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

Abstract

A main steam valve of turbine generator forecast Control Algorithm based on Nonlinear Disturbance Observer, the method has four large steps: step 1: main steam valve of turbine generator control system analysis and modeling; Step 2: main steam valve of turbine generator Predictive control design; Step 3: Nonlinear Disturbance Observer design; Step 4: design finishes. The present invention is directed to main steam valve control system model, design the control law with closed form analytic solutions, then designing Nonlinear Disturbance Observer compensates controlling to disturb, thereby in the situation that thering is strong input interference, the global stability that ensures closed-loop control system has realized the fast and accurately tracking of steam turbine generator merit angle to desired trajectory simultaneously.

Description

Steam turbine generator main throttle opening degree prediction control method based on nonlinear disturbance observer

Technical Field

The invention relates to a turbonator main steam opening degree prediction control method based on a nonlinear interference observer, which is provided for a single machine infinite bus system, is used for controlling a turbonator power angle and belongs to the technical field of automatic control.

Background

Excitation control and valve regulation of a turbonator are two important means for improving the stability of a power system. Since excitation control is limited by the excitation current top value, requiring the generator to have an excessively high excitation current top value increases the generator manufacturing cost; at the same time, the rising speed of the generator field current will also be limited by the field winding time constant. Therefore, improvement of system stability by relying only on excitation control is limited. Along with the application of a high-power intermediate reheating type steam turbine generator unit to an electric power system, the power-frequency electrohydraulic speed regulator increasingly replaces a mechanical hydraulic speed regulator, and the primary frequency modulation capability and the load adaptability of the intermediate reheating type steam turbine generator unit are improved by improving the control of the main throttle opening of the steam turbine generator, so that the stability of the electric power system is improved, and the power-frequency electrohydraulic speed regulator has a particularly important significance.

In recent years, many advanced control methods are used in the design of the control of the main throttle opening of the steam turbine generator, including a feedback linearization method, an optimal control method, and the like. But these methods are not robust to parameter and model variations and do not tolerate non-matching uncertainties in the system. The prediction control method is a novel control method, and the required model only emphasizes the prediction function and does not require the structural form, thereby bringing convenience for system modeling. More importantly, the prediction control draws the idea of optimization control, but the rolling finite-period optimization replaces invariable global optimization, the influence of uncertainty can be continuously considered, and correction can be carried out in time, so that the robustness is stronger. Therefore, predictive control is favored in complex industrial environments. Although the predictive control has certain robustness, when the control interference is large, the control effect cannot meet the ideal requirement, so the ideal control effect is achieved by designing a nonlinear interference observer for compensation.

Under the technical background, the invention provides a turbonator main throttle opening prediction control method based on a nonlinear disturbance observer aiming at a single-machine infinite bus system, which is used for controlling the power angle of the turbonator. Under the condition of strong interference, the control method not only ensures the stability of a closed-loop system, but also realizes the rapid and accurate tracking of the power angle of the turbonator to the preset track.

Disclosure of Invention

1. Objects of the invention

The purpose of the invention is: aiming at a main steam opening control system model, the defects of the prior control technology are overcome, and a steam turbine generator main steam opening prediction control method based on a nonlinear disturbance observer is provided, which realizes the rapid and accurate tracking of the power angle of a steam turbine generator of a closed loop system to a preset track on the basis of ensuring the stability of a closed loop global system.

The invention relates to a steam turbine generator main throttle opening degree prediction control method based on a nonlinear disturbance observer, which has the design idea that: a control law with a closed analytical solution is designed for a main steam valve opening control system model, and then a nonlinear disturbance observer is designed to compensate control disturbance, so that the overall stability of a closed-loop control system is ensured under the condition of strong input disturbance, and meanwhile, the rapid and accurate tracking of a power angle of a steam turbine generator on a preset track is realized.

2. Technical scheme

The technical scheme of the design method is specifically described below.

A single machine infinity bus system is schematically illustrated in figure 1.

The invention relates to a steam turbine generator main throttle opening degree prediction control method based on a nonlinear disturbance observer, which comprises the following specific steps:

the method comprises the following steps: analysis and modeling of main valve opening control system of steam turbine generator

The closed-loop control system adopts a negative feedback control structure, and the output quantity is the power angle of the turbonator. The designed closed-loop control system mainly comprises two parts, namely a controller link and a system model, and the structural layout of the closed-loop control system is shown in figure 2.

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

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\δ}}=\mathrm{\ω}-{\mathrm{\ω}}_0\\ \stackrel{\·}{\mathrm{\ω}}=-\frac{D}{H}(\mathrm{\ω}-{\mathrm{\ω}}_0)+\frac{{\mathrm{\ω}}_0}{H}(P_H+C_{\mathrm{ML}}{P}_{m0}-\frac{E_q^{\′}{V}_s}{X_{\mathrm{d\Σ}}^{\′}}\sin \mathrm{\δ})\\ {\stackrel{\·}{P}}_H=-\frac{1}{T_{\mathrm{H\Σ}}}(P_H-C_H{P}_{m0})+\frac{C_H}{T_{\mathrm{H\Σ}}}(u+d)\end{array}\right.---\left(1\right)$

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 a high-pressure cylinder power non-distribution coefficient;

E'_qrepresenting a generator q-axis transient potential;

v represents the 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 steam turbine generator.

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

then (1) can be written as

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=f\left(x\right)+g\left(x\right)u\left(t\right)+g_d\left(x\right)d\\ y\left(t\right)=h\left(x\right)\end{array}\right.---\left(2\right)$

Wherein: $f\left(x\right)=\left(\begin{array}{c}{x}_2\\ a_1\sin (x_1+{\mathrm{\δ}}_0)+a_2{x}_2+a_3{x}_3+b_1\\ a_4{x}_{30}\end{array}\right),g\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),g_d\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),h\left(x\right)=x_1$

$a_1=-\frac{{\mathrm{\ω}}_0{E}_q^{\′}{V}_s}{{\mathrm{HX}}_{\mathrm{d\Σ}}^{\′}}\sin (x_1+{\mathrm{\δ}}_0)$

$a_2=-\frac{D}{H}$

$a_3=\frac{{\mathrm{\ω}}_0}{H},$

$a_4=-\frac{1}{T_{\mathrm{H\Σ}}}$

$b_1=\frac{{\mathrm{\ω}}_0}{H}{P}_{m0}(C_H+C_{\mathrm{ML}})$

$k_1=\frac{C_H}{T_{\mathrm{H\Σ}}},$

step two: steam turbine generator main throttle opening prediction control design

The control task is to output y (t) a tracking command w (t) and overcome the control input interference d of the main throttle opening of the turbonator.

Optimizing an objective function of

$J=\frac{1}{2}{\∫}_0^T{(\hat{y}(t+\mathrm{\τ})-\hat{w}(t+\mathrm{\τ}))}^T(\hat{y}(t+\mathrm{\τ})-\hat{w}(t+\mathrm{\τ}))\mathrm{d\τ}+\frac{1}{2}{\∫}_0^T{(d(t+\mathrm{\τ})-\hat{d}(t+\mathrm{\τ}))}^2\mathrm{d\τ}---\left(3\right)$

WhereinIs an observed value of d (t + τ),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, $u=(t+\mathrm{\τ})=\hat{u}(t+\mathrm{\τ})=0---\left(4\right)$ 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

${\hat{u}}^{\left[r\right]}(t+\mathrm{\τ})\≠0,\mathrm{\τ}\∈[0,T]$

${\hat{u}}^{\left[k\right]}(t+\mathrm{\τ})=0,k>r,\mathrm{\τ}\∈[0,T]$

In the algorithm, approximation of a future output prediction signal is realized through Taylor expansion, aiming atApproximation of, take

$\hat{y}(t+\mathrm{\τ})\stackrel{\·}{=}\mathrm{\Γ}\left(\mathrm{\τ}\right)\stackrel{\widehat{\‾}}{Y}\left(t\right)$

Wherein $\stackrel{\‾}{\mathrm{\τ}}=\mathrm{diag}\{\mathrm{\τ},...,\mathrm{\τ}\}$ Is a matrix of m × m, m is the number of system outputs, $\mathrm{\Γ}\left(t\right)=\left[\begin{array}{cccc}I& \stackrel{\‾}{\mathrm{\τ}}& ...& \frac{{\stackrel{\‾}{\mathrm{\τ}}}^{(\mathrm{\ρ}+r)}}{(\mathrm{\ρ}+r)!}\end{array}\right],$ as is known from the model (2), since ρ is 3, r is 1, and m is 1, I is a unit matrix of m × m

$\stackrel{\widehat{\‾}}{Y}\left(t\right)=\left[\begin{array}{c}{\hat{y}}^{\left[0\right]}\\ {\hat{y}}^{\left[1\right]}\\ {\hat{y}}^{\left[3\right]}\\ {\hat{y}}^{\left[4\right]}\end{array}\right]=\left[\begin{array}{c}h\left(x\right)\\ L_f^{1}h\left(x\right)\\ L_f^{2}h\left(x\right)\\ L_f^{3}h\left(x\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ H\left(\hat{u}\right)\end{array}\right]H\left(\hat{u}\right)=\left[\begin{array}{c}{L}_g{L}_{f}h\left(x\right)\hat{u}\left(t\right)\\ p_{11}(\hat{u}\left(t\right),x\left(t\right))+L_g{L}_{f}h\left(x\right)\stackrel{\stackrel{\·}{^}}{u}\left(t\right)\end{array}\right]$

Wherein, $p_{11}(\hat{u}\left(t\right),x\left(t\right))=L_g{L}_f^{3}h\left(x\right)\hat{u}\left(t\right)+\frac{{\mathrm{dL}}_g{L}_f^{2}h\left(x\right)}{\mathrm{dt}}\hat{u}\left(t\right)$

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

$\hat{w}(t+\mathrm{\τ})=\mathrm{\Γ}\left(\mathrm{\τ}\right)\stackrel{\‾}{W}\left(t\right)$

Wherein,

$\stackrel{\‾}{W}\left(t\right)={\left[\begin{array}{cccc}w{\left(t\right)}^T& \stackrel{\·}{w}{\left(t\right)}^T& ...& w^{\left[4\right]}{\left(t\right)}^T\end{array}\right]}^T.$

getThe obtainable predictive control law is

$u\left(t\right)=-{\left(L_g{L}_f^{2}h\left(x\right)\right)}^{-1}({\mathrm{KM}}_{\mathrm{\ρ}}+L_f^{3}h\left(x\right)-w^{\left[3\right]}\left(t\right))---\left(5\right)$

Wherein, $L_{f}h\left(x\right)=\frac{\∂h}{\∂x}f\left(x\right)$ is the derivative of Lie of h with respect to f, $M_{\mathrm{\ρ}}=\left[\begin{array}{c}{x}_1-w\left(t\right)\\ L_{f}h\left(x\right)-\stackrel{\·}{w}\\ L_f^{2}h\left(x\right)-\stackrel{\·\·}{w}\left(t\right)\end{array},\left(t\right)\right],K=\stackrel{\‾}{\mathrm{\Γ}}(1,:),$ $\stackrel{\‾}{\mathrm{\Γ}}={\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{rr}}^{-1}{\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{\ρr}}^T={\stackrel{\‾}{\mathrm{\Γ}}}_{11}^{-1}{\stackrel{\‾}{\mathrm{\Γ}}}_{31}^T.$

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

${\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{rr}}={\stackrel{\‾}{\mathrm{\Γ}}}_{11}=\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{4,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{4,5}\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{5,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{5,5}\right)}\end{array}\right],{\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{\ρr}}={\stackrel{\‾}{\mathrm{\Γ}}}_{31}=\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{1,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{1,5}\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{2,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{2,5}\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{3,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{3,5}\right)}\end{array}\right]$

${\stackrel{\‾}{\mathrm{\Γ}}}_{(i,j)}=\frac{{\stackrel{\‾}{T}}^{i+j-1}}{(i-1)!(j-1)!(i+j-1)},i,j=1,...,\mathrm{\ρ}+r+1$

$\stackrel{\‾}{T}=T$

Step three: nonlinear disturbance observer design

And designing a nonlinear disturbance observer to estimate unknown disturbance and compensate the control input.

The observer is designed as follows:

$\hat{d}-z+p\left(x\right)$

$\stackrel{\·}{z}=-l\left(x\right)g_d\left(x\right)z-l\left(x\right)(g_d\left(x\right)p\left(x\right)+f\left(x\right)+g\left(x\right)u)$

the nonlinear observer gain is defined as:

$l\left(x\right)=\frac{\∂p\left(x\right)}{\∂x}$

the observation error is defined as:

and the interference is slowly time varying.

Selecting p (x) such that equationSatisfy the global index stable, thenThe index converges to d.

Selecting according to the model (2)Then the process of the first step is carried out,

$l\left(x\right)=\left[\begin{array}{ccc}0& 0& l_3(1+3c{x}_3^2)\end{array}\right]$

at this time, the process of the present invention,so the appropriate parameter c, for all l₃There is global exponential settling.

Thus, a predictive control law based on a non-linear disturbance observer can be obtained:

$u\left(t\right)=-{\left(L_g{L}_f^{2}h\left(x\right)\right)}^{-1}({\mathrm{KM}}_3+L_f^{3}h\left(x\right)-w^{\left[3\right]}\left(t\right))-\hat{d}$

thus, 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: end of 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. With respect to these three aspects, first, the specific configuration of the closed-loop control system is determined in the first step described above; in the second step, a predictive control design method of the main throttle opening of the steam turbine generator is given; the third step mainly provides the design of the nonlinear disturbance observer; after the steps, the design is finished.

3. Advantages and effects

The invention provides a steam turbine generator main steam valve opening prediction control method based on a nonlinear disturbance observer aiming at a single machine infinite bus system, which is used for controlling a steam turbine generator power angle. Specific advantages include two aspects: firstly, compared with the existing processing method, the method is very simple and convenient in the process of designing the controller, and avoids a large amount of calculation burden brought by online optimization so as to meet the real-time control requirement; secondly, the nonlinear disturbance observer is designed to compensate the input disturbance, so that the global stability of the closed-loop control system is ensured under the condition of strong input disturbance, and meanwhile, the rapid and accurate tracking of the power angle of the turbonator on the preset track is realized.

Drawings

FIG. 1: the invention discloses a single-machine infinite bus system schematic diagram.

FIG. 2: the invention discloses a schematic diagram of a closed-loop control system structure and a component connection relation.

FIG. 3: the invention discloses a design flow schematic diagram of a main valve opening predictive control (with a disturbance observer).

FIG. 4.1: a tracking effect graph of a non-interfering observer.

FIG. 4.2: a tracking error map of a non-interfering observer.

FIG. 4.3: a control input map of a non-interfering observer.

FIG. 5.1: the invention is implemented (with a disturbance observer) as a trace effect graph.

FIG. 5.2: the invention implements a tracking error map (with a disturbance observer).

FIG. 5.3: the invention is implemented (with a disturbance observer) as a control input map.

FIG. 5.4: the invention is implemented (with a disturbance observer) as an observer diagram of the effect of observation.

The abscissa in fig. 4.1-4.3, 5.1-5.4 represents simulation time in seconds; the ordinate in fig. 4.1 and 5.1 represents the power angle tracking effect of the steam turbine generator, and the unit is degree; the ordinate in fig. 4.2 and 5.2 represents the power angle tracking error of the turbonator, and the unit is degree; the ordinate in fig. 4.3 and 5.3 represents the control input of the main throttle opening of the turbonator, and the unit is newton; in FIG. 5.4, the ordinate represents the interference observation effect of the control input of the main throttle opening of the steam turbine generator, and the unit is Newton; the dotted lines in fig. 4.1 and 5.1 represent signal lines of a predetermined track, and the solid lines represent signal lines of a power angle of an actual turbonator; the dashed lines in fig. 5.4 represent the actual disturbing signal lines and the solid lines represent the observer disturbing signal lines.

Detailed Description

Referring to fig. 1-5.4, the design goals of the present invention include two aspects: firstly, the control design of the opening degree of a main valve of the steam turbine generator is simplified; secondly, the turbo generator power angle of the closed loop system is quickly and accurately tracked to the preset track, and the specific indexes are as follows: the tracking error of the power angle of the turbonator is less than 0.5 degree within 1 second. FIG. 1 is a schematic diagram of a single-machine infinite bus system of the present invention.

In specific implementation, the simulation and the test of the main steam opening prediction control method and the closed-loop control system are realized by means of a Simulink tool box in Matlab. The design of the present invention is further illustrated by the description of a certain representative embodiment. In simulation, according to the empirical data of an actual system of a certain power plant, the parameters are selected as follows:

₀＝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_HΣ0.4, initial value of state variable is set as x₁＝0、x₂＝0、x₃＝0。

Observer parameter l₃100, c is 0.001, T is 0.238, and w (T) is 5sin (tt).

The embodiment (I) realizes the accuracy and the rapidity of the power angle tracking of the steam turbine generator.

Embodiment mode 1

The method comprises the following steps: analysis and modeling of main valve opening control system of steam turbine generator

The closed-loop control system adopts a negative feedback control structure, and the output quantity is the power angle of the turbonator. The designed closed-loop control system mainly comprises two parts, namely a controller link and a system model, and the structural layout of the closed-loop control system is shown in figure 2.

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

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\δ}}=\mathrm{\ω}-{\mathrm{\ω}}_0\\ \stackrel{\·}{\mathrm{\ω}}=-\frac{D}{H}(\mathrm{\ω}-{\mathrm{\ω}}_0)+\frac{{\mathrm{\ω}}_0}{H}(P_H+C_{\mathrm{ML}}{P}_{m0}-\frac{E_q^{\′}{V}_s}{X_{\mathrm{d\Σ}}^{\′}}\sin \mathrm{\δ})\\ {\stackrel{\·}{P}}_H=-\frac{1}{T_{\mathrm{H\Σ}}}(P_H-C_H{P}_{m0})+\frac{C_H}{T_{\mathrm{H\Σ}}}(u+d)\end{array}\right.---\left(1\right)$

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 a high-pressure cylinder power non-distribution coefficient;

E'_qrepresenting a generator q-axis transient potential;

v represents the 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 steam turbine generator.

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

then (1) can be written as

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=f\left(x\right)+g\left(x\right)u\left(t\right)+g_d\left(x\right)d\\ y\left(t\right)=h\left(x\right)\end{array}\right.---\left(2\right)$

Wherein: $f\left(x\right)=\left(\begin{array}{c}{x}_2\\ a_1\sin (x_1+{\mathrm{\δ}}_0)+a_2{x}_2+a_3{x}_3+b_1\\ a_4{x}_{30}\end{array}\right),g\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),g_d\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),h\left(x\right)=x_1$

$a_1=-\frac{{\mathrm{\ω}}_0{E}_q^{\′}{V}_s}{{\mathrm{HX}}_{\mathrm{d\Σ}}^{\′}}\sin (x_1+{\mathrm{\δ}}_0)$

$a_2=-\frac{D}{H}$

$a_3=\frac{{\mathrm{\ω}}_0}{H},$

$a_4=-\frac{1}{T_{\mathrm{H\Σ}}}$

$b_1=\frac{{\mathrm{\ω}}_0}{H}{P}_{m0}(C_H+C_{\mathrm{ML}})$

$k_1=\frac{C_H}{T_{\mathrm{H\Σ}}},$

step two: steam turbine generator main throttle opening prediction control design

The control task is to output y (t) a tracking command w (t) and overcome the control input interference d of the main throttle opening of the turbonator.

Optimizing an objective function of

$J=\frac{1}{2}{\∫}_0^T{(\hat{y}(t+\mathrm{\τ})-\hat{w}(t+\mathrm{\τ}))}^T(\hat{y}(t+\mathrm{\τ})-\hat{w}(t+\mathrm{\τ}))\mathrm{d\τ}+\frac{1}{2}{\∫}_0^T{(d(t+\mathrm{\τ})-\hat{d}(t+\mathrm{\τ}))}^2\mathrm{d\τ}---\left(3\right)$

WhereinIs the observed value of d and is,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, $u=(t+\mathrm{\τ})=\hat{u}(t+\mathrm{\τ})=0---\left(4\right)$

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

${\hat{u}}^{\left[r\right]}(t+\mathrm{\τ})\≠0,\mathrm{\τ}\∈[0,T]$

${\hat{u}}^{\left[k\right]}(t+\mathrm{\τ})=0,k>r,\mathrm{\τ}\∈[0,T]$

In the algorithm, approximation of a future output prediction signal is realized through Taylor expansion, aiming atApproximation of, take

$\hat{y}(t+\mathrm{\τ})\stackrel{\·}{=}\mathrm{\Γ}\left(\mathrm{\τ}\right)\stackrel{\widehat{\‾}}{Y}\left(t\right)$

Wherein $\stackrel{\‾}{\mathrm{\τ}}=\mathrm{diag}\{\mathrm{\τ},...,\mathrm{\τ}\}$ Is a matrix of m × m, m is the number of system outputs, $\mathrm{\Γ}\left(t\right)=\left[\begin{array}{cccc}I& \stackrel{\‾}{\mathrm{\τ}}& ...& \frac{{\stackrel{\‾}{\mathrm{\τ}}}^{(\mathrm{\ρ}+r)}}{(\mathrm{\ρ}+r)!}\end{array}\right],$ as is known from the model (2), since ρ is 3, r is 1, and m is 1, I is a unit matrix of m × m

$\stackrel{\widehat{\‾}}{Y}\left(t\right)=\left[\begin{array}{c}{\hat{y}}^{\left[0\right]}\\ {\hat{y}}^{\left[1\right]}\\ {\hat{y}}^{\left[3\right]}\\ {\hat{y}}^{\left[4\right]}\end{array}\right]=\left[\begin{array}{c}h\left(x\right)\\ L_f^{1}h\left(x\right)\\ L_f^{2}h\left(x\right)\\ L_f^{3}h\left(x\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ H\left(\hat{u}\right)\end{array}\right]H\left(\hat{u}\right)=\left[\begin{array}{c}{L}_g{L}_{f}h\left(x\right)\hat{u}\left(t\right)\\ p_{11}(\hat{u}\left(t\right),x\left(t\right))+L_g{L}_{f}h\left(x\right)\stackrel{\stackrel{\·}{^}}{u}\left(t\right)\end{array}\right]$

Wherein, $p_{11}(\hat{u}\left(t\right),x\left(t\right))=L_g{L}_f^{3}h\left(x\right)\hat{u}\left(t\right)+\frac{{\mathrm{dL}}_g{L}_f^{2}h\left(x\right)}{\mathrm{dt}}\hat{u}\left(t\right)$

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

$\hat{w}(t+\mathrm{\τ})=\mathrm{\Γ}\left(\mathrm{\τ}\right)\stackrel{\‾}{W}\left(t\right)$

Wherein,

$\stackrel{\‾}{W}\left(t\right)={\left[\begin{array}{cccc}w{\left(t\right)}^T& \stackrel{\·}{w}{\left(t\right)}^T& ...& w^{\left[4\right]}{\left(t\right)}^T\end{array}\right]}^T.$

getThe obtainable predictive control law is

$u\left(t\right)=-{\left(L_g{L}_f^{2}h\left(x\right)\right)}^{-1}({\mathrm{KM}}_{\mathrm{\ρ}}+L_f^{3}h\left(x\right)-w^{\left[3\right]}\left(t\right))---\left(5\right)$

Wherein, $L_{f}h\left(x\right)=\frac{\∂h}{\∂x}f\left(x\right)$ is the derivative of Lie of h with respect to f, $M_{\mathrm{\ρ}}=\left[\begin{array}{c}{x}_1-w\left(t\right)\\ L_{f}h\left(x\right)-\stackrel{\·}{w}\\ L_f^{2}h\left(x\right)-\stackrel{\·\·}{w}\left(t\right)\end{array},\left(t\right)\right],K=\stackrel{\‾}{\mathrm{\Γ}}(1,:),$ $\stackrel{\‾}{\mathrm{\Γ}}={\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{rr}}^{-1}{\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{\ρr}}^T={\stackrel{\‾}{\mathrm{\Γ}}}_{11}^{-1}{\stackrel{\‾}{\mathrm{\Γ}}}_{31}^T.$

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

${\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{rr}}={\stackrel{\‾}{\mathrm{\Γ}}}_{11}=\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{4,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{4,5}\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{5,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{5,5}\right)}\end{array}\right],{\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{\ρr}}={\stackrel{\‾}{\mathrm{\Γ}}}_{31}=\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{1,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{1,5}\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{2,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{2,5}\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{3,4}\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(\mathrm{3,5}\right)}\end{array}\right]$

${\stackrel{\‾}{\mathrm{\Γ}}}_{(i,j)}=\frac{{\stackrel{\‾}{T}}^{i+j-1}}{(i-1)!(j-1)!(i+j-1)},i,j=1,...,\mathrm{\ρ}+r+1$

$\stackrel{\‾}{T}=T$

Step three: nonlinear disturbance observer design

And designing a nonlinear disturbance observer to estimate unknown disturbance and compensate the control input.

The observer is designed as follows:

$\hat{d}-z+p\left(x\right)$

$\stackrel{\·}{z}=-l\left(x\right)g_d\left(x\right)z-l\left(x\right)(g_d\left(x\right)p\left(x\right)+f\left(x\right)+g\left(x\right)u)$

the nonlinear observer gain is defined as:

$l\left(x\right)=\frac{\∂p\left(x\right)}{\∂x}$

the observation error is defined as:

and the interference is slowly time varying.

Selecting p (x) such that equationSatisfy the global index stable, thenThe index converges to d.

Selecting according to the model (2)Then the process of the first step is carried out,

$l\left(x\right)=\left[\begin{array}{ccc}0& 0& l_3(1+3c{x}_3^2)\end{array}\right]$

at this time, the process of the present invention,so the appropriate parameter c, for all l₃Are all provided withThe global index is stable.

Thus, a predictive control law based on a non-linear disturbance observer can be obtained:

$u\left(t\right)=-{\left(L_g{L}_f^{2}h\left(x\right)\right)}^{-1}({\mathrm{KM}}_3+L_f^{3}h\left(x\right)-w^{\left[3\right]}\left(t\right))-\hat{d}$

thus, 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: end of 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. With respect to these three aspects, first, the specific configuration of the closed-loop control system is determined in the first step described above; in the second step, a predictive control design method of the main throttle opening of the steam turbine generator is given; the third step mainly provides the design of the nonlinear disturbance observer; after the steps, the design is finished.

Claims (1)

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:

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\δ}}=\mathrm{\ω}-{\mathrm{\ω}}_0\\ \stackrel{\·}{\mathrm{\ω}}=-\frac{D}{H}(\mathrm{\ω}-{\mathrm{\ω}}_0)+\frac{{\mathrm{\ω}}_0}{H}(P_H+C_{ML}{P}_{m0}-\frac{E_q^{\′}{V}_s}{X_{d\mathrm{\Σ}}^{\′}}sin\mathrm{\δ})\\ {\stackrel{\·}{P}}_H=-\frac{1}{T_{H\mathrm{\Σ}}}(P_H-C_H{P}_{m0})+\frac{C_H}{T_{H\mathrm{\Σ}}}(u+d)\end{array}\right.---\left(1\right)$

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

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=f\left(x\right)+g\left(x\right)u\left(t\right)+g_d\left(x\right)d\\ y\left(t\right)=h\left(x\right)\end{array}\right.---\left(2\right)$

Wherein: $f\left(x\right)=\left(\begin{array}{c}{x}_2\\ a_{1}sin(x_1+{\mathrm{\δ}}_0)+a_2{x}_2+a_3{x}_3+b_1\\ a_4{x}_3\end{array}\right),g\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),g_d\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),$ h(x)＝x₁

$a_1=-\frac{{\mathrm{\ω}}_0{E}_q^{\′}{V}_s}{{\mathrm{HX}}_{d\mathrm{\Σ}}^{\′}}sin(x_1+{\mathrm{\δ}}_0),$

$a_2=-\frac{D}{H},$

$a_3=\frac{{\mathrm{\ω}}_0}{H},$

$a_4=-\frac{1}{T_{H\mathrm{\Σ}}},$

$b_1=\frac{{\mathrm{\ω}}_0}{H}{P}_{m0}(C_H+C_{ML}),$

$k_1=\frac{C_H}{T_{H\mathrm{\Σ}}},$

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

$J=\frac{1}{2}{\∫}_0^T{\left(\hat{y}\right(t+\mathrm{\τ})-\hat{w}(t+\mathrm{\τ}\left)\right)}^T\left(\hat{y}\right(t+\mathrm{\τ})-\hat{w}(t+\mathrm{\τ}\left)\right)d\mathrm{\τ}+\frac{1}{2}{\∫}_0^T{\left(d\right(t+\mathrm{\τ})-\hat{d}(t+\mathrm{\τ}\left)\right)}^{2}d\mathrm{\τ}---\left(3\right)$

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, $u(t+\mathrm{\τ})=\hat{u}(t+\mathrm{\τ})=0---\left(4\right)$

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+\mathrm{\τ})\≠0,\mathrm{\τ}\∈\[0,T\]$

${\hat{u}}^{\[k\]}(t+\mathrm{\τ})=0,k>r,\mathrm{\τ}\∈\[0,T\]$

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

$\hat{y}(t+\mathrm{\τ})\stackrel{\·}{=}\mathrm{\Γ}\left(\mathrm{\τ}\right)\widehat{\stackrel{\‾}{Y}}\left(t\right)$

Wherein $\stackrel{\‾}{\mathrm{\τ}}=\mathrm{diag}\{\mathrm{\τ},...,\mathrm{\τ}\}$ Is a matrix of m × m, m is the number of system outputs, $\mathrm{\Γ}\left(\mathrm{\τ}\right)=\left[\begin{array}{cccc}I& \stackrel{\‾}{\mathrm{\τ}}& ...& \frac{{\stackrel{\‾}{\mathrm{\τ}}}^{(\mathrm{\ρ}+r)}}{(\mathrm{\ρ}+r)!}\end{array}\right],$ 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

$\widehat{\stackrel{\‾}{Y}}\left(t\right)=\left[\begin{array}{c}{\hat{y}}^{\[0\]}\\ {\hat{y}}^{\[1\]}\\ {\hat{y}}^{\[2\]}\\ {\hat{y}}^{\[3\]}\end{array}\right]=\left[\begin{array}{c}h\left(x\right)\\ L_f^{1}h\left(x\right)\\ L_f^{2}h\left(x\right)\\ L_f^{3}h\left(x\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ H\left(\hat{u}\right)\end{array}\right]H\left(\hat{u}\right)=\left[\begin{array}{c}{L}_g{L}_{f}h\left(x\right)\hat{u}\left(t\right)\\ p_{11}\left(\hat{u}\left(t\right),x\left(t\right)\right)+L_g{L}_{f}h\left(x\right)\stackrel{\·}{\hat{u}}\left(t\right)\end{array}\right]$

Wherein, $p_{11}\left(\hat{u}\right(t),x(t\left)\right)=L_g{L}_f^{3}h\left(x\right)\hat{u}\left(t\right)+\frac{{\mathrm{dL}}_g{L}_f^{2}h\left(x\right)}{dt}\hat{u}\left(t\right)$

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

$\hat{w}(t+\mathrm{\τ})=\mathrm{\Γ}\left(\mathrm{\τ}\right)\stackrel{\‾}{W}\left(t\right)$

Wherein $\stackrel{\‾}{W}\left(t\right)={\left[\begin{array}{cccc}w{\left(t\right)}^T& \stackrel{\·}{w}{\left(t\right)}^T& ...& w^{\[4\]}{\left(t\right)}^T\end{array}\right]}^T;$

GetGet a predictive control law of

$u\left(t\right)=-{\left(L_g{L}_f^{2}h\right(x\left)\right)}^{-1}({\mathrm{KM}}_{\mathrm{\ρ}}+L_f^{3}h(x)-w^{\[3\]}(t\left)\right)---\left(5\right)$

Wherein, $L_{f}h\left(x\right)=\frac{\∂h}{\∂x}f\left(x\right)$ is the derivative of Lie of h with respect to f, $M_{\mathrm{\ρ}}=\left[\begin{array}{c}{x}_1-w\left(t\right)\\ L_{f}h\left(x\right)-\stackrel{\·}{w}\left(t\right)\\ L_f^{2}h\left(x\right)-\stackrel{\·\·}{w}\left(t\right)\end{array}\right],$

$K=\stackrel{\‾}{\mathrm{\Γ}}(1,:),\stackrel{\‾}{\mathrm{\Γ}}={\stackrel{\‾}{\mathrm{\Γ}}}_{rr}^{-1}{\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{\ρ}r}^T={\stackrel{\‾}{\mathrm{\Γ}}}_{11}^{-1}{\stackrel{\‾}{\mathrm{\Γ}}}_{31}^T;$

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

${\stackrel{\‾}{\mathrm{\Γ}}}_{rr}={\stackrel{\‾}{\mathrm{\Γ}}}_{11}=\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\Γ}}}_{\left(4,4\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(4,5\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(5,4\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(5,5\right)}\end{array}\right],{\stackrel{\‾}{\mathrm{\Γ}}}_{\mathrm{\ρ}r}={\stackrel{\‾}{\mathrm{\Γ}}}_{31}=\left[\begin{array}{cc}{\stackrel{\‾}{\mathrm{\Γ}}}_{\left(1,4\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(1,5\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(2,4\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(2,5\right)}\\ {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(3,4\right)}& {\stackrel{\‾}{\mathrm{\Γ}}}_{\left(3,5\right)}\end{array}\right]$

${\stackrel{\‾}{\mathrm{\Γ}}}_{(i,j)}=\frac{{\stackrel{\‾}{T}}^{i+j-1}}{(i-1)!(j-1)!(i+j-1)},i,j=1,...,\mathrm{\ρ}+r+1$

$\stackrel{\‾}{T}=T;$

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:

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

$\stackrel{\·}{z}=-l\left(x\right)g_d\left(x\right)z-l\left(x\right)\left(g_d\right(x\left)p\right(x)+f(x)+g(x\left)u\right);$

the nonlinear observer gain is defined as:

$l\left(x\right)=\frac{\∂p\left(x\right)}{\∂x}$

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 $p\left(x\right)=l_3(x_3+{\mathrm{cx}}_3^3),$ Then the process of the first step is carried out,

$l\left(x\right)=\left[\begin{array}{ccc}0& 0& l_3(1+3{\mathrm{cx}}_3^2)\end{array}\right]$

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\left(t\right)=-{\left(L_g{L}_f^{2}h\right(x\left)\right)}^{-1}({\mathrm{KM}}_3+L_f^{3}h(x)-w^{\[3\]}(t\left)\right)-\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.