CN104806302B

CN104806302B - A kind of main steam valve of turbine generator forecast Control Algorithm based on Nonlinear Disturbance Observer

Info

Publication number: CN104806302B
Application number: CN201510192215.2A
Authority: CN
Inventors: 陈宝林; 韩璞; 刘志杰; 刘金琨; 董泽; 王德华
Original assignee: North China Electric Power University; Guodian Science and Technology Research Institute Co Ltd
Current assignee: North China Electric Power University; Guodian Science and Technology Research Institute Co Ltd
Priority date: 2015-04-21
Filing date: 2015-04-21
Publication date: 2016-05-25
Anticipated expiration: 2035-04-21
Also published as: CN104806302A

Abstract

A predictive control method for the main steam valve opening of a turbogenerator based on a nonlinear disturbance observer. The method has four steps: Step 1: Analysis and modeling of the main steam valve opening control system of the turbogenerator; Step 2 : design of predictive control of steam turbine generator main valve opening; step 3: design of nonlinear disturbance observer; step 4: end of design. The present invention designs a control law with a closed-form analytical solution for the main valve opening control system model, and then designs a nonlinear disturbance observer to compensate the control disturbance, thereby ensuring closed-loop control under the condition of strong input disturbance The global stability of the system realizes fast and accurate tracking of the power angle of the turbogenerator to the predetermined trajectory.

Description

A Predictive Control Method of Turbogenerator Main Steam Valve Opening Based on Nonlinear Disturbance Observer

技术领域technical field

本发明涉及一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，它是针对单机无穷大总线系统，而给出的一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，用于控制汽轮发电机功角，属于自动控制技术领域。The invention relates to a method for predicting and controlling the opening of the main steam valve of a turbogenerator based on a nonlinear disturbance observer. It is aimed at a single-machine infinite bus system and provides a turbogenerator based on a nonlinear disturbance observer. The main steam valve opening predictive control method is used for controlling the work angle of a steam turbine generator and belongs to the technical field of automatic control.

背景技术Background technique

汽轮发电机的励磁控制和汽门调节是提高电力系统稳定性的两个重要手段。由于励磁控制受到励磁电流顶值的限制，而要求发电机具有过高的励磁电流顶值将增加发电机制造成本；同时，发电机励磁电流的上升速度也将受到励磁绕组时间常数的限制。因此，仅仅依靠励磁控制对系统稳定性的改善是有限的。随着大功率的中间再热式汽轮发电机组应用于电力系统，功率—频率电液式调速器日益取代机械液压式调速器，通过改善汽轮发电机主汽门开度控制来提高中间再热式汽轮发电机组的一次调频能力和负荷适应性，从而提高电力系统的稳定性，具有特别重要的意义。Excitation control and steam valve adjustment of turbogenerator are two important means to improve the stability of power system. Since the excitation control is limited by the top value of the excitation current, requiring the generator to have an excessively high top value of the excitation current will increase the manufacturing cost of the generator; at the same time, the rising speed of the excitation current of the generator will also be limited by the time constant of the excitation winding. Therefore, it is limited to improve the stability of the system only relying on the excitation control. With the application of high-power mid-reheat turbogenerators to power systems, power-frequency electro-hydraulic governors are increasingly replacing mechanical-hydraulic governors. The primary frequency regulation capability and load adaptability of the intermediate reheating turbogenerator set, so as to improve the stability of the power system, is of great significance.

近年来，许多先进的控制方法被用到汽轮发电机主汽门开度控制的设计中，其中包括反馈线性化方法、最优控制方法等。但是这些方法不具备对参数和模型变化的鲁棒性，并且对系统中非匹配不确定性无能为力。预测控制方法是一种新颖的控制方法，它所需要的模型只强调预测功能，不苛求其结构形式，从而为系统建模带来方便。更重要的是，预测控制汲取了优化控制的思想，但利用滚动的有限时段优化取代了一成不变的全局优化，能够不断顾及不确定性的影响并及时加以校正，从而有更强的鲁棒性。所以，预测控制在复杂的工业环境中受到青睐。虽然预测控制具有一定的鲁棒性，但当控制干扰较大时，控制效果不能达到理想的要求，所以通过设计非线性干扰观测器进行补偿，已达到理想的控制效果。In recent years, many advanced control methods have been used in the design of the main steam valve opening control of turbogenerator, including feedback linearization method, optimal control method and so on. However, these methods are not robust to parameter and model changes, and are powerless against mismatch uncertainties in the system. The predictive control method is a novel control method. The model it needs only emphasizes the predictive function, not its structural form, which brings convenience to the system modeling. More importantly, predictive control draws on the idea of optimal control, but replaces the immutable global optimization with rolling finite-period optimization, which can constantly take into account the influence of uncertainty and correct it in time, so it has stronger robustness. Therefore, predictive control is favored in complex industrial environments. Although the predictive control has a certain robustness, when the control disturbance is large, the control effect cannot meet the ideal requirements. Therefore, the ideal control effect has been achieved by designing a nonlinear disturbance observer to compensate.

这种技术背景下，本发明针对单机无穷大总线系统，给出一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，用于控制汽轮发电机功角。在较强干扰的情况下，采用这种控制方法不仅保证了闭环系统的稳定性，还实现了汽轮发电机功角对预定轨迹的快速且精确跟踪。Against this technical background, the present invention provides a predictive control method for the opening of the main steam valve of a turbogenerator based on a nonlinear disturbance observer for a single-unit infinite bus system, which is used to control the power angle of the turbogenerator. In the case of strong interference, the use of this control method not only ensures the stability of the closed-loop system, but also realizes the rapid and accurate tracking of the power angle of the turbogenerator to the predetermined trajectory.

发明内容Contents of the invention

1、发明目的1. Purpose of the invention

本发明的目的是：针对主汽门开度控制系统模型，克服现有控制技术的不足，而提供一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，它在保证闭环全局系统稳定的基础上，实现闭环系统汽轮发电机功角对预定轨迹的快速且精确跟踪。The purpose of the present invention is: for the main steam valve opening control system model, overcome the deficiency of existing control technology, and provide a kind of steam turbine generator main steam valve opening predictive control method based on nonlinear disturbance observer, it is in On the basis of ensuring the stability of the closed-loop global system, the fast and accurate tracking of the power angle of the closed-loop system turbogenerator to the predetermined trajectory is realized.

本发明是一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，其设计思想是：针对主汽门开度控制系统模型，设计出具有闭型解析解的控制律，然后设计非线性干扰观测器对控制干扰进行补偿，从而在具有较强输入干扰的情况下，保证闭环控制系统的全局稳定性，同时实现了汽轮发电机功角对预定轨迹的快速且精确跟踪。The present invention is a predictive control method for the main steam valve opening of a turbogenerator based on a nonlinear disturbance observer, and its design concept is: aiming at the main steam valve opening control system model, a control law with a closed-type analytical solution is designed , and then design a nonlinear disturbance observer to compensate the control disturbance, so as to ensure the global stability of the closed-loop control system in the case of strong input disturbance, and realize the rapid and accurate calculation of the turbine generator power angle to the predetermined trajectory track.

2、技术方案2. Technical solution

下面具体介绍该设计方法的技术方案。The technical scheme of the design method is introduced in detail below.

单机无穷大总线系统示意图如图1。The schematic diagram of the stand-alone infinite bus system is shown in Figure 1.

本发明一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，该方法具体步骤如下：The present invention is based on a nonlinear disturbance observer-based predictive control method for the opening of the main steam valve of a turbogenerator. The specific steps of the method are as follows:

步骤一：汽轮发电机主汽门开度控制系统分析与建模Step 1: Analysis and modeling of turbogenerator main steam valve opening control system

闭环控制系统采用负反馈的控制结构，输出量是汽轮发电机功角。所设计的闭环控制系统主要包括控制器环节和系统模型这两个部分，其结构布局情况见图2所示。The closed-loop control system adopts a negative feedback control structure, and the output is the power angle of the turbogenerator. The designed closed-loop control system mainly includes two parts, the controller link and the system model, and its structural layout is shown in Figure 2.

主汽门开度控制系统模型描述如下：The main valve opening control system model is described as follows:

$\{\begin{matrix} \overset{\cdot &Center Dot;}{δ δ} = = ω ω - - {ω ω}_{00} \\ \overset{\cdot &Center Dot;}{ω ω} = = - - \frac{D D.}{H h} ((ω ω - - {ω ω}_{00})) + + \frac{{ω ω}_{00}}{H h} (({P P}_{H h} + + {C C}_{ML ML} {P P}_{m m 00} - - \frac{{E E.}_{q q}^{' '} {V V}_{s the s}}{{X x}_{dΣ dΣ}^{' '}} sin sin δ δ)) \\ {\overset{\cdot \cdot}{P P}}_{H h} = = - - \frac{11}{{T T}_{HΣ HΣ}} (({P P}_{H h} - - {C C}_{H h} {P P}_{m m 00})) + + \frac{{C C}_{H h}}{{T T}_{HΣ HΣ}} ((u u + + d d)) \end{matrix} - - - - - - ((11))$

其中：δ表示汽轮发电机功角；Where: δ represents the turbine generator power angle;

δ₀表示汽轮发电机功角初值；δ ₀ represents the initial value of turbine generator power angle;

ω表示发电机转子速度；ω represents the generator rotor speed;

ω₀表示发电机转子速度初值；ω ₀ represents the initial value of the rotor speed of the generator;

P_H表示高压缸产生的机械功率；P _H represents the mechanical power generated by the high-pressure cylinder;

P_m表示原动机输出的机械功率；P _m represents the mechanical power output by the prime mover;

P_m0表示原动机输出的机械功率初值；P _m0 represents the initial value of the mechanical power output by the prime mover;

D表示阻尼系数；D represents the damping coefficient;

H表示发电机转子的转动惯量；H represents the moment of inertia of the generator rotor;

C_ML表示中低压功率分配系数；C _ML represents the medium and low voltage power distribution coefficient;

C_H表示高压缸功率非配系数；C _H represents the non-matching coefficient of high-pressure cylinder power;

E'_q表示发电机q轴暂态电势；E' _q represents the generator q-axis transient potential;

V表示无穷大总线电压；V represents the infinite bus voltage;

X'_dΣ表示发电机与无穷大系统间的等值电势；X' _dΣ represents the equivalent potential between the generator and the infinite system;

T_HΣ表示高压缸汽门控制系统等效时间常数；T _HΣ represents the equivalent time constant of the high-pressure cylinder valve control system;

u表示汽轮发电机主汽门开度控制；u represents the opening degree control of the main steam valve of the turbogenerator;

d表示汽轮发电机主汽门开度控制输入干扰。d represents the input disturbance of the turbine generator main steam valve opening control.

为了便于设计，分别定义三个状态变量x₁、x₂、x₃如下：For the convenience of design, three state variables x ₁ , x ₂ , and x ₃ are defined as follows:

x₁＝δ-δ₀ x ₁ = δ - δ ₀

x₂＝ω-ω₀ x ₂ =ω-ω ₀

x₃＝P_H-C_HP_m0 x ₃ ＝P _H _-CH P _m0

这时(1)就可以写成Then (1) can be written as

$\{\begin{matrix} \overset{\cdot \cdot}{x x} ((t t)) = = f f ((x x)) + + g g ((x x)) u u ((t t)) + + {g g}_{d d} ((x x)) d d \\ y the y ((t t)) = = h h ((x x)) \end{matrix} - - - - - - ((22))$

其中： $f (x) = (\begin{matrix} x_{2} \\ a_{1} \sin (x_{1} + δ_{0}) + a_{2} x_{2} + a_{3} x_{3} + b_{1} \\ a_{4} x_{30} \end{matrix}), g (x) = (\begin{matrix} 0 \\ 0 \\ k_{1} \end{matrix}), g_{d} (x) = (\begin{matrix} 0 \\ 0 \\ k_{1} \end{matrix}), h (x) = x_{1}$ in: $f (x) = (\begin{matrix} x_{2} \\ a_{1} \sin (x_{1} + δ_{0}) + a_{2} x_{2} + a_{3} x_{3} + b_{1} \\ a_{4} x_{30} \end{matrix}), g (x) = (\begin{matrix} 0 \\ 0 \\ k_{1} \end{matrix}), g_{d} (x) = (\begin{matrix} 0 \\ 0 \\ k_{1} \end{matrix}), h (x) = x_{1}$

${a a}_{11} = = - - \frac{{ω ω}_{00} {E E.}_{q q}^{' '} {V V}_{s the s}}{{HX HX}_{dΣ dΣ}^{' '}} sin sin (({x x}_{11} + + {δ δ}_{00}))$

${a a}_{22} = = - - \frac{D D.}{H h}$

${a a}_{33} = = \frac{{ω ω}_{00}}{H h},,$

${a a}_{44} = = - - \frac{11}{{T T}_{HΣ HΣ}}$

${b b}_{11} = = \frac{{ω ω}_{00}}{H h} {P P}_{m m 00} (({C C}_{H h} + + {C C}_{ML ML}))$

${k k}_{11} = = \frac{{C C}_{H h}}{{T T}_{HΣ HΣ}},,$

步骤二：汽轮发电机主汽门开度预测控制设计Step 2: Predictive Control Design of Turbogenerator Main Steam Valve Opening

控制任务为输出y(t)跟踪指令w(t)，并克服汽轮发电机主汽门开度控制输入干扰d。The control task is to output y(t) tracking command w(t), and overcome the input disturbance d of the main steam valve opening control of the turbogenerator.

优化目标函数为The optimization objective function is

$J J = = \frac{11}{22} {&Integral; &Integral;}_{00}^{T T} {((\overset{^^}{y the y} ((t t + + τ τ)) - - \overset{^^}{w w} ((t t + + τ τ))))}^{T T} ((\overset{^^}{y the y} ((t t + + τ τ)) - - \overset{^^}{w w} ((t t + + τ τ)))) dτ dτ + + \frac{11}{22} {&Integral; &Integral;}_{00}^{T T} {((d d ((t t + + τ τ)) - - \overset{^^}{d d} ((t t + + τ τ))))}^{22} dτ dτ - - - - - - ((33))$

其中为d(t+τ)的观测值，为y(t+τ)的预测值，为w(t+τ)的预测值，T为预测区间，τ为预测时间，0≤τ≤T，且有in is the observed value of d(t+τ), is the predicted value of y(t+τ), is the predicted value of w(t+τ), T is the prediction interval, τ is the prediction time, 0≤τ≤T, and

当τ＝0时， $u = (t + τ) = \hat{u} (t + τ) = 0 - - - (4)$ 其中为u(t+τ)的预测值。When τ=0, $u = (t + τ) = \hat{u} (t + τ) = 0 - - - (4)$ in is the predicted value of u(t+τ).

模型的相对阶数为ρ，控制阶数为r，定义为The relative order of the model is ρ, and the control order is r, which is defined as

${\overset{^^}{u u}}^{[[r r]]} ((t t + + τ τ)) &NotEqual; &NotEqual; 00,, τ τ &Element; &Element; [[00,, T T]]$

${\overset{^^}{u u}}^{[[k k]]} ((t t + + τ τ)) = = 00,, k k > > r r,, τ τ &Element; &Element; [[00,, T T]]$

本算法中，通过泰勒展开，实现对未来输出预测信号的逼近，针对的逼近，取In this algorithm, the approximation of the future output prediction signal is realized through Taylor expansion. approximation, take

$\overset{^^}{y the y} ((t t + + τ τ)) \overset{\cdot &Center Dot;}{= =} Γ Γ ((τ τ)) \overset{\overset{^^}{&OverBar; &OverBar;}}{Y Y} ((t t))$

其中 $\overset{&OverBar;}{τ} = diag {τ, . . ., τ}$ 为m×m矩阵，m为系统输出个数， $Γ (t) = [\begin{matrix} I & \overset{&OverBar;}{τ} & . . . & \frac{{\overset{&OverBar;}{τ}}^{(ρ + r)}}{(ρ + r)!} \end{matrix}],$ I为m×m的单位阵。由模型(2)可知，ρ＝3，r＝1,m＝1,所以可以取in $\overset{&OverBar;}{τ} = diag {τ, . . ., τ}$ is an m×m matrix, m is the number of system outputs, $Γ (t) = [\begin{matrix} I & \overset{&OverBar;}{τ} & . . . & \frac{{\overset{&OverBar;}{τ}}^{(ρ + r)}}{(ρ + r)!} \end{matrix}],$ I is an m×m unit matrix. It can be known from model (2) that ρ=3, r=1, m=1, so it can be taken

$\overset{\overset{^^}{&OverBar; &OverBar;}}{Y Y} ((t t)) = = [\begin{matrix} {\overset{^^}{y the y}}^{[[00]]} \\ {\overset{^^}{y the y}}^{[[11]]} \\ {\overset{^^}{y the y}}^{[[33]]} \\ {\overset{^^}{y the y}}^{[[44]]} \end{matrix}] = = [\begin{matrix} h h ((x x)) \\ {L L}_{f f}^{11} h h ((x x)) \\ {L L}_{f f}^{22} h h ((x x)) \\ {L L}_{f f}^{33} h h ((x x)) \end{matrix}] + + [\begin{matrix} 00 \\ 00 \\ H h ((\overset{^^}{u u})) \end{matrix}] H h ((\overset{^^}{u u})) = = [\begin{matrix} {L L}_{g g} {L L}_{f f} h h ((x x)) \overset{^^}{u u} ((t t)) \\ {p p}_{1111} ((\overset{^^}{u u} ((t t)),, x x ((t t)))) + + {L L}_{g g} {L L}_{f f} h h ((x x)) \overset{\overset{\cdot &Center Dot;}{^^}}{u u} ((t t)) \end{matrix}]$

其中， $p_{11} (\hat{u} (t), x (t)) = L_{g} L_{f}^{3} h (x) \hat{u} (t) + \frac{{dL}_{g} L_{f}^{2} h (x)}{dt} \hat{u} (t)$ in, $p_{11} (\hat{u} (t), x (t)) = L_{g} L_{f}^{3} h (x) \hat{u} (t) + \frac{L_{g} L_{f}^{2} h (x)}{dt} \hat{u} (t)$

通过泰勒展开，实现对未来指令预测信号的逼近，针对w(t+τ)的逼近，取Through Taylor expansion, the approximation of the future instruction prediction signal is realized. For the approximation of w(t+τ), take

$\overset{^^}{w w} ((t t + + τ τ)) = = Γ Γ ((τ τ)) \overset{&OverBar; &OverBar;}{W W} ((t t))$

其中,in,

$\overset{&OverBar; &OverBar;}{W W} ((t t)) = = {[\begin{matrix} w w {((t t))}^{T T} & \overset{\cdot \cdot}{w w} {((t t))}^{T T} & . . . . . . & {w w}^{[[44]]} {((t t))}^{T T} \end{matrix}]}^{T T} . .$

取可得预测控制律为Pick The predictive control law can be obtained as

$u u ((t t)) = = - - {(({L L}_{g g} {L L}_{f f}^{22} h h ((x x))))}^{- - 11} (({KM KM}_{ρ ρ} + + {L L}_{f f}^{33} h h ((x x)) - - {w w}^{[[33]]} ((t t)))) - - - - - - ((55))$

其中， $L_{f} h (x) = \frac{&PartialD; h}{&PartialD; x} f (x)$ 为h关于f的Lie导数， $M_{ρ} = [\begin{matrix} x_{1} - w (t) \\ L_{f} h (x) - \overset{\cdot}{w} \\ L_{f}^{2} h (x) - \overset{\cdot \cdot}{w} (t) \end{matrix}, (t)], K = \overset{&OverBar;}{Γ} (1, :),$ $\overset{&OverBar;}{Γ} = {\overset{&OverBar;}{Γ}}_{rr}^{- 1} {\overset{&OverBar;}{Γ}}_{ρr}^{T} = {\overset{&OverBar;}{Γ}}_{11}^{- 1} {\overset{&OverBar;}{Γ}}_{31}^{T} .$ in, $L_{f} h (x) = \frac{&PartialD; h}{&PartialD; x} f (x)$ is the Lie derivative of h with respect to f, $m_{ρ} = [\begin{matrix} x_{1} - w (t) \\ L_{f} h (x) - \overset{\cdot}{w} \\ L_{f}^{2} h (x) - \overset{&Center Dot; &Center Dot;}{w} (t) \end{matrix}, (t)], K = \overset{&OverBar;}{Γ} (1, :),$ $\overset{&OverBar;}{Γ} = {\overset{&OverBar;}{Γ}}_{rr}^{- 1} {\overset{&OverBar;}{Γ}}_{ρr}^{T} = {\overset{&OverBar;}{Γ}}_{11}^{- 1} {\overset{&OverBar;}{Γ}}_{31}^{T} .$

由于ρ+r+1＝5，则i,j＝1,2,3,4,5，则表示为Since ρ+r+1=5, then i,j=1,2,3,4,5, then Expressed as

${\overset{&OverBar; &OverBar;}{Γ Γ}}_{rr rr} = = {\overset{&OverBar; &OverBar;}{Γ Γ}}_{1111} = = [\begin{matrix} {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((4,4 4,4))} & {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((4,5 4,5))} \\ {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((5,4 5,4))} & {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((5,5 5,5))} \end{matrix}],, {\overset{&OverBar; &OverBar;}{Γ Γ}}_{ρr ρr} = = {\overset{&OverBar; &OverBar;}{Γ Γ}}_{3131} = = [\begin{matrix} {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((1,4 1,4))} & {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((1,5 1,5))} \\ {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((2,4 2,4))} & {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((2,5 2,5))} \\ {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((3,4 3,4))} & {\overset{&OverBar; &OverBar;}{Γ Γ}}_{((3,5 3,5))} \end{matrix}]$

${\overset{&OverBar; &OverBar;}{Γ Γ}}_{((i i,, j j))} = = \frac{{\overset{&OverBar; &OverBar;}{T T}}^{i i + + j j - - 11}}{((i i - - 11))!! ((j j - - 11))!! ((i i + + j j - - 11))},, i i,, j j = = 11,, . . . . . .,, ρ ρ + + r r + + 11$

$\overset{&OverBar; &OverBar;}{T T} = = T T$

步骤三：非线性干扰观测器设计Step 3: Nonlinear Disturbance Observer Design

设计非线性干扰观测器估计未知的干扰，对控制输入进行补偿。A nonlinear disturbance observer is designed to estimate the unknown disturbance and compensate the control input.

设计观测器为：The observer is designed as:

$\overset{^^}{d d} - - z z + + p p ((x x))$

$\overset{\cdot \cdot}{z z} = = - - l l ((x x)) {g g}_{d d} ((x x)) z z - - l l ((x x)) (({g g}_{d d} ((x x)) p p ((x x)) + + f f ((x x)) + + g g ((x x)) u u))$

非线性观测器增益定义为：The nonlinear observer gain is defined as:

$l l ((x x)) = = \frac{&PartialD; &PartialD; p p ((x x))}{&PartialD; &PartialD; x x}$

观测误差定义为：The observation error is defined as:

且干扰是慢时变的。 And the interference is slow and time-varying.

选择p(x)，使方程满足全局指数稳定，则指数收敛于d。Choose p(x) such that the equation Satisfying the global exponential stability, then The exponential converges to d.

根据模型(2)，选择则，According to model (2), choose but,

$l l ((x x)) = = [\begin{matrix} 00 & 00 & {l l}_{33} ((11 + + 33 c c {x x}_{33}^{22})) \end{matrix}]$

此时，所以适当的参数c,对所有的l₃都有全局指数稳定。at this time, So with the appropriate parameter c, there is global exponential stability for all l ₃ .

从而可得基于非线性干扰观测器的预测控制律：Thus, the predictive control law based on nonlinear disturbance observer can be obtained:

$u u ((t t)) = = - - {(({L L}_{g g} {L L}_{f f}^{22} h h ((x x))))}^{- - 11} (({KM KM}_{33} + + {L L}_{f f}^{33} h h ((x x)) - - {w w}^{[[33]]} ((t t)))) - - \overset{^^}{d d}$

至此，一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法设计完毕。So far, a predictive control method for the main steam valve opening of the turbogenerator based on the nonlinear disturbance observer has been designed.

步骤四：设计结束Step 4: End of Design

整个设计过程重点考虑了三个方面的控制需求，分别为设计的简便性，闭环系统的稳定性，跟踪的快速精确性。围绕这三个方面，首先在上述第一步中确定了闭环控制系统的具体构成；第二步中重点给出了汽轮发电机主汽门开度预测控制设计方法；第三步中主要给出了非线性干扰观测器的设计；经上述各步骤后，设计结束。The entire design process focuses on three aspects of control requirements, namely, the simplicity of design, the stability of the closed-loop system, and the fast and accurate tracking. Focusing on these three aspects, the specific composition of the closed-loop control system is determined in the first step above; in the second step, the design method of predictive control of the main steam valve opening of the turbogenerator is given; in the third step, the The design of the nonlinear disturbance observer is obtained; after the above steps, the design ends.

3、优点及功效3. Advantages and effects

本发明针对单机无穷大总线系统，给出一种基于非线性干扰观测器的汽轮发电机主汽门开度预测控制方法，用于控制汽轮发电机功角。具体优点包括两个方面：其一，与目前存在的处理方法相比，这种方法在设计控制器过程中十分简便，避免在线优化带来的大量计算负担从而满足实时控制要求；其二，通过设计非线性干扰观测器补偿输入干扰，从而在具有较强输入干扰的情况下，保证闭环控制系统的全局稳定性，同时实现了汽轮发电机功角对预定轨迹的快速且精确跟踪。Aiming at the single-unit infinite bus system, the invention provides a method for predicting and controlling the opening of the main steam valve of the steam turbine generator based on a nonlinear disturbance observer, which is used for controlling the power angle of the steam turbine generator. The specific advantages include two aspects: first, compared with the existing processing methods, this method is very simple in the process of designing the controller, avoiding a large amount of calculation burden brought by online optimization to meet the real-time control requirements; second, through A nonlinear disturbance observer is designed to compensate the input disturbance, so as to ensure the global stability of the closed-loop control system in the case of strong input disturbance, and realize fast and accurate tracking of the turbine generator power angle to the predetermined trajectory.

附图说明Description of drawings

图1：本发明单机无穷大总线系统示意图。Figure 1: Schematic diagram of the present invention's stand-alone infinite bus system.

图2：本发明闭环控制系统结构和组件连接关系示意图。Figure 2: Schematic diagram of the structure of the closed-loop control system of the present invention and the connection relationship of components.

图3：本发明主汽门开度预测控制(有干扰观测器)设计流程示意图。Fig. 3: Schematic diagram of the design process of the main valve opening predictive control (with disturbance observer) of the present invention.

图4.1：无干扰观测器的跟踪效果图。Figure 4.1: Tracking effect of the interference-free observer.

图4.2：无干扰观测器的跟踪误差图。Figure 4.2: Tracking error plot for the interference-free observer.

图4.3：无干扰观测器的控制输入图。Figure 4.3: Control input diagram for a disturbance-free observer.

图5.1：本发明实施(有干扰观测器)中的跟踪效果图。Figure 5.1: Tracking effect diagram in the implementation of the present invention (with interference observer).

图5.2：本发明实施(有干扰观测器)中的跟踪误差图。Figure 5.2: Tracking error plot in an implementation of the invention (with disturbance observer).

图5.3：本发明实施(有干扰观测器)中的控制输入图。Figure 5.3: Diagram of control inputs in an implementation of the invention (with disturbance observer).

图5.4：本发明实施(有干扰观测器)中的观测器的观测效果图。Figure 5.4: Observation effect diagram of the observer in the implementation of the present invention (with interference observer).

图4.1-4.3、图5.1-5.4中的横坐标表示仿真时间，单位是秒；图4.1、图5.1中纵坐标表示汽轮发电机功角跟踪效果，单位是度；图4.2、图5.2中纵坐标表示汽轮发电机功角跟踪误差，单位是度；图4.3、图5.3中纵坐标表示汽轮发电机主汽门开度控制输入，单位是牛顿；图5.4中纵坐标表示汽轮发电机主汽门开度控制输入干扰观测效果，单位是牛顿；图4.1、图5.1中的虚线代表预定轨迹信号线，实线代表实际汽轮发电机功角信号线；图5.4中的虚线代表实际干扰信号线，实线代表观测器观测干扰信号线。The abscissa in Figure 4.1-4.3 and Figure 5.1-5.4 represents the simulation time, the unit is second; the vertical axis in Figure 4.1 and Figure 5.1 represents the tracking effect of the steam turbine generator power angle, and the unit is degree; the vertical axis in Figure 4.2 and Figure 5.2 The coordinates indicate the tracking error of the steam turbine generator power angle, and the unit is degree; the ordinate in Figure 4.3 and Figure 5.3 indicates the control input of the main steam valve opening of the steam turbine generator, and the unit is Newton; the ordinate in Figure 5.4 indicates the steam turbine generator Main valve opening control input interference observation effect, unit is Newton; the dotted line in Figure 4.1 and Figure 5.1 represents the signal line of the predetermined trajectory, and the solid line represents the actual turbine generator power angle signal line; the dotted line in Figure 5.4 represents the actual interference Signal line, the solid line represents the interference signal line observed by the observer.

具体实施方式detailed description

见图1—图5.4，本发明设计目标包括两个方面：其一，实现汽轮发电机主汽门开度控制设计的简单化；其二，实现闭环系统的汽轮发电机功角快速精确跟踪预定轨迹，具体指标是：汽轮发电机功角在1秒内跟踪误差小于0.5度角。图1是本发明单机无穷大总线系统示意图。See Fig. 1-Fig. 5.4, the design goal of the present invention includes two aspects: first, to realize the simplification of the control design of the main steam valve of the turbo-generator; Track the predetermined trajectory, the specific index is: the tracking error of the turbine generator power angle within 1 second is less than 0.5 degrees. Fig. 1 is a schematic diagram of a stand-alone infinite bus system of the present invention.

具体实施中，主汽门开度预测控制方法和闭环控制系统的仿真和检验都借助于Matlab中的Simulink工具箱来实现。这里通过介绍一个具有一定代表性的实施方式，来进一步说明本发明技术方案中的相关设计。仿真中，根据某电厂的实际系统经验数据，参数选取如下：In the specific implementation, the simulation and verification of the main valve opening predictive control method and the closed-loop control system are realized by means of the Simulink toolbox in Matlab. Here, a certain representative implementation manner is introduced to further illustrate related designs in the technical solution of the present invention. In the simulation, according to the actual system experience data of a power plant, the parameters are selected as follows:

δ₀＝60，ω₀＝218，P_m0＝0.8，D＝5，H＝8，C_ML＝0.7，C_H＝0.3，E'_q＝1.08，V_s＝1，X'_dΣ＝0.94，T_HΣ＝0.4，状态变量初值设置为x₁＝0、x₂＝0、x₃＝0。δ ₀ =60, ω ₀ =218, P _m0 =0.8, D=5, _H =8, C _ML =0.7, CH =0.3, E' _q =1.08, V _s =1, X' _dΣ =0.94, T _HΣ =0.4, and the initial values of the state variables are set to x ₁ =0, x ₂ =0, x ₃ =0.

观测器参数取l₃＝100，c＝0.001，控制器参数为T＝0.238，指令信号w(t)＝5sin(πt)。Observer parameters are l ₃ =100, c=0.001, controller parameters are T=0.238, command signal w(t)=5sin(πt).

实施方式(一)实现汽轮发电机功角跟踪的精确性和快速性。Embodiment (1) Realize the accuracy and rapidity of turbine generator power angle tracking.

实施方式(一)Implementation Mode (1)

$\{\begin{matrix} \overset{\cdot &Center Dot;}{δ δ} = = ω ω - - {ω ω}_{00} \\ \overset{\cdot \cdot}{ω ω} = = - - \frac{D D.}{H h} ((ω ω - - {ω ω}_{00})) + + \frac{{ω ω}_{00}}{H h} (({P P}_{H h} + + {C C}_{ML ML} {P P}_{m m 00} - - \frac{{E E.}_{q q}^{' '} {V V}_{s the s}}{{X x}_{dΣ dΣ}^{' '}} sin sin δ δ)) \\ {\overset{\cdot \cdot}{P P}}_{H h} = = - - \frac{11}{{T T}_{HΣ HΣ}} (({P P}_{H h} - - {C C}_{H h} {P P}_{m m 00})) + + \frac{{C C}_{H h}}{{T T}_{HΣ HΣ}} ((u u + + d d)) \end{matrix} - - - - - - ((11))$

ω表示发电机转子速度；ω represents the generator rotor speed;

D表示阻尼系数；D represents the damping coefficient;

V表示无穷大总线电压；V represents the infinite bus voltage;

x₁＝δ-δ₀ x ₁ = δ - δ ₀

x₂＝ω-ω₀ x ₂ =ω-ω ₀

x₃＝P_H-C_HP_m0 x ₃ ＝P _H _-CH P _m0

这时(1)就可以写成Then (1) can be written as

${a a}_{22} = = - - \frac{D D.}{H h}$

${a a}_{33} = = \frac{{ω ω}_{00}}{H h},,$

${a a}_{44} = = - - \frac{11}{{T T}_{HΣ HΣ}}$

${k k}_{11} = = \frac{{C C}_{H h}}{{T T}_{HΣ HΣ}},,$

优化目标函数为The optimization objective function is

其中为d的观测值，为y(t+τ)的预测值，为w(t+τ)的预测值，T为预测区间，τ为预测时间，0≤τ≤T，且有in is the observed value of d, is the predicted value of y(t+τ), is the predicted value of w(t+τ), T is the prediction interval, τ is the prediction time, 0≤τ≤T, and

当τ＝0时， $u = (t + τ) = \hat{u} (t + τ) = 0 - - - (4)$ When τ=0, $u = (t + τ) = \hat{u} (t + τ) = 0 - - - (4)$

其中为u(t+τ)的预测值。in is the predicted value of u(t+τ).

$\overset{^^}{y the y} ((t t + + τ τ)) \overset{\cdot \cdot}{= =} Γ Γ ((τ τ)) \overset{\overset{^^}{&OverBar; &OverBar;}}{Y Y} ((t t))$

其中,in,

$\overset{&OverBar; &OverBar;}{W W} ((t t)) = = {[\begin{matrix} w w {((t t))}^{T T} & \overset{\cdot &Center Dot;}{w w} {((t t))}^{T T} & . . . . . . & {w w}^{[[44]]} {((t t))}^{T T} \end{matrix}]}^{T T} . .$

取可得预测控制律为Pick The predictive control law can be obtained as

其中， $L_{f} h (x) = \frac{&PartialD; h}{&PartialD; x} f (x)$ 为h关于f的Lie导数， $M_{ρ} = [\begin{matrix} x_{1} - w (t) \\ L_{f} h (x) - \overset{\cdot}{w} \\ L_{f}^{2} h (x) - \overset{\cdot \cdot}{w} (t) \end{matrix}, (t)], K = \overset{&OverBar;}{Γ} (1, :),$ $\overset{&OverBar;}{Γ} = {\overset{&OverBar;}{Γ}}_{rr}^{- 1} {\overset{&OverBar;}{Γ}}_{ρr}^{T} = {\overset{&OverBar;}{Γ}}_{11}^{- 1} {\overset{&OverBar;}{Γ}}_{31}^{T} .$ in, $L_{f} h (x) = \frac{&PartialD; h}{&PartialD; x} f (x)$ is the Lie derivative of h with respect to f, $m_{ρ} = [\begin{matrix} x_{1} - w (t) \\ L_{f} h (x) - \overset{&Center Dot;}{w} \\ L_{f}^{2} h (x) - \overset{&Center Dot; &Center Dot;}{w} (t) \end{matrix}, (t)], K = \overset{&OverBar;}{Γ} (1, :),$ $\overset{&OverBar;}{Γ} = {\overset{&OverBar;}{Γ}}_{rr}^{- 1} {\overset{&OverBar;}{Γ}}_{ρr}^{T} = {\overset{&OverBar;}{Γ}}_{11}^{- 1} {\overset{&OverBar;}{Γ}}_{31}^{T} .$

$\overset{&OverBar; &OverBar;}{T T} = = T T$

设计观测器为：The observer is designed as:

$\overset{^^}{d d} - - z z + + p p ((x x))$

$\overset{\cdot &Center Dot;}{z z} = = - - l l ((x x)) {g g}_{d d} ((x x)) z z - - l l ((x x)) (({g g}_{d d} ((x x)) p p ((x x)) + + f f ((x x)) + + g g ((x x)) u u))$

非线性观测器增益定义为：The nonlinear observer gain is defined as:

观测误差定义为：The observation error is defined as:

且干扰是慢时变的。 And the interference is slow and time-varying.

根据模型(2)，选择则，According to model (2), choose but,

此时，所以适当的参数c,对所有的l₃都有全局指数稳定。at this time, So the appropriate parameter c, for all l ₃ has The global index is stable.

步骤四：设计结束Step 4: End of Design

整个设计过程重点考虑了三个方面的控制需求，分别为设计的简便性，闭环系统的稳定性，跟踪的快速精确性。围绕这三个方面，首先在上述第一步中确定了闭环控制系统的具体构成；第二步中重点给出了汽轮发电机主汽门开度预测控制设计方法；第三步中主要给出了非线性干扰观测器的设计；经上述各步骤后，设计结束。The entire design process focuses on three aspects of control requirements, namely, the simplicity of design, the stability of the closed-loop system, and the fast and accurate tracking. Focusing on these three aspects, the specific composition of the closed-loop control system is determined in the first step above; in the second step, the design method of the predictive control of the main steam valve opening of the turbogenerator is given; in the third step, it is mainly given The design of the nonlinear disturbance observer is obtained; after the above steps, the design ends.

Claims

1. A steam turbine generator main throttle valve opening degree prediction control method based on a nonlinear disturbance observer is characterized in that: the method comprises the following specific steps:

the method comprises the following steps: analyzing and modeling a main valve opening control system of the turbonator:

the closed-loop control system adopts a negative feedback control structure, the output quantity is the power angle of the turbonator, and the designed closed-loop control system comprises a controller link and a system model;

the model of the main throttle opening control system is described as follows:

\{\begin{matrix} \overset{\cdot}{δ} = ω - ω_{0} \\ \overset{\cdot}{ω} = - \frac{D}{H} (ω - ω_{0}) + \frac{ω_{0}}{H} (P_{H} + C_{M L} P_{m 0} - \frac{E_{q}^{'} V_{s}}{X_{d Σ}^{'}} s i n δ) \\ {\overset{\cdot}{P}}_{H} = - \frac{1}{T_{H Σ}} (P_{H} - C_{H} P_{m 0}) + \frac{C_{H}}{T_{H Σ}} (u + d) \end{matrix} - - - (1)

wherein: representing the power angle of the turbonator;

₀representing the initial value of the power angle of the turbonator;

ω represents generator rotor speed;

ω₀representing an initial value of the speed of the generator rotor;

P_Hrepresenting the mechanical power generated by the high-pressure cylinder;

P_mrepresenting the mechanical power output by the prime mover;

P_m0representing an initial value of mechanical power output by the prime mover;

d represents a damping coefficient;

h represents the moment of inertia of the generator rotor;

C_MLrepresents the medium and low voltage power distribution coefficient;

C_Hrepresenting the power distribution coefficient of the high-pressure cylinder;

E'_qrepresenting a generator q-axis transient potential;

V_srepresents an infinite bus voltage;

X'_dΣrepresenting the equivalent potential between the generator and an infinite system;

T_HΣrepresenting the equivalent time constant of the high-pressure cylinder valve control system;

u represents the control of the main throttle opening of the steam turbine generator;

d represents the control input interference of the main throttle opening of the turbonator;

for design convenience, three state variables x are defined separately₁、x₂、x₃The following were used:

x₁＝-₀，

x₂＝ω-ω₀，

x₃＝P_H-C_HP_m0；

when the formula (1) is written

\{\begin{matrix} \overset{\cdot}{x} (t) = f (x) + g (x) u (t) + g_{d} (x) d \\ y (t) = h (x) \end{matrix} - - - (2)

Wherein:

f (x) = (\begin{matrix} x_{2} \\ a_{1} s i n (x_{1} + δ_{0}) + a_{2} x_{2} + a_{3} x_{3} + b_{1} \\ a_{4} x_{3} \end{matrix}), g (x) = (\begin{matrix} 0 \\ 0 \\ k_{1} \end{matrix}), g_{d} (x) = (\begin{matrix} 0 \\ 0 \\ k_{1} \end{matrix}),

h(x)＝x₁

a_{1} = - \frac{ω_{0} E_{q}^{'} V_{s}}{{HX}_{d Σ}^{'}} s i n (x_{1} + δ_{0}),

a_{2} = - \frac{D}{H},

a_{3} = \frac{ω_{0}}{H},

a_{4} = - \frac{1}{T_{H Σ}},

b_{1} = \frac{ω_{0}}{H} P_{m 0} (C_{H} + C_{M L}),

k_{1} = \frac{C_{H}}{T_{H Σ}},

step two: the method comprises the following steps of (1) predictive control design of the opening of a main steam valve of a steam turbine generator:

the control task is to output y (t) a tracking command w (t) and overcome the control input interference d of the opening degree of a main valve of the turbonator;

optimizing an objective function of

J = \frac{1}{2} {&Integral;}_{0}^{T} {(\hat{y} (t + τ) - \hat{w} (t + τ))}^{T} (\hat{y} (t + τ) - \hat{w} (t + τ)) d τ + \frac{1}{2} {&Integral;}_{0}^{T} {(d (t + τ) - \hat{d} (t + τ))}^{2} d τ - - - (3)

WhereinIs a predicted value of d (t + tau),is a predicted value of y (t + tau),is the predicted value of w (T + tau), T is the prediction interval, tau is the prediction time, 0 & lttau & gt & lt T & gt, and

when the value of tau is equal to 0,

u (t + τ) = \hat{u} (t + τ) = 0 - - - (4)

whereinIs the predicted value of u (t + τ);

the relative order of the model is rho, the control order is r, and the control order is defined as

{\hat{u}}^{[r]} (t + τ) &NotEqual; 0, τ &Element; [0, T]

{\hat{u}}^{[k]} (t + τ) = 0, k > r, τ &Element; [0, T]

By Taylor expansion, approximation of the future output prediction signal is achievedApproximation of, take

\hat{y} (t + τ) \overset{\cdot}{=} Γ (τ) \hat{\overset{&OverBar;}{Y}} (t)

Wherein

\overset{&OverBar;}{τ} = diag {τ, . . ., τ}

Is a matrix of m × m, m is the number of system outputs,

Γ (τ) = [\begin{matrix} I & \overset{&OverBar;}{τ} & ... & \frac{{\overset{&OverBar;}{τ}}^{(ρ + r)}}{(ρ + r)!} \end{matrix}],

i is a unit matrix of m × m, and is obtained from formula (2), where ρ is 3, r is 1, and m is 1

\hat{\overset{&OverBar;}{Y}} (t) = [\begin{matrix} {\hat{y}}^{[0]} \\ {\hat{y}}^{[1]} \\ {\hat{y}}^{[2]} \\ {\hat{y}}^{[3]} \end{matrix}] = [\begin{matrix} h (x) \\ L_{f}^{1} h (x) \\ L_{f}^{2} h (x) \\ L_{f}^{3} h (x) \end{matrix}] + [\begin{matrix} 0 \\ 0 \\ H (\hat{u}) \end{matrix}] H (\hat{u}) = [\begin{matrix} L_{g} L_{f} h (x) \hat{u} (t) \\ p_{11} (\hat{u} (t), x (t)) + L_{g} L_{f} h (x) \overset{\cdot}{\hat{u}} (t) \end{matrix}]

Wherein,

p_{11} (\hat{u} (t), x (t)) = L_{g} L_{f}^{3} h (x) \hat{u} (t) + \frac{{dL}_{g} L_{f}^{2} h (x)}{d t} \hat{u} (t)

realizing approximation of future instruction prediction signals through Taylor expansion, and taking the approximation of w (t + tau)

\hat{w} (t + τ) = Γ (τ) \overset{&OverBar;}{W} (t)

Wherein

\overset{&OverBar;}{W} (t) = {[\begin{matrix} w {(t)}^{T} & \overset{\cdot}{w} {(t)}^{T} & ... & w^{[4]} {(t)}^{T} \end{matrix}]}^{T};

GetGet a predictive control law of

u (t) = - {(L_{g} L_{f}^{2} h (x))}^{- 1} ({KM}_{ρ} + L_{f}^{3} h (x) - w^{[3]} (t)) - - - (5)

Wherein,

L_{f} h (x) = \frac{&PartialD; h}{&PartialD; x} f (x)

is the derivative of Lie of h with respect to f,

M_{ρ} = [\begin{matrix} x_{1} - w (t) \\ L_{f} h (x) - \overset{\cdot}{w} (t) \\ L_{f}^{2} h (x) - \overset{\cdot\cdot}{w} (t) \end{matrix}],

K = \overset{&OverBar;}{Γ} (1, :), \overset{&OverBar;}{Γ} = {\overset{&OverBar;}{Γ}}_{r r}^{- 1} {\overset{&OverBar;}{Γ}}_{ρ r}^{T} = {\overset{&OverBar;}{Γ}}_{11}^{- 1} {\overset{&OverBar;}{Γ}}_{31}^{T};

since ρ + r +1 is 5, i, j is 1,2,3,4,5, thenIs shown as

{\overset{&OverBar;}{Γ}}_{r r} = {\overset{&OverBar;}{Γ}}_{11} = [\begin{matrix} {\overset{&OverBar;}{Γ}}_{(4, 4)} & {\overset{&OverBar;}{Γ}}_{(4, 5)} \\ {\overset{&OverBar;}{Γ}}_{(5, 4)} & {\overset{&OverBar;}{Γ}}_{(5, 5)} \end{matrix}], {\overset{&OverBar;}{Γ}}_{ρ r} = {\overset{&OverBar;}{Γ}}_{31} = [\begin{matrix} {\overset{&OverBar;}{Γ}}_{(1, 4)} & {\overset{&OverBar;}{Γ}}_{(1, 5)} \\ {\overset{&OverBar;}{Γ}}_{(2, 4)} & {\overset{&OverBar;}{Γ}}_{(2, 5)} \\ {\overset{&OverBar;}{Γ}}_{(3, 4)} & {\overset{&OverBar;}{Γ}}_{(3, 5)} \end{matrix}]

{\overset{&OverBar;}{Γ}}_{(i, j)} = \frac{{\overset{&OverBar;}{T}}^{i + j - 1}}{(i - 1)! (j - 1)! (i + j - 1)}, i, j = 1, ..., ρ + r + 1

\overset{&OverBar;}{T} = T;

Step three: designing a nonlinear disturbance observer:

designing a nonlinear disturbance observer to estimate unknown disturbance and compensating control input;

the observer is designed as follows:

\hat{d} = z + p (x),

\overset{\cdot}{z} = - l (x) g_{d} (x) z - l (x) (g_{d} (x) p (x) + f (x) + g (x) u);

the nonlinear observer gain is defined as:

l (x) = \frac{\partial p (x)}{\partial x}

the observation error is defined as:

and interference is slowly time varying;

selecting p (x) such that equationSatisfy the global index stable, thenThe exponent converges to d;

according to the formula (2), selecting

p (x) = l_{3} (x_{3} + {cx}_{3}^{3}),

Then the process of the first step is carried out,

l (x) = [\begin{matrix} 0 & 0 & l_{3} (1 + 3 {cx}_{3}^{2}) \end{matrix}]

at this time, the process of the present invention,so the appropriate parameter c, for all l₃All global indexes are stable, so that a prediction control law based on a nonlinear disturbance observer is obtained:

u (t) = - {(L_{g} L_{f}^{2} h (x))}^{- 1} ({KM}_{3} + L_{f}^{3} h (x) - w^{[3]} (t)) - \hat{d}

the design of the method for predicting and controlling the main throttle opening of the steam turbine generator based on the nonlinear disturbance observer is finished;

step four: and (5) finishing the design:

the whole design process mainly considers the control requirements of three aspects, namely the simplicity and convenience of design, the stability of a closed-loop system and the rapid accuracy of tracking; in the three aspects, firstly, the specific structure of the closed-loop control system is determined in the step one; in the second step, a predictive control design method for the main throttle opening of the steam turbine generator is given; the design of the nonlinear disturbance observer is given in the third step; after the steps, the design is finished.