基于微分—代数混合方程机理模型的非线性预测控制
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摘要
在节能减排要求的不断提高及生产成本的日益增加下,生产过程变工况运行的要求越来越迫切。大范围变工况控制必须考虑非线性动态特性的影响,因此对非线性控制器问题的研究具有重要的理论意义和应用价值。另一方面,预测控制作为一种面向工业过程发展起来的计算机控制算法,具有控制性能较好、鲁棒性强、能有效处理约束等特点,一直深受控制界的关注。基于机理模型的非线性预测控制具有清晰的物理意义,适合工作点大范围变动。流程工业中,往往采用微分-代数方程组(DAEs)描述其动态机理模型,然而这类模型不仅求解困难,而且难以从理论上保证优化求解过程的稳定性。本文通过研究实际运行的生产过程模型特点,深入研究非线性预测控制器的相关理论和算法设计,以及相应的变负荷优化控制命题,构造出适于该类机理模型的通用的非线性预测控制算法,并以高温气冷堆核电站的集总参数模型为例进行变负荷控制的仿真验证。
本文的主要内容和创新点包括：
1.分析DAEs特征,在全联立算法框架下,研究正交配置离散算法以及各种常用的正交配置点的计算原理与性质,并提出相应的判别公式,避免配置点选择不当引起自由度不够,导致系统无解,为DAEs的离散化和数值求解奠定基础。最后,以连续和不连续两种优化命题对算法进行仿真验证。
2.研究有限元正交配置法模拟求解DAEs的存在惟一性和基于Radau正交配置点的全联立算法的稳定性,从而为稳定地模拟求解DAEs模型提供依据。提出开环动态优化问题的两层结构,该结构采用统一的非线性过程模型,可在变负荷情况下,同时实现暂态控制性能与稳态经济指标的优化。
3.完成了基于一类DAEs机理模型的通用非线性预测控制系统软件原型设计。首先针对实际运行的流程工业系统模型特点,采用理论联系工业实际的方法分析DAEs优化问题解的存在惟一性与DAEs模型的index特点,为联立算法在滚动优化中的应用提供保障。然后构造出前馈补偿与反馈校正结合的闭环控制结构,并证明该系统的稳定性。最后,对于工业过程存在的不确定干扰或模型失配,本文提出的根据在线误差进行模式切换的控制系统具有一定的抗干扰能力。
4.采用基于Radau正交配置点的联立法求解核电站的反应堆模型。该方法不仅保证了离散的精度,对于求解刚性问题也有很好的稳定性。针对不同变量扰动的仿真表明联立法比传统的嵌套算法具有更高的效率,能够实现系统的快速仿真。
5.分析高温气冷堆核电站机理模型的特点,对模型进行验证。并提出非线性模型预测控制器与PID控制器相结合的控制方法以及相应的block技术,以实现对该大规模系统的实时控制。针对高温气冷堆核电站模型,设计从反应堆到蒸汽机以及从蒸汽机到反应堆的不同变负荷的控制方案,进行仿真验证。
最后,对全文进行了总结,并指出若干有待于今后进一步研究的内容。
With the pressure from energy saving and increasing production costs, chemical processes are more than ever expected to operate under variable conditions. Process control need to consider nonlinear dynamics of the process under significant changes. Therefore research on nonlinear controller is important in theory and applications. As a kind of computer control algorithm developed for industrial processes, predictive control method has been attracting considerable attentions for its good performance, strong robustness and ability to deal with constraints. Nonlinear predictive control based on first principle models has clear physical meaning and adapts to wide range of operating points. Differential-algebraic equations (DAEs) arise naturally as dynamic models of chemical applications which is difficult to solve and to guarantee the stability of optimization based on this kind of model. This dissertation studies the theory and algorithms of nonlinear predictive control for varying load processes, which can be described as Hessenberg DAEs. Numerical tests on a high temperature gas cooled reactor pebble bed module (HTR-PM) of a nuclear power plant validate the research on varying load control.
The main research work and contributions of the thesis are listed as follows:
1. Characteristics of DAEs are analyzed firstly. Discretization strategies with different orthogonal collocation points are studied in the frame of simultaneous approach, and criteria are put forward to ensure the degrees of freedom of the resulting NLP. At last, continuous and discontinuous cases are presented to compare these strategies and conclusions are drawn from the results.
2. The uniqueness of solutions to DAEs and the stability of the simultaneous approach based on Radau collocation points are studied. A two-layer optimization is presented for open-loop dynamic optimization. Here the same process model is used for both layers and the optimization of control performance and economic benefit can be implemented synchronously. The upper layer is a steady state optimization whose objective is the economic maximization in the terminal time. This layer is used to compute the set points for the controlled variables and the manipulated variables in the lower layer. The lower layer is a dynamic optimization whose objective includes both economic objective and terminal conditions.
3. A two-layer closed-loop control structure combining feedforward compensation with feedback correction is constructed to deal with the nonlinear production process under varying load. Existence and uniqueness of the solution in rolling optimization are investigated from the practical point of view and asymptotic stability is proved under certain assumptions. The proposed algorithm has anti-interference ability in the presence of uncertain disturbances. An universal NMPC system based on DAEs model is completed.
4. A simultaneous approach based on Radau collocation points is presented to solve the DAEs model of the reactor of a nuclear plant. This approach has good accuracy in discretization as well as has very good stability in solving stiff problems. Simulation results of the varying load processes demonstrate high efficiency of the approach, which takes much less time than the nested approach.
5. Characteristics of HTR nuclear mechanism model are analyzed, and the model is verified. A controller combining nonlinear model predictive control with PID control is proposed to deal with the large-scale model, and the block technique is applied to achieve the purpose of online real-time applications. Different control schemes of varying load are designed and simulation results verify the effectiveness of the controller.
At the end of the dissertation, contributions of this research are concluded and possible extensions in future research are discussed.
本文的主要内容和创新点包括：
1.分析DAEs特征,在全联立算法框架下,研究正交配置离散算法以及各种常用的正交配置点的计算原理与性质,并提出相应的判别公式,避免配置点选择不当引起自由度不够,导致系统无解,为DAEs的离散化和数值求解奠定基础。最后,以连续和不连续两种优化命题对算法进行仿真验证。
2.研究有限元正交配置法模拟求解DAEs的存在惟一性和基于Radau正交配置点的全联立算法的稳定性,从而为稳定地模拟求解DAEs模型提供依据。提出开环动态优化问题的两层结构,该结构采用统一的非线性过程模型,可在变负荷情况下,同时实现暂态控制性能与稳态经济指标的优化。
3.完成了基于一类DAEs机理模型的通用非线性预测控制系统软件原型设计。首先针对实际运行的流程工业系统模型特点,采用理论联系工业实际的方法分析DAEs优化问题解的存在惟一性与DAEs模型的index特点,为联立算法在滚动优化中的应用提供保障。然后构造出前馈补偿与反馈校正结合的闭环控制结构,并证明该系统的稳定性。最后,对于工业过程存在的不确定干扰或模型失配,本文提出的根据在线误差进行模式切换的控制系统具有一定的抗干扰能力。
4.采用基于Radau正交配置点的联立法求解核电站的反应堆模型。该方法不仅保证了离散的精度,对于求解刚性问题也有很好的稳定性。针对不同变量扰动的仿真表明联立法比传统的嵌套算法具有更高的效率,能够实现系统的快速仿真。
5.分析高温气冷堆核电站机理模型的特点,对模型进行验证。并提出非线性模型预测控制器与PID控制器相结合的控制方法以及相应的block技术,以实现对该大规模系统的实时控制。针对高温气冷堆核电站模型,设计从反应堆到蒸汽机以及从蒸汽机到反应堆的不同变负荷的控制方案,进行仿真验证。
最后,对全文进行了总结,并指出若干有待于今后进一步研究的内容。
With the pressure from energy saving and increasing production costs, chemical processes are more than ever expected to operate under variable conditions. Process control need to consider nonlinear dynamics of the process under significant changes. Therefore research on nonlinear controller is important in theory and applications. As a kind of computer control algorithm developed for industrial processes, predictive control method has been attracting considerable attentions for its good performance, strong robustness and ability to deal with constraints. Nonlinear predictive control based on first principle models has clear physical meaning and adapts to wide range of operating points. Differential-algebraic equations (DAEs) arise naturally as dynamic models of chemical applications which is difficult to solve and to guarantee the stability of optimization based on this kind of model. This dissertation studies the theory and algorithms of nonlinear predictive control for varying load processes, which can be described as Hessenberg DAEs. Numerical tests on a high temperature gas cooled reactor pebble bed module (HTR-PM) of a nuclear power plant validate the research on varying load control.
The main research work and contributions of the thesis are listed as follows:
1. Characteristics of DAEs are analyzed firstly. Discretization strategies with different orthogonal collocation points are studied in the frame of simultaneous approach, and criteria are put forward to ensure the degrees of freedom of the resulting NLP. At last, continuous and discontinuous cases are presented to compare these strategies and conclusions are drawn from the results.
2. The uniqueness of solutions to DAEs and the stability of the simultaneous approach based on Radau collocation points are studied. A two-layer optimization is presented for open-loop dynamic optimization. Here the same process model is used for both layers and the optimization of control performance and economic benefit can be implemented synchronously. The upper layer is a steady state optimization whose objective is the economic maximization in the terminal time. This layer is used to compute the set points for the controlled variables and the manipulated variables in the lower layer. The lower layer is a dynamic optimization whose objective includes both economic objective and terminal conditions.
3. A two-layer closed-loop control structure combining feedforward compensation with feedback correction is constructed to deal with the nonlinear production process under varying load. Existence and uniqueness of the solution in rolling optimization are investigated from the practical point of view and asymptotic stability is proved under certain assumptions. The proposed algorithm has anti-interference ability in the presence of uncertain disturbances. An universal NMPC system based on DAEs model is completed.
4. A simultaneous approach based on Radau collocation points is presented to solve the DAEs model of the reactor of a nuclear plant. This approach has good accuracy in discretization as well as has very good stability in solving stiff problems. Simulation results of the varying load processes demonstrate high efficiency of the approach, which takes much less time than the nested approach.
5. Characteristics of HTR nuclear mechanism model are analyzed, and the model is verified. A controller combining nonlinear model predictive control with PID control is proposed to deal with the large-scale model, and the block technique is applied to achieve the purpose of online real-time applications. Different control schemes of varying load are designed and simulation results verify the effectiveness of the controller.
At the end of the dissertation, contributions of this research are concluded and possible extensions in future research are discussed.
引文
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