CN107450325B - A multi-model predictive control method for post-combustion CO2 capture system - Google Patents
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Abstract
本发明公开了一种燃烧后CO2捕集系统的多模型预测控制方法,该预测控制方法以基于化学吸附的燃烧后CO2捕集系统为被控对象,贫液阀门开度和汽轮机低压缸抽汽阀门开度为系统控制输入量,CO2捕集率和再沸器温度为系统输出量;首先基于子空间辨识方法,利用系统运行产生的数据,在不同工况点处建立系统的局部状态空间模型;接着使用间隙度量的方法调研被控对象的非线性分布;进而在合适的局部工况点处建立预测控制器,并设计隶属度函数将其加权组合,建立燃烧后CO2捕集系统多模型预测控制系统。本发明的方法具有良好的全局非线性控制能力,能够有效适应系统大范围变工况的需求,快速追踪CO2捕集率设定值,提高CO2捕集系统深度快速灵活运行的水平。
The invention discloses a multi-model predictive control method for a post-combustion CO2 capture system. The predictive control method takes the post-combustion CO2 capture system based on chemical adsorption as the controlled object, and the opening of the lean liquid valve and the low-pressure cylinder of the steam turbine The extraction valve opening is the system control input, and the CO2 capture rate and reboiler temperature are the system output; firstly, based on the subspace identification method, using the data generated by the system operation, the local State space model; then use the gap metric method to investigate the nonlinear distribution of the controlled object; then establish a predictive controller at a suitable local operating point, and design a membership function to combine them weightedly to establish post-combustion CO 2 capture System Multi-Model Predictive Control System. The method of the present invention has good global non-linear control capability, can effectively adapt to the needs of the system in a wide range of variable working conditions, quickly track the set value of the CO2 capture rate, and improve the level of deep, fast and flexible operation of the CO2 capture system.
Description
技术领域technical field
本发明涉及预测控制方法技术领域,尤其是一种燃烧后CO2捕集系统的多模型预测控制方法。The invention relates to the technical field of predictive control methods, in particular to a multi-model predictive control method for a post-combustion CO2 capture system.
背景技术Background technique
随着温室效应及相关气候生态问题的日益严峻,减排CO2已成为国际社会应对气候变化的关键举措。作为电力供应的主要设备,火电机组是CO2最稳定、最集中的排放源,世界30%-40%、我国40%~50%的CO2排放来自于火电机组。在积极发展新能源技术、努力提高火电机组发电效率的同时,火电机组CO2捕集被众多权威机构公认为未来30 年内实现大规模CO2减排最直接有效的技术手段。With the increasing severity of the greenhouse effect and related climate and ecological problems, reducing CO2 emissions has become a key measure for the international community to deal with climate change. As the main equipment for power supply, thermal power units are the most stable and concentrated source of CO 2 emissions. 30%-40% of the world's CO 2 emissions and 40%-50% of China's CO 2 emissions come from thermal power units. While actively developing new energy technologies and striving to improve the power generation efficiency of thermal power units, CO 2 capture by thermal power units has been recognized by many authoritative organizations as the most direct and effective technical means to achieve large-scale CO 2 emission reductions in the next 30 years.
在现有火电机组CO2捕集技术中,基于化学吸收法的燃烧后CO2捕集技术直接从电厂燃烧后的烟气中分离CO2,具有对已有机组优秀的继承性和较好的技术适用性,是当前CO2捕集电站采用的主流技术。由于CO2捕集需要从火电机组中、低压缸中抽取大量蒸汽用于贫液再生,其实施对于火电机组发电效率影响很大。为此,CO2捕集系统必须实现大范围的灵活运行,比如,在供电需求紧迫或电价较高时期降低CO2捕集率,而在环保压力较大或碳价较高时期提高捕集率。然而,随着CO2捕集设备大范围变工况运行,其系统呈现出较强的非线性特性,导致传统基于线性模型设计的预测控制器控制性能降低、稳定性下降。因此一种在燃烧后CO2捕集系统中加入对烟气信号利用的预测控制算法的开发很有必要。Among the existing CO 2 capture technologies for thermal power units, the post-combustion CO 2 capture technology based on chemical absorption method directly separates CO 2 from the flue gas after combustion in power plants, which has excellent inheritance and good influence on existing units. Technical applicability is the mainstream technology adopted by current CO2 capture power plants. Since CO2 capture needs to extract a large amount of steam from the middle and low pressure cylinders of thermal power units for lean liquid regeneration, its implementation has a great impact on the power generation efficiency of thermal power units. For this reason, the CO 2 capture system must achieve a wide range of flexible operation, for example, reduce the CO 2 capture rate during the period of urgent power supply demand or high electricity price, and increase the capture rate during the period of high environmental protection pressure or high carbon price . However, as the CO2 capture equipment operates under a wide range of variable operating conditions, its system exhibits strong nonlinear characteristics, which leads to a decrease in the control performance and stability of the traditional predictive controller based on linear model design. Therefore, the development of a predictive control algorithm that incorporates the utilization of flue gas signals in post-combustion CO2 capture systems is necessary.
发明内容Contents of the invention
本发明所要解决的技术问题在于,提供一种燃烧后CO2捕集系统的多模型预测控制方法,能够提高CO2捕集系统的大范围变工况的调节品质,改善其快速深度灵活运行的能力。The technical problem to be solved by the present invention is to provide a multi-model predictive control method for the post-combustion CO 2 capture system, which can improve the adjustment quality of the CO 2 capture system in a wide range of variable working conditions, and improve its fast, deep and flexible operation. ability.
为解决上述技术问题,本发明提供一种燃烧后CO2捕集系统的多模型预测控制方法,包括如下步骤:In order to solve the above-mentioned technical problems, the present invention provides a multi-model predictive control method for a post-combustion CO capture system, comprising the following steps:
(1)将燃烧后CO2捕集系统切换到手动状态,在不同捕集率工况点附近,以贫液流量阀门开度ua和汽轮机低压缸抽汽阀门开度信号ub为输入,对CO2捕集系统进行激励,获取CO2捕集率ya和再沸器温度yb的开环响应数据;(1) Switch the post-combustion CO2 capture system to the manual state, and take the lean liquid flow valve opening u a and the steam turbine low-pressure cylinder extraction valve opening signal u b as inputs near the operating points of different capture rates, Energize the CO2 capture system to obtain open-loop response data for CO2 capture rate y a and reboiler temperature y b ;
(2)选定采样周期Ts,以为输入,为输出,利用子空间辨识方法,构建不同捕集率工况点处CO2捕集系统局部状态空间模型;(2) Select the sampling period Ts to for input, As the output, the local state space model of the CO 2 capture system at different capture rate operating points is constructed by using the subspace identification method;
(3)使用间隙度量的方法,分析各相邻局部模型间的差异,调研CO2捕集系统的非线性分布;(3) Use the method of gap measurement to analyze the difference between adjacent local models and investigate the nonlinear distribution of CO2 capture system;
(4)在合适的局部工作点处建立模型预测控制器;在每一采样时刻,分别利用各子模型预估在未来一定时间内系统的CO2捕集率和再沸器温度通过优化计算得到局部最优的贫液流量阀门开度ui a-op和汽轮机低压缸抽汽阀门开度信号ui b-op;(4) Establish a model predictive controller at a suitable local operating point; at each sampling time, use each sub-model to predict the CO 2 capture rate of the system in a certain period of time in the future and reboiler temperature The local optimal lean liquid flow valve opening u i a-op and steam turbine low pressure cylinder extraction valve opening signal u i b-op are obtained through optimization calculation;
(5)设计最终适宜的隶属度函数,将各控制器输出加权组合,得到最终的贫液流量阀门开度ua-op和汽轮机低压缸抽汽阀门开度信号ub-op并作用于CO2捕集系统;其中ωi为第i个控制器对应的隶属度函数,其为调度变量,捕集率CR的函数,ui a-op和ui b-op为第i个控制器计算出的最优控制信号;(5) Design the final appropriate membership function, and combine the weighted outputs of each controller to obtain the final lean liquid flow valve opening u a-op and steam turbine low-pressure cylinder extraction valve opening signal u b-op , and act on the CO 2 capture system; where ω i is the membership function corresponding to the i-th controller, which is a function of the scheduling variable and the capture rate CR, u i a-op and u i b-op are the optimal control signals calculated by the i-th controller ;
(6)固定各局部控制器中来输出的预测矩阵ψx、ψu、ψy,重复步骤(3)-(4)实现连续控制。(6) Fix the prediction matrices ψ x , ψ u , ψ y output from each local controller, and repeat steps (3)-(4) to realize continuous control.
优选的,步骤(2)中,T95/Ts=5~15,其中T95为过渡过程上升到95%的调节时间。Preferably, in step (2), T95/T s =5-15, wherein T95 is the adjustment time for the transition process to rise to 95%.
优选的,步骤(2)中,构建不同捕集率工况点处CO2捕集系统局部状态空间模型,具体步骤为:Preferably, in step (2), a CO2 capture system local state space model is constructed at different capture rate working conditions, and the specific steps are:
(21)将在某一给定工况点附近连续获得的从第0时刻到第2N+j-2时刻的输出数据y 和输入数据u分别排列为Hankel矩阵形式:(21) Arrange the output data y and input data u obtained continuously from the 0th moment to the 2N+j-2 moment near a given operating point in the form of Hankel matrix:
其中,N为矩阵行数,N大于CO2捕集系统阶次,j为矩阵列数,Y和U分别表示输出与输入数据组成的Hankel矩阵,Yf和Yp分别表示输出数据的未来数据和过去数据,Uf和Up分别表示输入数据的未来数据和过去数据,yj表示第j个输出数据,uj表示第j个输入数据;Among them, N is the number of rows of the matrix, N is greater than the order of the CO2 capture system, j is the number of columns of the matrix, Y and U represent the Hankel matrix composed of output and input data, respectively, Y f and Y p represent the future data of the output data and past data, U f and U p represent the future data and past data of the input data respectively, y j represents the jth output data, u j represents the jth input data;
(22)令Wp=[(Yp)T (Up)T]T,对如下矩阵进行QR分解:(22) Let W p =[(Y p ) T (U p ) T ] T , perform QR decomposition on the following matrix:
获得矩阵L:Obtain the matrix L:
(23)从而获得矩阵Lw=L(:,1:N(m+l)),Lu=L(:,N(m+l)+1:end),m为输入变量维数,l为输出变量维数,L(:,1:N(m+l))表示矩阵L的前N(m+l)列, L(:,N(m+l)+1:end)表示矩阵L自第N(m+l)+1列之后的所有列;(23) To obtain the matrix L w =L(:,1:N(m+l)), L u =L(:,N(m+l)+1:end), m is the dimension of the input variable, l is the output variable dimension, L(:,1:N(m+l)) represents the first N(m+l) columns of the matrix L, L(:,N(m+l)+1:end) represents the matrix L All columns after column N(m+l)+1;
(24)对Lw矩阵做奇异值分解:(24) Perform singular value decomposition on the L w matrix:
获得矩阵ΓN=U1(S1)1/2,进而得到:模型参数其中表示去掉前l行的ΓN,Γ N表示去掉后l行的ΓN,表示Moore-Penrose伪逆;模型参数C=ΓN(1:l,:) 可从ΓN的前l行中直接获取;Obtain the matrix Γ N =U 1 (S 1 ) 1/2 , and then get: model parameters in means to remove the Γ N of the first row, and Γ N means to remove the Γ N of the last row, Indicates the Moore-Penrose pseudo-inverse; the model parameter C=Γ N (1:l,:) can be obtained directly from the first l rows of Γ N ;
(25)求解线性方程组:(25) Solving linear equations:
获得模型参数B和D。Obtain model parameters B and D.
优选的,步骤(3)中,计算相邻局部模型间的间隙度量值,具体步骤为:Preferably, in step (3), the gap metric value between adjacent local models is calculated, and the specific steps are:
(31)对两相邻局部模型P1、P2做正交右互质分解,得: (31) Do orthogonal right coprime decomposition on two adjacent local models P 1 and P 2 , get:
(32)计算模型P1、P2间的距离:(32) Calculate the distance between models P 1 and P 2 :
其中,H∞为一特殊的Hardy赋范空间:σmax(G(jω))表示G(jω)的最大奇异值;Q为H∞空间内的任意函数;Among them, H ∞ is a special Hardy normed space: σ max (G(jω)) means the maximum singular value of G(jω); Q is any function in H ∞ space;
(33)两系统间的间隙度量 (33) Gap measure between two systems
优选的,步骤(4)中,采用公式(1)预估在未来一段时间内系统的CO2捕集率和再沸器温度 Preferably, in step (4), use formula (1) to predict the CO capture rate and reboiler temperature of the system within a certain period of time in the future
其中,预测矩阵ψx、ψu、ψy分别为:Among them, the prediction matrices ψ x , ψ u , ψ y are respectively:
分别为k时刻CO2捕集系统的估计状态、输入和输出,F为观测器增益, uf为未来Nu个时刻的输入数据, 是未来Ny时刻系统的预估输出, are the estimated state, input and output of the CO2 capture system at time k, respectively, F is the observer gain, u f is the input data at Nu time in the future, is the estimated output of the system at time N y in the future,
采用如下公式计算性能指标函数J:Use the following formula to calculate the performance index function J:
其中,Qf和Rf是调节输入输出控制品质的权值矩阵, rf是未来N1时刻系统CO2捕集率和再沸器温度设定值序列,Among them, Q f and R f are the weight matrix for adjusting the quality of input and output control, r f is the sequence of system CO2 capture rate and reboiler temperature setpoint at time N in the future,
分别表示k+1时刻到k+N1时刻系统CO2捕集率ra和再沸器温度rb设定值, 是未来Ny时刻系统CO2捕集率和再沸器温度预估值序列, Respectively represent the system CO 2 capture rate r a and reboiler temperature r b set values from time k+1 to time k+N 1 , is the estimated value sequence of CO2 capture rate and reboiler temperature of the system at time N y in the future,
分别表示k+1时刻到k+Ny时刻系统CO2捕集率ya和再沸器温度yb预估值, Respectively represent the estimated value of system CO 2 capture rate y a and reboiler temperature y b from time k+1 to time k+N y ,
Δuf是未来Nu时刻的贫液流量阀门开度信号ua和低压缸抽汽阀门开度信号ub序列的增量;Δu f is the sequence of lean liquid flow valve opening signal u a and low pressure cylinder extraction valve opening signal u b at time Nu in the future increment;
其中 in
CO2捕集系统贫液流量阀门和低压缸抽汽阀门开度信号u的幅值约束(umin,umax)和增量约束(Δumin,Δumax)为:The amplitude constraints (u min , u max ) and increment constraints (Δu min , Δu max ) of the opening signal u of the lean liquid flow valve and the extraction valve of the low-pressure cylinder in the CO 2 capture system are:
其中,umin,umax分别表示贫液流量阀门和低压缸抽汽阀门开度信号u的最小值与最大值,Δumin,Δumax分别表示贫液流量阀门和低压缸抽汽阀门开度信号u的最小增量与最大增量;Among them, u min and u max represent the minimum value and maximum value of the opening signal u of the lean liquid flow valve and the extraction valve of the low-pressure cylinder respectively, and Δu min and Δu max represent the opening signals of the lean liquid flow valve and the extraction valve of the low-pressure cylinder respectively The minimum increment and maximum increment of u;
每一采样时刻,将公式(1)代入公式(2),并在满足公式(3)和(4)的情况下最小化性能指标函数J,得到最优的控制增量序列uf:At each sampling moment, formula (1) is substituted into formula (2), and the performance index function J is minimized under the condition of satisfying formulas (3) and (4), to obtain the optimal control increment sequence u f :
提取最优控制增量序列uf中的第一块uk+1,作为最优的贫液流量阀门和低压缸抽汽阀门开度信号 Extract the first block u k+1 in the optimal control increment sequence u f as the optimal lean liquid flow valve and low pressure cylinder extraction valve opening signal
本发明的有益效果为:本发明的多模型预测控制方法具有良好的全局非线性控制能力,应用于火电站燃烧后CO2捕集系统能够有效适应系统大范围变工况的需求,快速追踪CO2捕集率设定值,提高CO2捕集系统深度快速灵活运行的水平。The beneficial effect of the present invention is that: the multi-model predictive control method of the present invention has good global nonlinear control ability, can effectively adapt to the needs of the system in a wide range of variable working conditions when applied to the post-combustion CO2 capture system of thermal power plants, and quickly track CO 2 capture rate setting value, improve the level of CO 2 capture system depth fast and flexible operation.
附图说明Description of drawings
图1为本发明的方法原理示意图。Fig. 1 is a schematic diagram of the method principle of the present invention.
图2为本发明的非线性调研结果示意图。Fig. 2 is a schematic diagram of the non-linear research results of the present invention.
图3为本发明所设计的隶属度函数示意图。Fig. 3 is a schematic diagram of the membership function designed in the present invention.
图4为本发明多模型预测控制(实线)与常规比例积分微分控制(虚线)在CO2捕集率设定值小范围变化下的控制效果对比示意图(点画线为设定值)。Fig. 4 is a schematic diagram of the control effect comparison between the multi-model predictive control (solid line) of the present invention and the conventional proportional integral differential control (dashed line) under the small range change of the set value of the CO2 capture rate (the dotted line is the set value).
图5为本发明多模型预测控制(实线)与常规线性预测控制(虚线)在CO2捕集率设定值大范围变化下的控制效果对比示意图(点画线为设定值)。Fig. 5 is a schematic diagram of the control effect comparison between the multi-model predictive control (solid line) of the present invention and the conventional linear predictive control (dotted line) when the set value of CO2 capture rate varies in a wide range (the dotted line is the set value).
具体实施方式Detailed ways
将本发明的多模型预测控制方法应用于某1MW火电机组燃烧后CO2捕集系统系统仿真模型中,控制的目标是在满足输入约束的条件下,使CO2捕集率和再沸器温度跟踪设定值,实现CO2捕集系统的大范围变工况运行。The multi-model predictive control method of the present invention is applied to the simulation model of the post-combustion CO2 capture system of a 1MW thermal power unit. The control goal is to make the CO2 capture rate and reboiler temperature Track the set value to realize the operation of the CO2 capture system in a wide range of variable working conditions.
本发明的燃烧后CO2捕集系统多模型预测控制方法,该预测控制方法以基于化学吸附的燃烧后CO2捕集系统为被控对象,贫液阀门开度和汽轮机低压缸抽汽阀门开度为系统控制输入量,CO2捕集率和再沸器温度为系统输出量,首先基于子空间辨识方法,利用系统运行产生的数据,在不同工况点处建立系统的局部状态空间模型;接着使用间隙度量的方法调研被控对象的非线性分布,进而在合适的局部工况点处建立预测控制器,并设计隶属度函数将其加权组合,建立燃烧后CO2捕集系统多模型预测控制系统。与传统预测控制相比,本发明提高了CO2捕集系统大范围变工况运行的控制品质,增强了其灵活运行的能力。The post-combustion CO2 capture system multi-model predictive control method of the present invention, the predictive control method takes the post-combustion CO2 capture system based on chemical adsorption as the controlled object, the lean liquid valve opening and the steam turbine low-pressure cylinder extraction valve opening The degree is the system control input, and the CO 2 capture rate and reboiler temperature are the system output. First, based on the subspace identification method, using the data generated by the system operation, the local state space model of the system is established at different operating points; Then use the gap measurement method to investigate the nonlinear distribution of the controlled object, and then establish a predictive controller at a suitable local operating point, and design a membership function to combine them weightedly to establish a multi-model prediction of the post-combustion CO 2 capture system Control System. Compared with the traditional predictive control, the invention improves the control quality of the CO 2 capture system in a wide range of variable working conditions, and enhances its flexible operation capability.
如图1所示,本发明的燃烧后CO2捕集系统多模型预测控制方法,具体包括如下步骤:As shown in Figure 1, the multi-model predictive control method of the post-combustion CO capture system of the present invention specifically includes the following steps:
步骤1,在某一给定捕集率工况点附近,设计30秒变化一次,持续30000秒的贫液流量阀门开度信号ua和汽机低压缸抽汽阀门开度信号ub,对系统进行激励,获取一系列CO2捕集率ya和再沸器温度yb的开环响应数据;Step 1, in the vicinity of a given capture rate operating point, design the lean liquid flow valve opening signal u a and the turbine low-pressure cylinder extraction valve opening signal u b to change once every 30 seconds and last for 30,000 seconds. Stimulate and acquire open-loop response data for a range of CO2 capture rates y a and reboiler temperatures y b ;
步骤2,选定采样周期Ts=30s,以为输入,为输出,利用子空间辨识方法,构建不同捕集率工况点处CO2捕集系统局部状态空间模型,具体步骤为:Step 2, select sampling period T s =30s, with for input, As the output, the subspace identification method is used to construct the local state space model of the CO2 capture system at different capture rate operating points, and the specific steps are as follows:
A:将连续获得的1000组输出数据Y和扩增输入数据U分别排列为Hankel矩阵形式(2N+j-2=1000):A: Arrange 1000 sets of output data Y and amplified input data U obtained continuously into Hankel matrix form (2N+j-2=1000):
其中,N为矩阵行数,,取N=10;N大于CO2捕集系统阶次,j为矩阵列数,在硬件条件允许的情况下越大越好,Y和U分别表示输出与输入数据组成的Hankel矩阵,Yf和Yp分别表示输出数据的未来数据和过去数据,Uf和Up分别表示输入数据的未来数据和过去数据,yj表示第j个输出数据,uj表示第j个输入数据;Among them, N is the number of matrix rows, and N=10; N is greater than the order of the CO 2 capture system, j is the number of matrix columns, the larger the better if the hardware conditions allow, Y and U represent the composition of output and input data respectively The Hankel matrix of , Y f and Y p represent the future data and past data of the output data respectively, U f and U p represent the future data and past data of the input data respectively, y j represents the jth output data, u j represents the jth input data;
B:令Wp=[(Yp)T (Up)T]T,对如下矩阵进行QR分解:B: Let W p =[(Y p ) T (U p ) T ] T , perform QR decomposition on the following matrix:
获得矩阵L:Obtain the matrix L:
C:获得矩阵Lw=L(:,1:N(m+l)),Lu=L(:,N(m+l)+1:end),m=2,m为输入变量维数,l=2,l为输入输出变量维数,L(:,1:N(m+l))表示L的前N(m+l)列, L(:,N(m+l)+1:end)表示L自第N(m+l)+1列之后的所有列;C: Obtain the matrix L w =L(:,1:N(m+l)), L u =L(:,N(m+l)+1:end), m=2, m is the input variable dimension , l=2, l is the dimension of input and output variables, L(:,1:N(m+l)) means the first N(m+l) columns of L, L(:,N(m+l)+1 :end) indicates all the columns of L after the N(m+l)+1 column;
D:对Lw矩阵做奇异值分解:D: Do a singular value decomposition of the L w matrix:
获得矩阵ΓN=U1(S1)1/2,进而得到:模型参数其中表示去掉前l行的ΓN,Γ N表示去掉后l行的ΓN,表示Moore-Penrose伪逆;模型参数C=ΓN(1:l,:) 可从ΓN的前l行中直接获取。Obtain the matrix Γ N =U 1 (S 1 ) 1/2 , and then get: model parameters in means to remove the Γ N of the first row, and Γ N means to remove the Γ N of the last row, Indicates the Moore-Penrose pseudo-inverse; the model parameters C = Γ N (1:l,:) can be obtained directly from the first l rows of Γ N.
子空间矩阵lw=Lw(1:l,:),lu=Lu(1:l,1:m);Subspace matrix l w =L w (1:l,:), l u =L u (1:l,1:m);
E:求解线性方程组:E: Solve a system of linear equations:
获得模型参数B和D。Obtain model parameters B and D.
步骤3,使用间隙度量的方法,分析各相邻局部模型间的差异,调研CO2捕集系统的非线性分布,具体步骤为:Step 3, using the method of gap measurement, analyze the difference between adjacent local models, and investigate the nonlinear distribution of the CO2 capture system, the specific steps are:
A:对两相邻局部模型P1、P2做正交右互质分解,得: A: Perform orthogonal right coprime decomposition on two adjacent local models P 1 and P 2 to get:
B:计算模型P1、P2间的距离:B: Calculate the distance between models P 1 and P 2 :
其中,H∞为一特殊的Hardy赋范空间:σmax(G(jω))表示G(jω)的最大奇异值;Q为H∞空间内的任意函数,取Q=1。Among them, H ∞ is a special Hardy normed space: σ max (G(jω)) represents the maximum singular value of G(jω); Q is any function in H ∞ space, and Q=1.
C:两系统间的间隙度量 C: Gap measure between two systems
D:根据间隙度量的结果选择局部工况点并设计隶属度函数。本例中,其间隙度调研结果如图2所示,可见,在低捕集率和高捕集率区间,系统非线性较强,为此设计隶属度函数如图3所示。D: According to the results of the gap measurement, select the local working point and design the membership function. In this example, the investigation results of the gap degree are shown in Figure 2. It can be seen that the nonlinearity of the system is strong in the range of low capture rate and high capture rate, and the membership function designed for this is shown in Figure 3.
步骤4:在合适的局部工作点处建立模型预测控制器。每一采样时刻,采用公式(1)预估在未来一段时间内系统的CO2捕集率和再沸器温度 Step 4: Build a model predictive controller at a suitable local operating point. At each sampling moment, use formula (1) to estimate the CO2 capture rate and reboiler temperature of the system in the future
其中,预测矩阵ψx、ψu、ψy分别为:Among them, the prediction matrices ψ x , ψ u , ψ y are respectively:
分别为k时刻CO2捕集系统的估计状态、输入和输出,F为观测器增益。 uf为未来Nu个时刻的输入数据, 是未来Ny时刻系统的预估输出,本例中,取Nu=2,Ny=100。 are the estimated state, input and output of the CO2 capture system at time k, respectively, and F is the observer gain. u f is the input data of N u moments in the future, is the estimated output of the system at time N y in the future, In this example, N u =2, N y =100.
取式(2)作为性能指标函数式:Take formula (2) as the performance index function formula:
其中,是调节输入输出控制品质的权值矩阵,rf是未来Ny时刻系统CO2捕集率和再沸器温度设定值序列, 分别表示k+1时刻到k+Ny时刻系统 CO2捕集率ra和再沸器温度rb设定值, in, is the weight matrix for adjusting the quality of input and output control, r f is the sequence of system CO2 capture rate and reboiler temperature setpoint at time N y in the future, Respectively represent the system CO 2 capture rate r a and reboiler temperature r b set values from time k+1 to time k+N y ,
是未来Ny时刻系统CO2捕集率和再沸器温度预估值序列, is the estimated value sequence of CO2 capture rate and reboiler temperature of the system at time Ny in the future,
分别表示k+1时刻到k+Ny时刻系统CO2捕集率ya和再沸器温度yb预估值,可由式(1)描述,取Ny=10;Δuf是未来Nu刻的贫液流量阀门开度信号和低压缸抽汽阀门开度信号序列的增量,其中Nu=2。 Respectively represent the estimated value of system CO 2 capture rate y a and reboiler temperature y b from time k+1 to time k+N y , It can be described by formula (1), taking N y =10; Δu f is the lean liquid flow valve opening signal and low - pressure cylinder extraction valve opening signal sequence at Nu moment in the future increment, of which N u =2.
考虑CO2捕集系统阀门开度信号的幅值约束(umin=[0.4 0.02]T,umax=[1 0.075]T)和增量约束(Δumin=[-0.007 -0.001]T,Δumax=[0.007 0.001]T):Consider the amplitude constraints (u min =[0.4 0.02] T ,u max =[ 1 0.075] T ) and increment constraints (Δu min =[-0.007 -0.001] T ,Δu max = [0.007 0.001] T ):
每一采样时刻,将(1)代入性能指标式(2),并在满足约束(3)和(4)的情况下最小化(2),得到局部的控制增量序列uf:提取局部控制增量序列uf中的第一块uk+1,作为局部的贫液流量阀门和低压缸抽汽阀门开度信号 At each sampling moment, substituting (1) into performance index formula (2), and minimizing (2) under the condition of satisfying constraints (3) and (4), to obtain the local control increment sequence u f : Extract the first block u k+1 in the local control incremental sequence u f as the local lean liquid flow valve and low pressure cylinder extraction valve opening signal
步骤5,利用隶属度函数,将各控制器输出加权组合,得到最终的贫液流量阀门开度ua-op和汽轮机低压缸抽汽阀门开度信号ub-op并作用于CO2捕集系统。其中ωi为第i个控制器对应的隶属度函数,其为调度变量,捕集率CR的函数,ui a-op和ui b-op为第i个控制器计算出的最优控制信号。Step 5: Use the membership function to combine the weighted outputs of each controller to obtain the final lean liquid flow valve opening u a-op and steam turbine low-pressure cylinder extraction valve opening signal u b-op and act on CO 2 capture system. in ω i is the membership function corresponding to the i-th controller, which is a function of the scheduling variable and the capture rate CR, u i a-op and u i b-op are the optimal control signals calculated by the i-th controller .
步骤6,固定各局部控制器中来输出的预测矩阵ψx、ψu、ψy,重复步骤3~4以实现连续控制。Step 6, fix the prediction matrices ψ x , ψ u , ψ y output from each local controller, and repeat steps 3-4 to realize continuous control.
本实施例为了比较本发明中的燃烧后CO2捕集系统多模型预测控制方法、常规比例积分微分控制方法和一般预测控制方法的控制效果,做了两组仿真试验:仿真实验1,CO2捕集系统初始捕集率稳定于80%,在t=15min和115min,CO2捕集率设定值从80%分别缓慢变化至70%和75%,再沸器温度设定值保持在383K不变;仿真实验2,CO2捕集系统初始捕集率稳定于80%,t=15min和115min,CO2捕集率设定值从80%分别缓慢变化至90%和55%,再沸器温度设定值保持在383K不变。In this embodiment, in order to compare the control effects of the post-combustion CO2 capture system multi-model predictive control method, conventional proportional-integral-derivative control method and general predictive control method in the present invention, two sets of simulation experiments were done: simulation experiment 1, CO2 The initial capture rate of the capture system was stable at 80%. At t=15min and 115min, the set value of CO2 capture rate was slowly changed from 80% to 70% and 75%, respectively, and the set value of reboiler temperature was maintained at 383K In simulation experiment 2, the initial capture rate of the CO 2 capture system is stable at 80%, t=15min and 115min, the set value of CO 2 capture rate changes slowly from 80% to 90% and 55% respectively, and the reboil The temperature set point of the device remains unchanged at 383K.
如图4所示,在CO2捕集率设定值增加或减小情况下,本发明对燃烧后CO2捕集系统的优化控制效果曲线明显优于常规比例加积分控制器,具有满意的设定值跟踪和调节能力。如图5所示,在CO2捕集率设定值大范围变化的情况下,本发明的优化控制方法可以更好地协调使用再沸器抽汽与贫液流量,实现对捕集率的快速追踪控制,同时可以有效避免大范围变工况运行下线性模型失配带来的控制器震荡,具有更平稳的控制效果,提高了CO2捕集系统的运行品质。As shown in Figure 4, when the set value of the CO2 capture rate increases or decreases, the optimal control effect curve of the present invention for the post-combustion CO2 capture system is obviously better than that of the conventional proportional plus integral controller, and has satisfactory Setpoint tracking and adjustment capability. As shown in Figure 5, under the condition that the set value of the CO2 capture rate varies in a wide range, the optimal control method of the present invention can better coordinate the use of reboiler extraction and lean liquid flow, and realize the control of the capture rate. Fast tracking control can effectively avoid the controller oscillation caused by the mismatch of the linear model under large-scale variable working conditions, and has a more stable control effect, improving the operation quality of the CO 2 capture system.
本发明燃烧后CO2捕集系统多模型预测控制方法,利用子空间辨识方法建立CO2捕集系统在不同工况点下的模型,在对捕集系统非线性调研的基础上,选择局部模型、建立预测控制器并设计隶属度函数,在保有常规线性预测控制所有优点的前提下大幅提高系统大范围变工况运行水平,从而进一步提高CO2捕集系统快速深度灵活运行的能力。The multi-model predictive control method of the post-combustion CO2 capture system of the present invention uses the subspace identification method to establish the model of the CO2 capture system at different operating points, and selects the local model on the basis of the nonlinear investigation of the capture system , Establish a predictive controller and design a membership function to greatly improve the system's wide-ranging and variable operating conditions while maintaining all the advantages of conventional linear predictive control, thereby further improving the ability of the CO 2 capture system to operate quickly, deeply and flexibly.
尽管本发明就优选实施方式进行了示意和描述,但本领域的技术人员应当理解,只要不超出本发明的权利要求所限定的范围,可以对本发明进行各种变化和修改。Although the present invention has been illustrated and described in terms of preferred embodiments, those skilled in the art should understand that various changes and modifications can be made to the present invention without departing from the scope defined by the claims of the present invention.
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