CN109062030A - Thermal power unit plant load prediction PID control method based on laguerre function model - Google Patents

Abstract

The present invention discloses a thermal power unit load forecasting PID control method based on the Laguerre function model. The thermal power unit load system includes a control system and a controlled system. The specific operation steps are as follows: S1, the control output of the control system U( k) Input the controlled system to obtain the controlled output Y(k) ; S2, use Y(k) to identify the parameters of the Laguerre function prediction model; S3, transmit the control output U(k) to the Laguerre as the model input function prediction model to obtain the model prediction output Y _M (k+1) ; S4, use Y(k) to perform feedback correction on the model prediction output Y _M (k+1) , and obtain the compensation model prediction output Y _P (k+1 ) ; S5, utilize the PID control algorithm to scroll and optimize the compensation model output to obtain a new control output U(k+ 1) ; S6, repeat steps S1‑S5 to realize the stable operation of the thermal power unit load system. The method of the invention has the advantages of fast tracking speed, strong anti-interference ability, small steady-state error, short calculation time, etc., and has strong self-adaptive ability.

Description

PID control method for thermal power unit load forecasting based on Laguerre function model

technical field

The invention belongs to the technical field of thermal power unit load control, and mainly relates to a thermal power unit load forecasting PID control method based on a Laguerre function model.

Background technique

With the continuous expansion of the power grid and unit unit capacity, the user's requirements for the quality of power consumption are also increasing, and it is becoming more and more important to study the application of multivariable control strategies in thermal processes. Unit unit load control in thermal power plants is a typical complex and multivariable system. The main requirement for unit unit load control in thermal power plants is to keep the main steam pressure within a specified range and enable units to quickly meet external load requirements.

At present, experts have proposed some advanced control strategies for unit unit load control in thermal power plants. Network control, but this control method requires a large amount of calculation and takes a long time.

Model Predictive Control (MPC) is a new type of control strategy developed in the late 1970s with broad application prospects. Because of its good control effect, it has been successfully applied in actual industrial control. Most experiments show that for thermal processes with large inertia and large hysteresis, the performance of MPC is obviously better than that of traditional PID control strategy. However, the traditional MPC has certain limitations. Model algorithmic control (MAC) and dynamic matrix control (DMC) use non-parametric models, which use a lot of data and a large amount of calculation, which is not easy to realize adaptive control; generalized predictive control (GPC) ), etc., are sensitive to the time delay and order of the controlled object. In recent years, Canadian Dumont et al. have studied the adaptive predictive control algorithm based on the Laguerre function model, and found that applying this algorithm to the diffusion furnace system can obtain better control effects. The Laguerre function model has the characteristics that the non-parametric model is not sensitive to the system order and delay changes, and the representation model has fewer parameters than the traditional parametric model, the parameters are easy to identify online, and it is easy to implement an adaptive control strategy.

Contents of the invention

The invention provides a thermal power unit load forecasting PID control method based on a Laguerre function model, and combines the adaptive predictive control based on the Laguerre function model with a PID control strategy to obtain a new control method.

In order to solve the problems of the technologies described above, the present invention adopts the following technical means:

The thermal power unit load forecasting PID control method based on the Laguerre function model. The thermal power unit load system includes a control system and a controlled system. The specific operation steps are as follows:

S1, the control output U(k) of the control system is used as the input of the controlled system, and the controlled system outputs Y(k);

S2, using the output Y(k) of the controlled system to identify the parameters of the Laguerre function prediction model;

S3, the control output U(k) of the control system is transmitted to the Laguerre function prediction model as a model input, and the model prediction output Y _M (k+1) is obtained through the Laguerre function prediction model;

S4, using the output Y(k) of the controlled system to perform feedback correction on the model prediction output Y _M (k+1), and obtain the compensation model prediction output Y _P (k+1) after feedback correction;

S5, using the PID control algorithm to scroll and optimize the model prediction output to obtain a new control output U(k+1);

S6, steps S1-S5 are repeated to realize stable operation of the thermal power unit load system.

Further, the load system of thermal power units satisfies the mathematical model:

Among them, y _i is the output of the i-th system, there are m system outputs in total, u _j is the input of the j-th system, there are n system inputs in total, G _ij (z ^-1 ) is the relationship between the i-th output and the j-th input Transfer function, i=1,...,m; j=1,...,n.

Further, the control system control output U(k) satisfies the formula:

Among them, ΔU(k) is the system input increment, K=diag(K ₁ ,…,K _m ) _m×mM , K _i(i=1,…,m) =[1 0 …0] _{1× M} , M is the model control time domain, is the optimal control increment of the system.

Further, the Laguerre function prediction model parameter is the coefficient matrix C in the model, which can be identified online by the least squares method with a forgetting factor:

Among them, Δy _i (k) is the output increment of the i-th system output at time k, ΔL _i (k) is the model state increment of the i-th system output at k time, λ _i is the forgetting factor, and the value range is 0.9 ~0.99, C _i (0)=[0.001,0.001,0.001], P(0)=10^8I, I is the identity matrix, i=1,...,m.

Further, the model prediction output Y _M (k+1) satisfies the formula:

Y _M (k+1)＝SH _l ΔL(k)+ΦY _M (k)+SH _u ΔU _M (k) (4)

Among them, ΔL(K) is the model state increment, ΔU _M (k) is the model input state increment,

S=diag(S ₁ ,...,S _m ) _Pm×Pm ,

Φ=diag(Φ ₁ ,…,Φ _m ) _mP×m ,

Φ _i(i=1,...,m) =[1 1 ...1] ^T _P×1 ,

η=1-a ² ,

In the above formula, a is the pole of the Laguerre function model, N is the series of the Laguerre function model, C is the coefficient matrix of the Laguerre function model, and P is the model prediction step size.

Further, the compensation model prediction output Y _P (k+1) satisfies the formula:

Y _P (k+1)=Y _M (k+1)+H _f [Y(k)-Y _M (k)] (5)

Wherein, H _f is the feedback gain matrix, H _f =diag(h _f1 ,...,h _fm ) _Pm×m , h _{fi(i=1,...,m)} =[1 1...1] ^T _P×1 .

Further, the step S5 utilizes the PID control algorithm to optimize the prediction output rolling, and the specific formula is:

J＝K _I E(k+1) ^T QE(k+1)+K _p ΔE(k+1) ^T QΔE(k+1)+ (6)

K _D Δ ² E(k+1) ^T QΔ ² E(k+1)+ΔU _M (k) ^T RΔU _M (k)

Among them, E(k+1)= _Yp (k+1) _-Yr (k+1),

ΔE(k+1)=ΔD(k+1)+SH _u Δ ² U _M (k),

Δ ² E(k+1)=Δ ² D(k+1)+SH _u Δ ³ U _M (k),

Δ ² U _m (k) = (1-q ^-1 )Δ U _m (k),

Δ ³ U _m (k) = (1-q ^-1 ) ² Δ U _m (k),

ΔD(k+1)=(1-q ^-1 )D(k+1),

Δ ² D(k+1)=(1-q ^-1 ) ² ΔD(k+1),

D(k+1)=SH _l ΔL(k)+ΦY(k)-Y _r (k+1),

In the above formula, Y _r (k+1) is the reference trajectory, q ^-1 is the backward shift operator, Q is the error weighting matrix, R is the control weighting matrix, J is the objective function, K _P , K _I , K _D are generalized proportional term coefficients, integral term coefficients and differential term coefficients.

The method of the present invention loads the control quantity U(K) of the control system into the RAM of the microprocessor DSP in the form of an executable file, and the CAP port capture unit of the DSP reads the position signal, and passes through the predictive PID control algorithm based on the Laguerre function model The model output of the thermal power unit load system is obtained after the controller, and the deviation is obtained by comparing the model output with the actual output feedback value of the controlled system, and the control value is adjusted through the deviation feedback to control the operation of the thermal power unit load system.

The following advantages can be obtained by using the above technical means:

The present invention combines the PID control system with the predictive control based on the Laguerre function model to obtain a new control method applicable to the multi-input multi-output system, and introduces the method into the unit load control system of thermal power plants to replace the original Traditional control provides a new type of control strategy. The method of the present invention not only has the characteristics of small steady-state error and short rise time of PID control, but also has high control precision, fast tracking speed and strong anti-interference ability compared with traditional predictive control. Timing and external interference have stronger adaptability, and have better control quality.

Description of drawings

Fig. 1 is a block diagram of the predictive PID control method based on the Laguerre function model.

Figure 2 is a simplified block diagram of the mathematical model of the thermal power unit unit load system.

Figure 3 is the response curve of thermal power unit load system.

Fig. 4 is the response curve of thermal power unit load system during disturbance.

Fig. 5 is the response curve of thermal power unit load system when the model is mismatched.

Among them, DMC-PID refers to the control system based on the dynamic matrix control-PID algorithm, and LMPC-PID refers to the control system based on the predictive PID algorithm of the Laguerre function model.

Detailed ways

Below in conjunction with accompanying drawing, technical scheme of the present invention will be further described:

The present invention proposes a thermal power unit load forecasting PID control method based on the Laguerre function model, as shown in Figure 1, the control output U(k) of the control system based on the Laguerre function model predicting PID algorithm acts on the controlled system, as The input of the controlled system, in addition, U(k) is also used as the model input to obtain the model prediction output Y _M (k+1) through the Laguerre function model, and the output value Y(k) of the controlled system is used for model parameter identification and Model output feedback correction, model parameter identification and model output feedback correction are all to further optimize the control system and ensure the control effect. The new model output value Y _P (k+1) is obtained through correction and compensation, and the PID control algorithm is introduced, and the reference trajectory, proportional coefficient, integral coefficient and differential coefficient are added, and rolling optimization is performed to obtain a new system control output. The present invention ensures the normal operation of thermal power units within the required range through such cycle regulation.

The thermal power unit load system includes a control system and a controlled system, which satisfy the mathematical model:

Among them, y _i is the output of the i-th system, there are m system outputs in total, u _j is the input of the j-th system, there are n system inputs in total, G _ij (z ^-1 ) is the relationship between the i-th output and the j-th input Transfer function, i=1,...,m; j=1,...,n.

In the following, it is assumed that the thermal power unit load system is an m×m multivariable system, and the public derivation is carried out.

The transfer function matrix of the thermal power unit load system is:

The Laguerre function approximation model of the same structure is used to represent the transfer function G _ij (z ^-1 ) (i=1,...,m; j=1,...,m) of each channel, and the increment of the Laguerre function approximation for the entire multivariable system The state space model is:

Where ΔL(k) is the model state increment, ΔU(k) is the system input increment, ΔY _M (k) is the model output increment,

A _i(i=1,...m) = diag(A ₁ ,...,A _m ) _mN×mN ,

C=[c ₁ ,c ₂ ,c ₃ ,...,c _N ] ^T ,

η=1-a ² ,

In the above formula, a is the pole of the Laguerre function model, N is the series of the Laguerre function model, and C is the coefficient matrix of the Laguerre function model.

The model output Y _M (k+1) of the Laguerre function model satisfies the following formula:

Y _M (k+1)＝SH _l ΔL(k)+ΦY _M (k)+SH _u ΔU _M (k) (10)

where S=diag(S ₁ ,...,S _m ) _Pm×Pm ,

Φ=diag(Φ ₁ ,…,Φ _m ) _mP×m ,

Φ _i(i=1,...,m) =[1 1...1] ^T _P×1 ,

In the above formula, ΔU _M (k) is the model input state increment, P is the model prediction step size, and M is the model control time domain.

Using the output Y(k) feedback correction model of the controlled system to predict the output, the output of the compensated Laguerre function model satisfies the following formula:

Y _P (k+1)=Y _M (k+1)+H _f [Y(k)-Y _M (k)] (11)

Wherein, H _f is the feedback gain matrix, H _f =diag(h _f1 ,...,h _fm ) _Pm×m , h _{fi(i=1,...,m)} =[1 1...1] ^T _P×1 .

After sorting and simplifying the formula (11), we can get:

Y _P (k+1)＝SH _l ΔL(k)+ΦY(k)+SH _u ΔU _M (k) (12)

In the multivariable control system, PID control and Laguerre function model predictive control are combined, and a new formula with proportional, integral and differential is adopted:

J＝K _I E(k+1) ^T QE(k+1)+K _p ΔE(k+1) ^T QΔE(k+1)+ (13)K _D Δ ² E(k+1) ^T QΔ ² E(k+1)+ΔU _M (k) ^T RΔU _M (k)

Among them, E(k+1)=Y _p (k+1)-Y _r (k+1), Y _r (k+1) is the reference trajectory, Q is the error weighting matrix, R is the control weighting matrix, J is the objective function, K _P , K _I , K _D are the coefficients of generalized proportional term, integral term and differential term respectively.

After finishing and simplifying E(k+1), we can get:

E(k+1)＝Y _P (k+1)-Y _r (k+1)

=SH _l ΔL(k)+ΦY(k)+SH _u ΔU _M (k)-Y _r (k+1) (14)

＝D(k+1)+SH _u ΔU _M (k)

Wherein, D(k+1)=SH _l ΔL(k)+ΦY(k)-Y _r (k+1).

reference trajectory satisfy the following formula:

Wherein, i=(1,...,m), j=(1,...,P), α _i is a softening factor, and _ri is a setting value.

According to the principle of recursion, it can be obtained from formula (14):

ΔE(k+1)=ΔD(k+1)+SH _u Δ ² U _M (k) (16)

Δ ² E(k+1)=Δ ² D(k+1)+SH _u Δ ³ U _M (k) (17)

Introducing the backward shift operator q ^-1 , then:

Δ ² U _m (k) = (1-q ^-1 )Δ U _m (k) (18)

Δ ³ U _m (k) = (1-q ^-1 ) ² Δ U _m (k) (19)

ΔD(k+1)=(1-q ^-1 )D(k+1) (20)

Δ ² D(k+1)=(1-q ^-1 ) ² ΔD(k+1) (21)

make From formula (13), we can get:

Simplify formula (22) to get:

[K _I +(1-q ^-1 )K _P +(1-q ^-1 ) ² K _D ]·[H _u ^T S ^T QD(k+1)+H _u ^T S ^T QSH _u ΔU _m (k )]+RΔU _m (k)=0(23)

Let W＝K _I +(1-q ^-1 )K _p +(1-q ^-1 ) ² K _D , then the optimal control quantity increment of the system Can be expressed as:

ΔU ^* _m (k)＝-[WH _u ^T S ^T QSH _u +R] ^-1 WH _u ^T S ^T QD(k+1) (24)

Using the rolling optimization method, taking the first element of ΔU _m (k) as the current control increment of the system, the control output U(k) of the predictive PID control algorithm based on the Laguerre function model can be obtained to satisfy the following formula:

Wherein, K=diag(K ₁ ,...,K _m ) _m×mM , K _i(i=1,...,m) =[1 0...0] _1×M .

In order to verify the control effect of the method of the present invention, a simulation experiment is carried out in this embodiment, and the method of the present invention is compared with the dynamic matrix control-PID (hereinafter referred to as DMC-PID) algorithm. It should be pointed out that this simulation experiment is only for better explaining the method of the present invention, and does not limit the content of the method of the present invention.

The 2×2 thermal power unit load system shown in Figure 2 includes several parts such as boilers, steam turbines, generators, and control systems. The mathematical model is as follows:

in, u ₁ is the turbine door adjustment command, u ₂ is the boiler combustion command, _Ne is the actual power, P _t is the main steam pressure, u ₁ and u ₂ are the two inputs of the system, Ne _and P _t are the two output.

Laguerre function prediction model series N=3, pole a=0.8, sampling time T=10s, softening factor α _i =0.92, prediction step size P=10, control time domain M=1, forgetting factor λ _i =0.99 , setting value The simulation time is 8000s.

As shown in Figure 3, the system response curves of the two control algorithms can reach the set value smoothly, and the output of power and pressure has no oscillation and no overshoot. It can be seen that both algorithms meet the performance requirements of the control system, but The adjustment time of the thermal power unit load control coefficient response curve based on the Laguerre function model prediction PID control algorithm is shorter than that based on the DMC-PID algorithm, indicating that the method of the present invention can realize system control more quickly.

In order to further test the control effects of the two control algorithms, the set value of the power was suddenly changed at 3000s of the simulation process, and a step disturbance with an amplitude of 0.01 was added at 6000s. As shown in Figure 4, when the set value of power output is changed, the power output curve of the thermal power unit load control coefficient based on the Laguerre function model prediction PID control algorithm still reaches the set value quickly and steadily, and the steam pressure response curve There is no major change, which shows that the method of the present invention can play a certain role in decoupling and has excellent tracking performance. After the disturbance is added, the control system based on the DMC-PID algorithm oscillates, while the system based on the Laguerre function model prediction PID control algorithm does not oscillate when solving the disturbance, and the control is stable, indicating that the method of the present invention has better anti-interference ability.

When a large mismatch occurs in the model, its parameter settings are not changed, and the response curves before and after the model mismatch are compared, as shown in Figure 5, when the model is mismatched, only a slight overshoot occurs in the output curve of the method of the present invention, still Better control effect is arranged, and the validity of the method of the present invention is further verified.

The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, within the knowledge of those of ordinary skill in the art, you can also Make various changes.

Claims (7)

1. The thermal power unit load forecasting PID control method based on the Laguerre function model. The thermal power unit load system includes a control system and a controlled system. It is characterized in that the specific operation steps are as follows: S1, the control output U(k) of the control system is used as the input of the controlled system, and the controlled system outputs Y(k); S2, using the output Y(k) of the controlled system to identify the parameters of the Laguerre function prediction model; S3, the control output U(k) of the control system is transmitted to the Laguerre function prediction model as a model input, and the model prediction output Y _M (k+1) is obtained through the Laguerre function prediction model; S4, using the output Y(k) of the controlled system to perform feedback correction on the model prediction output Y _M (k+1), and obtain the compensation model prediction output Y _P (k+1) after feedback correction; S5, using the PID control algorithm to scroll and optimize the model prediction output to obtain a new control output U(k+1); S6, steps S1-S5 are repeated to realize stable operation of the thermal power unit load system. 2. the thermal power unit unit load forecasting PID control method based on Laguerre function model according to claim 1, is characterized in that, described thermal power unit unit load system satisfies mathematical model: Among them, y _i is the output of the i-th system, there are m system outputs in total, u _j is the input of the j-th system, there are n system inputs in total, G _ij (z ^-1 ) is the relationship between the i-th output and the j-th input Transfer function, i=1,...,m; j=1,...,n. 3. the thermal power unit unit load forecasting PID control method based on Laguerre function model according to claim 1, is characterized in that, described control system control output U (k) satisfies formula: Among them, ΔU(k) is the system input increment, K=diag(K ₁ ,…,K _m ) _m×mM , K _i(i=1,…,m) =[1 0… 0] _{1× M} , M is the model control time domain, is the optimal control increment of the system. 4. the thermal power unit unit load forecasting PID control method based on the Laguerre function model according to claim 1, is characterized in that, described Laguerre function forecasting model parameter is the coefficient matrix C in the model, can pass band Least squares online identification of forgetting factor: Among them, Δy _i (k) is the output increment of the i-th system output at time k, ΔL _i (k) is the model state increment of the i-th system output at k time, λ _i is the forgetting factor, and the value range is 0.9 ~0.99, C _i (0)=[0.001,0.001,0.001], P(0)=10^8I, I is the identity matrix, i=1,...,m. 5. the thermal power unit unit load forecasting PID control method based on Laguerre function model according to claim 1, is characterized in that, described model prediction output Y _M (k+1) satisfies formula: Y _M (k+1)＝SH _l ΔL(k)+ΦY _M (k)+SH _u ΔU _M (k) Among them, ΔL(K) is the model state increment, ΔU _M (k) is the model input state increment, S=diag(S ₁ ,...,S _m ) _Pm×Pm , Φ=diag(Φ ₁ ,…,Φ _m ) _mP×m , Φ _i(i=1,…,m) ＝[1 1 … 1] ^T _P×1 , η=1-a ² , In the above formula, a is the pole of the Laguerre function model, N is the series of the Laguerre function model, C is the coefficient matrix of the Laguerre function model, and P is the model prediction step size. 6. the thermal power unit unit load forecasting PID control method based on Laguerre function model according to claim 1, is characterized in that, described compensation model prediction output Y _P (k+1) satisfies formula: Y _P (k+1)＝Y _M (k+1)+H _f [Y(k)-Y _M (k)] Wherein, H _f is the feedback gain matrix, H _f =diag(h _f1 ,...,h _fm ) _Pm×m , h _{fi(i=1,...,m)} =[1 1 ... 1] ^T _P×1 . 7. the thermal power unit unit load forecasting PID control method based on the Laguerre function model according to claim 5, is characterized in that, step S5 utilizes PID control algorithm rolling optimization forecasting output, and concrete formula is: J＝K _I E(k+1) ^T QE(k+1)+K _p ΔE(k+1) ^T QΔE(k+1)+ K _D Δ ² E(k+1) ^T QΔ ² E(k+1)+ΔU _M (k) ^T RΔU _M (k) Among them, E(k+1)= _Yp (k+1) _-Yr (k+1), ΔE(k+1)=ΔD(k+1)+SH _u Δ ² U _M (k), Δ ² E(k+1)=Δ ² D(k+1)+SH _u Δ ³ U _M (k), Δ ² U _m (k) = (1-q ^-1 )Δ U _m (k), Δ ³ U _m (k) = (1-q ^-1 ) ² Δ U _m (k), ΔD(k+1)=(1-q ^-1 )D(k+1), Δ ² D(k+1)=(1-q ^-1 ) ² ΔD(k+1), D(k+1)=SH _l ΔL(k)+ΦY(k)-Y _r (k+1), In the above formula, Y _r (k+1) is the reference trajectory, q ^-1 is the backward shift operator, Q is the error weighting matrix, R is the control weighting matrix, J is the objective function, K _P , K _I , K _D are generalized proportional term coefficients, integral term coefficients and differential term coefficients.