器在求解字典序多目标非线性控制问题时的有效性。
(4)为克服模块多变量非线性预测控制器的局限性,提出了字典序多目标遗传算法,结合阶梯式控制策略设计了通用性较强的字典序多目标非线性预测控制器,并在此控制器框架结构下,提出了新的主控量选择策略。以水箱液位控制系统为对象的仿真实验验证了控制器的有效性及其与模块多变量非线性预测控制器的等效性。
最后对本文的研究工作进行了总结,指出了尚待进一步研究的问题。
As a class of computer control algorithms, which are relatively well-studied, model predictive control (MPC) based on linear models has be applied to many fields successfully. In recent years, because of the increasing requirement of industrial control, the theoretical value and practical usefulness of nonlinear model predictive control (NMPC) become more and more evident, which makes NMPC be a focus of the research on control theory.
At present, there are two theoretical obstacles in the application of NMPC. Firstly, the computational load of NMPC algorithms is generally too heavy to satisfy the demand on computing speed of online optimization in industrial engineering. Secondly, in recent research on NMPC, the multi-objective control problem is often transformed into a single-objective control problem for the convenience in solving, which, however, lacks consideration of the constrained, multi-objective control problem resulted from actual industrial control. To handle with above problem, this dissertation mainly worked on the structure and efficient algorithms of the lexicographic multi-objective nonlinear model predictive controller. The achievements are:
(1) As the essential work, research on multi-objective model predictive controller for linear systems has been done at first. For a multi-zone furnace for crystal growth, by introducing the stair-like control strategy, the stair-like multivariable model predictive controller based on genetic algorithm has been proposed and the simulations were carried out. Based on lexicographic method, the characters of modular multivariable controller was investigated, including the structure, selection of the primary control input and the management of control constraints and objectives in different forms. Then the modular multivariable model algorithmic controller was proposed and demonstrated by simulations of the Shell standard control problem.
(2) For modular multivariable controller, some efficient algorithms of NMPC have been improved. The cause of error in existing one-step NMPC was studied, and the expression of the error was then presented analytically, so the compensation could be raised. Using several one-step predictions instead of a multi-step prediction, a stair-like efficient NMPC algorithm has been proposed, and it could solve the multi-step NMPC with light computational load. Simulations and experiments on the water-tank control system have been done to validate the efficiency of the above algorithms, especially the efficiency with model mismatch.
(3) The structure of modular multivariable NMPC was discussed, the management of objectives and the selection of control input was also studied. Based on one-step NMPC, modular multivariable NMPC has been realized, simulations on the water-tank control system validated its efficiency in solving nonlinear lexicographic multi-objective control problem.
(4) To overcome the limitations of modular multivariable NMPC, the lexicographic multi-objective genetic algorithm was proposed. Then, the lexicographic multi-objective NMPC, which is more universal than the modular multivariable NMPC, has been established based on this genetic algorithm with stair-like control strategy. In this structure, a new strategy of selection of the primary control input has been proposed. Simulations on the water-tank control system verified its efficiency and equivalency to modular multivariable NMPC in solving nonlinear lexicographic multi-objective control problem.
At last, a summarization of the dissertation was given and the remaining problems were pointed out for future research.
目前,有两个阻碍非线性预测控制实际应用的理论问题:算法的计算量一般较大,难以满足实际工程中在线优化对计算速度的要求;在目前的非线性预测控制研究中,往往将多目标控制问题转换为单目标控制问题,以便求解,缺乏对实际工程中常见的有约束、多目标控制问题的研究,难以满足工业控制的需求。为解决上述理论问题,推动非线性预测控制的实际应用,本文对字典序多目标非线性预测控制器的框架结构、快速算法等内容进行了研究,主要的工作成果如下:
(1)作为工作基础,首先研究了线性系统的多目标预测控制器:以多温区空间晶体生长炉为对象,采用遗传算法作为优化方法,引入阶梯式控制策略,设计了阶梯式多变量预测控制器,并进行了仿真研究。基于字典序方法,研究了模块多变量控制器的框架结构、主控量选择策略、不同形式控制约束与控制目标的处理;在此基础上,设计了模块多变量模型算法控制器,并以Shell标准控制问题为对象进行了仿真研究。
(2)针对模块多变量预测控制器,研究了非线性预测控制的快速算法:分析了一步快速非线性预测控制算法的误差来源,得出了解析的误差表达式,并提出了校正方法;通过以多个一步预测代替多步预测,提出了基于参考轨迹的阶梯式快速非线性预测算法,能解析求解多步预测控制律,同时可保持较小的计算量;以水箱液位控制系统为对象,对这两种算法进行的仿真和实验控制研究,验证了算法的有效性,特别是在模型失配时的性能。
(3)研究了模块多变量非线性预测控制器的框架结构,对控制目标的处理和控制输入的选择进行了讨论,并以一步快速非线性预测控制为具体算法,实现了模块多变量非线性预测控制器。以水箱液位控制系统为对象的仿真实验验证了控制器在求解字典序多目标非线性控制问题时的有效性。
(4)为克服模块多变量非线性预测控制器的局限性,提出了字典序多目标遗传算法,结合阶梯式控制策略设计了通用性较强的字典序多目标非线性预测控制器,并在此控制器框架结构下,提出了新的主控量选择策略。以水箱液位控制系统为对象的仿真实验验证了控制器的有效性及其与模块多变量非线性预测控制器的等效性。
最后对本文的研究工作进行了总结,指出了尚待进一步研究的问题。
As a class of computer control algorithms, which are relatively well-studied, model predictive control (MPC) based on linear models has be applied to many fields successfully. In recent years, because of the increasing requirement of industrial control, the theoretical value and practical usefulness of nonlinear model predictive control (NMPC) become more and more evident, which makes NMPC be a focus of the research on control theory.
At present, there are two theoretical obstacles in the application of NMPC. Firstly, the computational load of NMPC algorithms is generally too heavy to satisfy the demand on computing speed of online optimization in industrial engineering. Secondly, in recent research on NMPC, the multi-objective control problem is often transformed into a single-objective control problem for the convenience in solving, which, however, lacks consideration of the constrained, multi-objective control problem resulted from actual industrial control. To handle with above problem, this dissertation mainly worked on the structure and efficient algorithms of the lexicographic multi-objective nonlinear model predictive controller. The achievements are:
(1) As the essential work, research on multi-objective model predictive controller for linear systems has been done at first. For a multi-zone furnace for crystal growth, by introducing the stair-like control strategy, the stair-like multivariable model predictive controller based on genetic algorithm has been proposed and the simulations were carried out. Based on lexicographic method, the characters of modular multivariable controller was investigated, including the structure, selection of the primary control input and the management of control constraints and objectives in different forms. Then the modular multivariable model algorithmic controller was proposed and demonstrated by simulations of the Shell standard control problem.
(2) For modular multivariable controller, some efficient algorithms of NMPC have been improved. The cause of error in existing one-step NMPC was studied, and the expression of the error was then presented analytically, so the compensation could be raised. Using several one-step predictions instead of a multi-step prediction, a stair-like efficient NMPC algorithm has been proposed, and it could solve the multi-step NMPC with light computational load. Simulations and experiments on the water-tank control system have been done to validate the efficiency of the above algorithms, especially the efficiency with model mismatch.
(3) The structure of modular multivariable NMPC was discussed, the management of objectives and the selection of control input was also studied. Based on one-step NMPC, modular multivariable NMPC has been realized, simulations on the water-tank control system validated its efficiency in solving nonlinear lexicographic multi-objective control problem.
(4) To overcome the limitations of modular multivariable NMPC, the lexicographic multi-objective genetic algorithm was proposed. Then, the lexicographic multi-objective NMPC, which is more universal than the modular multivariable NMPC, has been established based on this genetic algorithm with stair-like control strategy. In this structure, a new strategy of selection of the primary control input has been proposed. Simulations on the water-tank control system verified its efficiency and equivalency to modular multivariable NMPC in solving nonlinear lexicographic multi-objective control problem.
At last, a summarization of the dissertation was given and the remaining problems were pointed out for future research.
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