基于逆系统方法的非线性预测控制的研究
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摘要
针对非线性系统的控制问题,深入研究了基于逆系统方法的预测控制。逆系统方法是一种反馈线性化方法,在非线性系统逆模型存在的前提下,通过构造非线性系统逆模型,并将逆模型与原系统串联组成伪线性系统的方法,完成非线性系统的线性化处理。进而根据伪线性系统设计预测控制器,实现非线性系统的预测控制。
本文重点进行了以下几方面的探讨研究:
(1)基于逆系统方法的非线性系统建模。在非线性系统逆模型存在的前提下,通过采样非线性系统的输入输出数据,采用BP神经网络离线训练非线性系统的逆模型。大量的仿真研究发现,由于BP神经网络存在过训练和泛化能力差的问题,造成建立的伪线性系统模型存在较大误差。因此,本文又进一步分析研究了基于最小二乘支持向量机的建模方法,有效的克服了BP神经网络建模的缺陷。仿真结果表明,最小二乘支持向量机在逆系统方法建模方面比BP神经网络具有更高的精度和更好的泛化能力。
(2)基于逆系统方法的单变量非线性系统控制器设计。针对伪线性系统对于外界干扰和内部参数变化鲁棒性差的问题,设计了PID、动态矩阵控制和广义预测控制器。理论分析和仿真表明,虽然PID控制器可以抑制伪线性系统出现的干扰,但存在无法控制大滞后系统和最优参数调节困难的问题。因此,本文针对伪线性系统分别设计了动态矩阵控制器和广义预测控制器。进一步的分析研究和仿真证明,对于伪线性系统出现的各种干扰和参数变化,两种控制器都能很好的抑制,并取得较好的动静态性能和较强的鲁棒性。
(3)基于逆系统方法的多变量非线性控制系统设计。在对单变量非线性系统控制的基础上,对多变量非线性系统进行了讨论。本文在构造多变量伪线性系统的基础上,将多变量非线性耦合系统剥离为多个单变量线性系统,并设计了动态矩阵控制器组。通过仿真发现,多变量逆系统方法的解耦和线性化效果是有限的。而通过设计动态矩阵控制器组可以弥补伪线性系统构造过程中产生的误差,并取得较好的控制效果。
通过文中的理论研究和仿真分析,基于逆系统方法的非线性系统预测控制器的设计方法可以将线性系统的预测控制策略应用到非线性系统中,并能取得很好的控制效果。证明了该方法的有效性,为非线性预测控制提供了一种新颖的控制策略。
The predictive control is researched for the problem of nonlinear system control based on inverse system method. Inverse system method is a feedback linearization method. If the inverse model of nonlinear system exists, the linearization of the nonlinear system is achieved by building inverse model of nonlinear system and cascading the inverse model of nonlinear system with the original system. Then predictive controller is designed in accordance with pseudo-linear system to realize the predictive control for nonlinear system.
This paper focuses on the following aspects.
First, nonlinear system model is built based on inverse system method. At the premise of the existing of inverse model, the input and output data of nonlinear system are sampling. And then the inverse model of nonlinear system is approximated by BP neural network offline. Simulation results show that there is big error in pseudo-linear system model because of the bad training and generalization ability of BP neural network. Therefore, the Least squares support vector machines modeling is researched in this paper. It overcomes the shortcomings of neural network effectively. Simulation results show that the least squares support vector machines has higher accuracy and better generalization ability than neural network in inverse system modeling.
Second, the controller of single variable nonlinear system is designed based on inverse system method. The PID controller, dynamic matrix controller and generalized predictive controller are designed for the reasons that pseudo-linear system does not have robustness for the external disturbances and internal parameter changes. Theoretical analysis and simulation show that PID controller can control the pseudo-linear system with disturbances. But, PID controller can not control large delay system and the optimal parameters are difficult to find. Therefore, dynamic matrix controller and generalized predictive controller are designed for pseudo-linear system in this paper. Further analysis and simulation studies prove that both of the dynamic and static performance of the pseudo-linear system is excellent when disturbances and parameter changes appear. It is also shown that the pseudo-linear system has strong robustness.
Third, the control system is designed for multivariable nonlinear system based on inverse system method. The multivariable nonlinear system is discussed based on single variable nonlinear control system. After the multivariable pseudo-linear system is built, the multivariable nonlinear coupling system is stripped into a number of single variable linear systems and dynamic matrix controller group is designed. Simulation results show that the decoupling and linearization function of multivariable inverse system method are limited. And through the designing of dynamic matrix controller group, the pseudo-linear system errors can be made up and the control system can obtain better control performance.
Through the theoretical study and simulation analysis in this paper, the predictive controller design method of nonlinear system based on inverse system method can introduce the linear predictive control strategy to nonlinear system and obtain excellent control performance. The paper validates the effectiveness of this method and proposes a novel method for nonlinear predictive control.
本文重点进行了以下几方面的探讨研究:
(1)基于逆系统方法的非线性系统建模。在非线性系统逆模型存在的前提下,通过采样非线性系统的输入输出数据,采用BP神经网络离线训练非线性系统的逆模型。大量的仿真研究发现,由于BP神经网络存在过训练和泛化能力差的问题,造成建立的伪线性系统模型存在较大误差。因此,本文又进一步分析研究了基于最小二乘支持向量机的建模方法,有效的克服了BP神经网络建模的缺陷。仿真结果表明,最小二乘支持向量机在逆系统方法建模方面比BP神经网络具有更高的精度和更好的泛化能力。
(2)基于逆系统方法的单变量非线性系统控制器设计。针对伪线性系统对于外界干扰和内部参数变化鲁棒性差的问题,设计了PID、动态矩阵控制和广义预测控制器。理论分析和仿真表明,虽然PID控制器可以抑制伪线性系统出现的干扰,但存在无法控制大滞后系统和最优参数调节困难的问题。因此,本文针对伪线性系统分别设计了动态矩阵控制器和广义预测控制器。进一步的分析研究和仿真证明,对于伪线性系统出现的各种干扰和参数变化,两种控制器都能很好的抑制,并取得较好的动静态性能和较强的鲁棒性。
(3)基于逆系统方法的多变量非线性控制系统设计。在对单变量非线性系统控制的基础上,对多变量非线性系统进行了讨论。本文在构造多变量伪线性系统的基础上,将多变量非线性耦合系统剥离为多个单变量线性系统,并设计了动态矩阵控制器组。通过仿真发现,多变量逆系统方法的解耦和线性化效果是有限的。而通过设计动态矩阵控制器组可以弥补伪线性系统构造过程中产生的误差,并取得较好的控制效果。
通过文中的理论研究和仿真分析,基于逆系统方法的非线性系统预测控制器的设计方法可以将线性系统的预测控制策略应用到非线性系统中,并能取得很好的控制效果。证明了该方法的有效性,为非线性预测控制提供了一种新颖的控制策略。
The predictive control is researched for the problem of nonlinear system control based on inverse system method. Inverse system method is a feedback linearization method. If the inverse model of nonlinear system exists, the linearization of the nonlinear system is achieved by building inverse model of nonlinear system and cascading the inverse model of nonlinear system with the original system. Then predictive controller is designed in accordance with pseudo-linear system to realize the predictive control for nonlinear system.
This paper focuses on the following aspects.
First, nonlinear system model is built based on inverse system method. At the premise of the existing of inverse model, the input and output data of nonlinear system are sampling. And then the inverse model of nonlinear system is approximated by BP neural network offline. Simulation results show that there is big error in pseudo-linear system model because of the bad training and generalization ability of BP neural network. Therefore, the Least squares support vector machines modeling is researched in this paper. It overcomes the shortcomings of neural network effectively. Simulation results show that the least squares support vector machines has higher accuracy and better generalization ability than neural network in inverse system modeling.
Second, the controller of single variable nonlinear system is designed based on inverse system method. The PID controller, dynamic matrix controller and generalized predictive controller are designed for the reasons that pseudo-linear system does not have robustness for the external disturbances and internal parameter changes. Theoretical analysis and simulation show that PID controller can control the pseudo-linear system with disturbances. But, PID controller can not control large delay system and the optimal parameters are difficult to find. Therefore, dynamic matrix controller and generalized predictive controller are designed for pseudo-linear system in this paper. Further analysis and simulation studies prove that both of the dynamic and static performance of the pseudo-linear system is excellent when disturbances and parameter changes appear. It is also shown that the pseudo-linear system has strong robustness.
Third, the control system is designed for multivariable nonlinear system based on inverse system method. The multivariable nonlinear system is discussed based on single variable nonlinear control system. After the multivariable pseudo-linear system is built, the multivariable nonlinear coupling system is stripped into a number of single variable linear systems and dynamic matrix controller group is designed. Simulation results show that the decoupling and linearization function of multivariable inverse system method are limited. And through the designing of dynamic matrix controller group, the pseudo-linear system errors can be made up and the control system can obtain better control performance.
Through the theoretical study and simulation analysis in this paper, the predictive controller design method of nonlinear system based on inverse system method can introduce the linear predictive control strategy to nonlinear system and obtain excellent control performance. The paper validates the effectiveness of this method and proposes a novel method for nonlinear predictive control.
引文
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