CN104806302A - Steam turbine generator main steam valve opening degree prediction control method based on non-linear interference observer - Google Patents

Abstract

The invention provides a steam turbine generator main steam valve opening degree prediction control method based on a non-linear interference observer. The method comprises the four major steps that 1, a steam turbine generator main steam valve opening degree control system carries out analysis and modeling; 2, the steam turbine generator main steam valve opening degree prediction control design is carried out; 3, the non-linear interference observer is designed; 4, the design is completed. The method aims at a main steam valve opening degree control system model, a control rule with the closed type analytical solution is designed, and then, the non-linear interference observer is designed for controlling the interference for compensation, so that the global stability of the closed loop control system is ensured under the condition with higher input interference, and meanwhile, the fast and precise tracking of a steam turbine generator power angle on the preset tracks is realized.

Description

A kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer

Technical field

The present invention relates to a kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer, it is for Infinite bus power system bus system, and a kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer provided, for controlling steam turbine generator merit angle, belong to automatic control technology field.

Background technique

It is two important means improving stability of power system that the excitation con-trol of steam turbine generator and porthole regulate.Because excitation con-trol is subject to the restriction of field current top value, and require that generator has too high field current top value and will increase generator manufacture cost; Meanwhile, the rate of climb of exciter current of generator also will be subject to the restriction of exciting winding time constant.Therefore, only the improvement of excitation con-trol to the stability of a system is relied on to be limited.Along with powerful Reheat-type turbogenerator group is applied to electric power system, power-frequency electrolyte type speed regulator replaces mechanical hydraulic-pressure type speed regulator day by day, Primary frequency control ability and the load adaptability of Reheat-type turbogenerator group is controlled to improve by improving main steam valve of turbine generator, thus improve the stability of electric power system, there is the meaning of particular importance.

In recent years, the controlling method of many advanced persons is used in the design of main steam valve of turbine generator control, comprising feedback linearization method, method for optimally controlling etc.But these methods do not possess the robustness to parameter and model change, and helpless to mismatched uncertainties in system.Predictive control method is a kind of controlling method of novelty, and the model required for it only emphasizes forecast function, its structural type overcritical, thus brings convenience for system modelling.The more important thing is, predictive control has drawn the thought of optimization control, but utilizes the limited period of time optimization of rolling to instead of unalterable global optimization, constantly can take probabilistic impact into account and be corrected in time, thus having stronger robustness.So predictive control is favored in the industrial environment of complexity.Although predictive control has certain robustness, when controlling interference and being larger, control effects can not reach desirable requirement, so compensated by design Nonlinear Disturbance Observer, has reached desirable control effects.

Under this technical background, the present invention is directed to Infinite bus power system bus system, provide a kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer, for controlling steam turbine generator merit angle.In more strongly disturbing situation, adopt this controlling method not only to ensure that the stability of closed-loop system, also achieve the fast and accurately tracking of steam turbine generator merit angle to desired trajectory.

Summary of the invention

1, goal of the invention

The object of the invention is: for main steam valve control system model, overcome the deficiency of existing control technique, and a kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer is provided, it is ensureing, on the basis that closed loop global system is stable, to realize the fast and accurately tracking of closed-loop system steam turbine generator merit angle to desired trajectory.

The present invention is a kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer, its design philosophy is: for main steam valve control system model, design the control law with closed form analytic solutions, then design Nonlinear Disturbance Observer to compensate control interference, thus when having stronger input nonlinearities, ensure the global stability of closed loop control system, achieve the fast and accurately tracking of steam turbine generator merit angle to desired trajectory simultaneously.

2, technological scheme

Lower mask body introduces the technological scheme of this design method.

Infinite bus power system bus system schematic diagram is as Fig. 1.

A kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer of the present invention, the method concrete steps are as follows:

Step one: main steam valve of turbine generator control system analysis and modeling

Closed loop control system adopts degenerative control structure, and output quantity is steam turbine generator merit angle.Designed closed loop control system mainly comprises controller link and these two parts of system model, and its topology layout situation as shown in Figure 2.

Main steam valve control system model is described below:

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

Wherein: δ represents steam turbine generator merit angle;

δ ₀represent steam turbine generator merit angle initial value;

ω represents generator amature speed;

ω ₀represent generator amature speed initial value;

P _hrepresent the mechanical output that high-pressure cylinder produces;

P _mrepresent the mechanical output that prime mover exports;

P _m0represent the mechanical output initial value that prime mover exports;

D represents damping constant;

H represents the rotary inertia of generator amature;

C _mLrepresent mesolow power partition coefficient;

C _hrepresent the non-distribution coefficient of high-pressure cylinder power;

E' _qrepresent generator q axle transient potential;

V represents infinite busbar voltage;

X' _{d Σ}represent the equivalent electromotive force between generator and Infinite bus system;

T _{h Σ}represent high-pressure cylinder steam valving control system equivalent time constant;

U represents that main steam valve of turbine generator controls;

D represents that main steam valve of turbine generator control inputs disturbs.

For the ease of design, define three state variable x respectively ₁, x ₂, x ₃as follows:

x ₁＝δ-δ ₀

x ₂＝ω-ω ₀

x ₃＝P _H-C _HP _m0

At this moment (1) just can be write 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 2: main steam valve of turbine generator Predictive control design

Control task for exporting y (t) trace command w (t), and overcomes main steam valve of turbine generator control inputs interference d.

Optimization object function is

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

Wherein for the Observed value of d (t+ τ), for the predicted value of y (t+ τ), for the predicted value of w (t+ τ), T is forecast interval, and τ is predicted time, 0≤τ≤T, and has

When τ=0, $u=(t+\mathrm{\τ})=\hat{u}(t+\mathrm{\τ})=0---\left(4\right)$ Wherein for the predicted value of u (t+ τ).

The relative exponent number of model is ρ, and control exponent number is r, 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 this algorithm, by Taylor expansion, realize approaching following prediction of output signal, for approach, get

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

Wherein $\stackrel{\‾}{\mathrm{\τ}}=\mathrm{diag}\{\mathrm{\τ},...,\mathrm{\τ}\}$ For m × m matrix, m is that system exports number, $\mathrm{\Γ}\left(t\right)=\left[\begin{array}{cccc}I& \stackrel{\‾}{\mathrm{\τ}}& ...& \frac{{\stackrel{\‾}{\mathrm{\τ}}}^{(\mathrm{\ρ}+r)}}{(\mathrm{\ρ}+r)!}\end{array}\right],$ I is the unit matrix of m × m.From model (2), ρ=3, r=1, m=1, so can get

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

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

By Taylor expansion, realize approaching future instructions prediction signal, for approaching of w (t+ τ), get

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

Wherein,

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

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

Due to ρ+r+1=5, then i, j=1,2,3,4,5, then be expressed 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 3: Nonlinear Disturbance Observer designs

Design Nonlinear Disturbance Observer estimates unknown interference, compensates control inputs.

Design visualizer is:

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

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

Nonlinear observer gain definitions is:

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

Observational error is defined as:

and interference is slow time-varying.

Select p (x), make equation meet Global Exponential Stability, then exponential convergence is in d.

According to model (2), select then,

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

Now, so suitable parameter c, to all l ₃there is Global Exponential Stability.

Thus can based on the Predictive control law of Nonlinear Disturbance Observer:

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

So far, a kind of design of the main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer is complete.

Step 4: design terminates

Whole design process emphasis considers the demand for control of three aspects, is respectively the simplicity of design, the stability of closed-loop system, the quick accuracy of tracking.Around these three aspects, in the above-mentioned first step, first determine the concrete formation of closed loop control system; In second step, emphasis gives main steam valve of turbine generator Predictive control design method; The design of Nonlinear Disturbance Observer is mainly given in 3rd step; After above steps, design terminates.

3, advantage and effect

The present invention is directed to Infinite bus power system bus system, provide a kind of main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer, for controlling steam turbine generator merit angle.Concrete advantage comprises two aspects: one, and compared with the processing method existed at present, this method is very easy in CONTROLLER DESIGN process, a large amount of computation burden avoiding on-line optimization to bring thus meet requirement of real-time control; Its two, compensate input nonlinearities by design Nonlinear Disturbance Observer, thus when having stronger input nonlinearities, ensureing the global stability of closed loop control system, achieving the fast and accurately tracking of steam turbine generator merit angle to desired trajectory simultaneously.

Accompanying drawing explanation

Fig. 1: Infinite bus power system bus system schematic diagram of the present invention.

Fig. 2: closed loop control system structure of the present invention and assembly annexation schematic diagram.

Fig. 3: main steam valve predictive control (having interference observer) design cycle schematic diagram of the present invention.

Fig. 4 .1: the tracking effect figure of noiseless visualizer.

Fig. 4 .2: the tracking error figure of noiseless visualizer.

Fig. 4 .3: the control inputs figure of noiseless visualizer.

Fig. 5 .1: the tracking effect figure in the invention process (having interference observer).

Fig. 5 .2: the tracking error figure in the invention process (having interference observer).

Fig. 5 .3: the control inputs figure in the invention process (having interference observer).

Fig. 5 .4: the observation effect figure of the visualizer in the invention process (having interference observer).

Abscissa in Fig. 4 .1-4.3, Fig. 5 .1-5.4 represents simulation time, and unit is second; In Fig. 4 .1, Fig. 5 .1, y coordinate represents steam turbine generator merit angle tracking effect, unit degree of being; In Fig. 4 .2, Fig. 5 .2, y coordinate represents steam turbine generator merit angle tracking error, unit degree of being; In Fig. 4 .3, Fig. 5 .3, y coordinate represents main steam valve of turbine generator control inputs, and unit is newton; In Fig. 5 .4, y coordinate represents main steam valve of turbine generator control inputs disturbance-observer effect, and unit is newton; Represented by dotted arrows desired trajectory signaling line in Fig. 4 .1, Fig. 5 .1, solid line represents actual steam turbine generator power-angle signal line; Represented by dotted arrows actual interference signaling line in Fig. 5 .4, solid line represents visualizer observation undesired signal line.

Embodiment

See Fig. 1-Fig. 5 .4, design object of the present invention comprises two aspects: one, realizes the simplification of main steam valve of turbine generator control design case; Its two, realize the quick accurate tracking desired trajectory in steam turbine generator merit angle of closed-loop system, specific targets are: steam turbine generator merit angle tracking error in 1 second is less than 0.5 degree of angle.Fig. 1 is Infinite bus power system bus system schematic diagram of the present invention.

In concrete enforcement, emulation and the inspection of main steam valve predictive control method and closed loop control system all realize by means of the Simulink toolbox in Matlab.Here by introducing one, there is certain representational mode of execution, further illustrating the relevant design in technical solution of the present invention.In emulation, according to the real system posterior infromation of certain power plant, parameter choose is as follows:

δ ₀=60, ω ₀=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' _{d Σ}=0.94, T _{h Σ}=0.4, state variable initial value is set to x ₁=0, x ₂=0, x ₃=0.

Visualizer parameter gets l ₃=100, c=0.001, controller parameter is T=0.238, command signal w (t)=5sin (π t).

Mode of execution (one) realizes accuracy and the rapidity of the angle tracking of steam turbine generator merit.

Mode of execution (one)

Step one: main steam valve of turbine generator control system analysis and modeling

Closed loop control system adopts degenerative control structure, and output quantity is steam turbine generator merit angle.Designed closed loop control system mainly comprises controller link and these two parts of system model, and its topology layout situation as shown in Figure 2.

Main steam valve control system model is described below:

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

Wherein: δ represents steam turbine generator merit angle;

δ ₀represent steam turbine generator merit angle initial value;

ω represents generator amature speed;

ω ₀represent generator amature speed initial value;

P _hrepresent the mechanical output that high-pressure cylinder produces;

P _mrepresent the mechanical output that prime mover exports;

P _m0represent the mechanical output initial value that prime mover exports;

D represents damping constant;

H represents the rotary inertia of generator amature;

C _mLrepresent mesolow power partition coefficient;

C _hrepresent the non-distribution coefficient of high-pressure cylinder power;

E' _qrepresent generator q axle transient potential;

V represents infinite busbar voltage;

X' _{d Σ}represent the equivalent electromotive force between generator and Infinite bus system;

T _{h Σ}represent high-pressure cylinder steam valving control system equivalent time constant;

U represents that main steam valve of turbine generator controls;

D represents that main steam valve of turbine generator control inputs disturbs.

For the ease of design, define three state variable x respectively ₁, x ₂, x ₃as follows:

x ₁＝δ-δ ₀

x ₂＝ω-ω ₀

x ₃＝P _H-C _HP _m0

At this moment (1) just can be write 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 2: main steam valve of turbine generator Predictive control design

Control task for exporting y (t) trace command w (t), and overcomes main steam valve of turbine generator control inputs interference d.

Optimization object function is

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

Wherein for the Observed value of d, for the predicted value of y (t+ τ), for the predicted value of w (t+ τ), T is forecast interval, and τ is predicted time, 0≤τ≤T, and has

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

Wherein for the predicted value of u (t+ τ).

The relative exponent number of model is ρ, and control exponent number is r, 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 this algorithm, by Taylor expansion, realize approaching following prediction of output signal, for approach, get

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

Wherein $\stackrel{\‾}{\mathrm{\τ}}=\mathrm{diag}\{\mathrm{\τ},...,\mathrm{\τ}\}$ For m × m matrix, m is that system exports number, $\mathrm{\Γ}\left(t\right)=\left[\begin{array}{cccc}I& \stackrel{\‾}{\mathrm{\τ}}& ...& \frac{{\stackrel{\‾}{\mathrm{\τ}}}^{(\mathrm{\ρ}+r)}}{(\mathrm{\ρ}+r)!}\end{array}\right],$ I is the unit matrix of m × m.From model (2), ρ=3, r=1, m=1, so can get

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

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

By Taylor expansion, realize approaching future instructions prediction signal, for approaching of w (t+ τ), get

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

Wherein,

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

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

Due to ρ+r+1=5, then i, j=1,2,3,4,5, then be expressed 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 3: Nonlinear Disturbance Observer designs

Design Nonlinear Disturbance Observer estimates unknown interference, compensates control inputs.

Design visualizer is:

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

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

Nonlinear observer gain definitions is:

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

Observational error is defined as:

and interference is slow time-varying.

Select p (x), make equation meet Global Exponential Stability, then exponential convergence is in d.

According to model (2), select then,

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

Now, so suitable parameter c, to all l ₃have global Exponential Stability.

Thus can based on the Predictive control law of Nonlinear Disturbance Observer:

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

So far, a kind of design of the main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer is complete.

Step 4: design terminates

Whole design process emphasis considers the demand for control of three aspects, is respectively the simplicity of design, the stability of closed-loop system, the quick accuracy of tracking.Around these three aspects, in the above-mentioned first step, first determine the concrete formation of closed loop control system; In second step, emphasis gives main steam valve of turbine generator Predictive control design method; The design of Nonlinear Disturbance Observer is mainly given in 3rd step; After above steps, design terminates.

Claims (1)

1. based on a main steam valve of turbine generator predictive control method for Nonlinear Disturbance Observer, it is characterized in that: the method concrete steps are as follows:

Step one: main steam valve of turbine generator control system analysis and modeling

Closed loop control system adopts degenerative control structure, and output quantity is steam turbine generator merit angle, and designed closed loop control system comprises controller link and system model two-part;

Main steam valve control system model is described below:

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

Wherein: δ represents steam turbine generator merit angle;

δ ₀represent steam turbine generator merit angle initial value;

ω represents generator amature speed;

ω ₀represent generator amature speed initial value;

P _hrepresent the mechanical output that high-pressure cylinder produces;

P _mrepresent the mechanical output that prime mover exports;

P _m0represent the mechanical output initial value that prime mover exports;

D represents damping constant;

H represents the rotary inertia of generator amature;

C _mLrepresent mesolow power partition coefficient;

C _hrepresent the non-distribution coefficient of high-pressure cylinder power;

E' _qrepresent generator q axle transient potential;

V represents infinite busbar voltage;

X' _{d Σ}represent the equivalent electromotive force between generator and Infinite bus system;

T _{h Σ}represent high-pressure cylinder steam valving control system equivalent time constant;

U represents that main steam valve of turbine generator controls;

D represents that main steam valve of turbine generator control inputs disturbs;

For the ease of design, define three state variable x respectively ₁, x ₂, x ₃as follows:

x ₁＝δ-δ ₀

x ₂＝ω-ω ₀

x ₃＝P _H-C _HP _m0

At this moment (1) is just write 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: $f\left(x\right)=\left(\begin{array}{c}{x}_2\\ a_1\sin (x_1+{\mathrm{\δ}}_0)+a_2{x}_2+a_3{x}_3+b_1\\ a_4{x}_3\end{array}\right),g\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),g_d\left(x\right)=\left(\begin{array}{c}0\\ 0\\ k_1\end{array}\right),h\left(x\right)=x_1$

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

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

$a_3=\frac{{\mathrm{\ω}}_0}{H},$

$a_4=-\frac{1}{T_{\mathrm{H\Σ}}}$

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

$k_1=\frac{C_H}{T_{\mathrm{H\Σ}}},$

Step 2: main steam valve of turbine generator Predictive control design

Control task for exporting y (t) trace command w (t), and overcomes main steam valve of turbine generator control inputs interference d;

Optimization object function is

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

Wherein for the Observed value of d (t+ τ), for the predicted value of y (t+ τ), for the predicted value of w (t+ τ), T is forecast interval, and τ is predicted time, 0≤τ≤T, and has

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

Wherein for the predicted value of u (t+ τ);

The relative exponent number of model is ρ, and control exponent number is r, 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 this algorithm, by Taylor expansion, realize approaching following prediction of output signal, for approach, get

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

Wherein for m × m matrix, m is that system exports number, $\mathrm{\Γ}\left(\mathrm{\τ}\right)=\left[\begin{array}{cccc}I& \stackrel{\‾}{\mathrm{\τ}}& ...& \frac{{\stackrel{\‾}{\mathrm{\τ}}}^{(\mathrm{\ρ}+r)}}{(\mathrm{\ρ}+r)!}\end{array}\right],$ I is the unit matrix of m × m; From model (2), ρ=3, r=1, m=1, so get

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

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

By Taylor expansion, realize approaching future instructions prediction signal, for approaching of w (t+ τ), get

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

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

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

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

Due to ρ+r+1=5, then i, j=1,2,3,4,5, then be expressed 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 3: Nonlinear Disturbance Observer designs

Design Nonlinear Disturbance Observer estimates unknown interference, compensates control inputs;

Design visualizer is:

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

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

Nonlinear observer gain definitions is:

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

Observational error is defined as:

and interference is slow time-varying;

Select p (x), make equation meet Global Exponential Stability, then exponential convergence is in d;

According to model (2), select then,

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

Now, so suitable parameter c, to all l ₃there is Global Exponential Stability, thus can based on the Predictive control law of Nonlinear Disturbance Observer:

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

So far, a kind of design of the main steam valve of turbine generator predictive control method based on Nonlinear Disturbance Observer is complete;

Step 4: design terminates

Whole design process emphasis considers the demand for control of three aspects, is respectively the simplicity of design, the stability of closed-loop system, the quick accuracy of tracking; Around these three aspects, in the above-mentioned first step, first determine the concrete formation of closed loop control system; In second step, emphasis gives main steam valve of turbine generator Predictive control design method; The design of Nonlinear Disturbance Observer is given in 3rd step; After above steps, design terminates.