CN113325696A - Hybrid control method for combining single neuron PID and model prediction applied to crosslinked cable production equipment - Google Patents

Abstract

The invention discloses a mixed control method combining single neuron PID and model prediction applied to cross-linked cable production equipment, which combines a control method of MPC to specifically adjust PID parameters, establishes a temperature system model, performs steps of analyzing the model, performing feedback correction on the model parameters, adjusting the PID parameters, finally outputting the PID and the like to obtain the future approximate change trend of the system, and correspondingly adjusts the PID parameters by using the principle of the least square sum of errors in a period of time in the future.

Description

A hybrid control method combining single neuron PID and model prediction for cross-linked cable production equipment

technical field

The invention relates to a temperature control method, in particular to a hybrid control method which is applied to a cross-linked cable production equipment combined with a single neuron PID and model prediction.

Background technique

Generally, if the exact model of the system is known, it is very easy to control the system, but it is very difficult to accurately model the temperature system. Based on this situation, at present, the main methods applied to temperature control include PID control, fuzzy logic control, neural network control and other methods. The expected control effect can be achieved only by adjusting the parameters without involving system modeling. Among them, PID control is the most widely used. It has the advantages of simple principle, easy implementation, wide application range, direct effect and so on. However, when faced with some systems that have certain requirements for control accuracy, the PID method has a general control effect; the fuzzy logic control is to formulate a fuzzy table by professionals, and look up the table to infer the corresponding control strategy for different states of the system, which is very suitable for The system only works in some specific states, but the disadvantage is that the formulation of a good fuzzy table generally needs to be obtained by professional technicians through long-term field operation experience accumulation and continuous testing; neural network control is an emerging intelligent control in recent years. The method has good adaptability and good control quality for nonlinear time-varying systems, time-delay systems, and complex systems that are difficult to model. High performance requirements and high development difficulty require a large amount of actual data training.

The single neuron PID controller is based on the PID controller, combined with the adaptability of neural network control and its self-learning properties, it will produce a better control effect than simply using PID control when the system model is unknown. It has been confirmed in the literature in recent years, and its learning rules generally use Hebb learning rules. The selection of rules needs to select more appropriate learning rules according to the nature of the system, but how to select learning rules for single neuron PID control, and how This learning method can achieve better results, and there is currently no relevant literature to explore this aspect.

SUMMARY OF THE INVENTION

Aiming at the problem of single selection of learning rules in the existing single neuron PID technology, the present invention provides a single neuron PID learning method combined with a model predictive control method (MPC). Control effect. The method combines the control idea of MPC to make specific adjustments to the PID parameters. This method uses a simple and effective modeling method for the temperature system. Through the analysis of the model, the general change trend of the system in the future is obtained, and the PID parameters are adjusted accordingly based on the principle of the minimum sum of squares of errors in the future period to make up for The blindness in the selection of learning rules improves the control accuracy of the system.

A hybrid control method combining single neuron PID and model prediction applied to cross-linked cable production equipment, the specific steps are as follows:

Step 1: Build a temperature system model;

The temperature system model used is:

Among them, Y(k) is the system output at the k-th sampling time calculated by the model; C(k) is the system historical output at the k-th sampling time, and A _i is the i-th historical system output corresponding to the previous sampling time The initial value is set as follows: A ₁ (0)=A ₂ (0)=A ₃ (0)=...A ₇ (0)=0, A ₈ (0)=A ₉ (0)=A ₁₀ (0)=0.33; U(k) is the historical input of the system at the k-th sampling time, B _i (k) is the corresponding weighting coefficient of the i-th historical system input before the sampling time, and the initial value is set to B ₁ (0)=B ₂ (0)=...=B ₁₀ (0)=0, the model will be revised later, so the above initial values of A _i and B _i can be fine-tuned;

Step 2: Model parameter feedback correction;

Using the real output of the system as feedback, the model parameters A _i (k), B _i (k), i=1, 2, ... 10 in step 1 are corrected in real time; the adjustment increments at each sampling time are: ΔA _i , ΔB _i ;

ΔA _i =ZA _i *E _F (k)*C(ki)

ΔB _i =ZB _i *E _F (k)*U(ki)

The above ZA _i and ZB _i are learning rate parameters that need to be adjusted according to the actual situation of the system, wherein ZA ₁ =ZA ₂ =ZA ₃ =... ZA ₇ =0, ZB ₉ =ZB ₁₀ =0; the remaining learning rate parameters need to be adjusted according to the system Adjust according to the actual situation; E _F (k) is the error value at the sampling moment; among them,

E _F (k)=C(k)-Y(k);

Therefore, the corrected model parameters at this moment are as follows:

A _i (k)=A _i (k-1)+ΔA _i

B _i (k)=B _i (k-1)+ΔB _i

Step 3: This step starts to adjust the PID parameters, that is, the mean square error of 10 sampling moments after the sampling time is calculated by using the model obtained in Step 1 and Step 2;

Let J be the learning basis:

in,

E _Y (k+i)=RY(k+i)

的增量如下：The three pre-parameters of the single neuron PID are obtained by performing partial differentiation on the proportional coefficient K _P , the integral coefficient K _I and the differential coefficient K _D of the PID

The increments are as follows:

Among them, R is the system output setting value, Z _P , Z _I , and Z _D are the learning rate parameters that need to be adjusted according to the actual situation of the system;

Get the adjusted PID pre-parameters:

Step 4: PID output;

进行归一化处理得到PID的比例系数K_P、积分系数K_I、微分系数K_D：Three pre-parameters to the PID in step 3

Perform normalization to obtain the proportional coefficient K _P , the integral coefficient K _I , and the differential coefficient K _D of the PID:

Obtain the input U(k) that the controller finally gives to the system at this sampling time:

U(k)=K _P (k)*E(k)+K _I (k)*E _I (k)+K _D (k)*E _D (k)

in

E(k)=R-C(k)

E _D (k)=E(k)-E(k-1)

Among them, K is the PID gain parameter that needs to be adjusted according to the actual situation of the system. In addition, due to the control of the temperature system, it is necessary to appropriately add integral saturation to limit E _I (k) according to the actual situation of the system. If the output U(k) is given to the system, the operations that need to be performed for this sampling are completed, and the loop returns to step 2 for execution.

Compared with the prior art, the advantages of the present invention are as follows:

1. The adjustment process includes the future information of the system, which reduces the disturbance to the controller due to the time delay characteristics of the temperature system;

2. Use the sum of squares of errors in the future period as the adjustment basis to make the control effect more stable;

3. Due to the dynamic adjustment of PID parameters and strong anti-interference ability, this method has strong robustness.

Description of drawings

Fig. 1 is a kind of principle block diagram of the hybrid control method that is applied to the single neuron PID of the cross-linked cable production equipment combined with model prediction according to the present invention;

Fig. 2 is a kind of prediction model diagram of the hybrid control method that is applied to the single neuron PID of the cross-linked cable production equipment combined with model prediction according to the present invention;

3 is a learning basis diagram of a hybrid control method applied to a single neuron PID and model prediction combination of a cross-linked cable production equipment according to the present invention;

FIG. 4 is a schematic diagram of a system to which a hybrid control method combining single neuron PID and model prediction applied to a cross-linked cable production equipment according to the present invention is attached.

Detailed ways

The solution of the present invention will be further described below in conjunction with the accompanying drawings.

The temperature control system block diagram involved in the present invention is shown in Figure 4:

The model of the main control screen adopted in the present invention is Siemens SIMATIC HMI, the controller is Siemens PLC300, and the control screen uses WINCC7.3 version as configuration software to control and monitor the production process.

A complete control process is as follows:

Input the set temperature R through the main control screen; the controller reads the temperature signal C(k) of the thermocouple; obtains the output U(k) through the above control method, and controls the heating signal and cooling signal according to the size of U(k) to give To the heating tile and circulating water cooling valve installed on the extruder, one control is completed.

The specific implementation object of this embodiment is an extruder of a cross-linked cable production line. The parameters used in this embodiment are applicable to this system, and can also be used as a reference for other temperature systems. The specific implementation needs to be appropriately adjusted according to the actual operating conditions. The implementation method is to realize through microcontroller programming. By sampling the output of the system every 1 second, and executing the learning algorithm and PID algorithm at the same time, the output value of this time is calculated and then output to the system. The output value U is in the range of -1000. ~+1000.

Initialization: The initial value is set as: A1 ₌ A2 ₌ A3=... _A7 = ₀ , _A8 = _A9 = _A10 =0.33; B1 ₌ B2=...= _B10 = ₀ ; K= 30. K _P =30, K _I =1, K _D =100;

The parameters are set as: ZA1=ZA2=ZA3=...ZA7= ₀ , _ZA8 = _ZA9 = _ZA10 = _10-4 , _{ZB1 = ZB2} = ^ZB3 ₌ ... _{ZB8 =} ^10-7 , ZB ₉ =ZB ₁₀ =0. Z _P =1, Z _I =10 ^-3 , Z _D =0.1;

The operations performed for each sample are as follows:

Step 1: Use the Temperature Model

and historical data, C(k-i), U(k-i), i=1, 2, 3...10 Calculate the predicted system output Y(k) at this sampling time, and sample the system output to obtain the actual output value C(k), Difference from the predicted value Y(k):

E _F (k)=C(k)-Y(k)

Step 2: Calculate the model increments ΔA _i , ΔB _i , i=1, 2, 3...10 using the following formulas.

ΔA _i =ZA _i *E _F (k)*C(ki)

ΔB _i =ZB _i *E _F (k)*U(ki)

Update all A _i , B _i , i=1,2,3...10 using the above increments.

A _i (k)=A _i (k-1)+ΔA _i

B _i (k)=B _i (k-1)+ΔB _i

Step 3: Calculate the forecast data.

Calculate the following data:

E(k)=R-C(k)

E _D (k)=E(k)-E(k-1)

U(k)=K _P *E(k)+K _I *E _I (k)+K _D *E _D (k)

Add anti-integration windup, if E _I (k)>200, then E _I (k)=200; if E _I (k)<-200, then E _I (k)=-200. At the same time, the output size is limited. If U(k)>1000, then U(k)=1000; if U(k)<-1000, then U(k)=-1000.

Using the updated weighting parameters A _i (k), B _i (k), i=1, 2, 3...10 in step 2, and the above data U(k), Y(k) (values predicted by the model Instead of the actual system output C(k)), Y(k) is brought into the model formula in step 1, and Y(k+1) is obtained;

Continue to calculate the following data:

E _Y (k+1)=RY(k+1)

E _YI (k+1)=E _I (k)+E _Y (k+1)

E _YD (k+1)=E _Y (k+1)-E(k)

U _Y (k+1)=K _P *E _Y (k+1)+K _I *E _YI (k+1)+K _D *E _YD (k+1)

Similarly, adding anti-integration saturation, if E _YI (k+i)>200, then E _YI (k+1)=200; if E _YI (k+1)<-200, then E _YI (k+1) =-200.

At the same time limit the output size, if U _Y (k+i)>1000, then U _Y (k+i)=1000; if U _Y (k+i)<-1000, then U _Y (k+i)=-1000 .

Using the updated weighting parameters A _i (k), B _i (k), i=1, 2, 3...10 in step 2, and U(k), Y(k+1) of the above data (predicted by the model The value of Y(k+1), instead of the actual system output C(k)), is brought into the model formula in step 1 to obtain Y(k+2);

Iterating the above process, we can calculate Y(k+i), U _Y (k+i), E _Y (k+i), E _YI (k+i), E _YD (k+i), i=1,2 ,3…10.

Step 4: Calculate

First, after simplification we get:

When i=2,3...10. There is the following formula:

The above formula can be calculated one by one to get

Step 5: Calculate

First, after simplification we get:

When i=2,3...10. There is the following formula:

The above formula can be calculated one by one to get

Step 6: Calculate

First, after simplification we get:

When i=2,3...10. There is the following formula:

The above formula can be calculated one by one to get

的增量

进而更新得到调整后的

Step 7: Calculate

increment

Then update the adjusted

can be derived by

Z_P为学习速率。Substitute the data calculated in steps 3 and 4 into the above formula to get

_ZP is the learning rate.

的增量

进而更新得到调整后的

Step 8: Calculate

increment

Then update the adjusted

can be derived by

Z_I为学习速率。Substitute the data calculated in steps 3 and 4 into the above formula to get

Z _I is the learning rate.

的增量

进而更新得到调整后的

Step 9: Calculate

increment

Then update the adjusted

can be derived by

Z_D为学习速率。Substitute the data calculated in steps 3 and 4 into the above formula to get

Z _D is the learning rate.

Step 10: Substitute the data updated in Step 9 into the following formula to update K _P , K _I , and K _D .

Step 11: Calculate the final output of this sampling by the following formula and the data in Step 3 and Step 10.

U(k)=K _P *E(k)+K _I *E _I (k)+K _D *E _D (k)

Limit the output size, if U(k)>1000, then U(k)=1000; if U(k)<-1000, then U(k)=-1000.

Claims (3)

1. A hybrid control method for combining single neuron PID and model prediction applied to crosslinked cable production equipment is characterized by comprising the following specific steps:

step 1: establishing a temperature system model;

the temperature system model used was:

wherein, Y (k) is the system output of the k sampling moment calculated by the model; c (k) is the system history output at the kth sampling time, A_iOutputting corresponding weighting coefficients for the ith historical system ahead of the sampling time, U (k) being the historical input of the system at the kth sampling time, B_i(k) Inputting a corresponding weighting coefficient for the ith historical system ahead of the sampling moment, and correcting the model;

step 2: feedback correction of model parameters;

and (3) correcting the model parameter A in the step (1) in real time by taking the real output of the system as feedback_i(k)，B_i(k) 1,2, … 10; the increment of each sampling time adjustment is as follows: delta A_i，ΔB_i；

ΔA_i＝ZA_i*E_F(k)*C(k-i)

ΔB_i＝ZB_i*E_F(k)*U(k-i)

The above ZA_i，ZB_iIn order to learn the rate parameters that need to be adjusted according to the actual conditions of the system,

E_F(k) the error value of the sampling moment is; wherein,

E_F(k)＝C(k)-Y(k)；

therefore, the model parameters corrected at this time are as follows:

A_i(k)＝A_i(k-1)+ΔA_i

B_i(k)＝B_i(k-1)+ΔB_i；

and step 3: the PID parameters are adjusted, namely the mean square error of 10 sampling moments after the sampling moment is calculated through the model obtained in the step 2 in the step 1;

let J be the basis for learning:

wherein,

E_Y(k+i)＝R-Y(k+i)

by proportional coefficient K to PID_PIntegral coefficient K_IDifferential coefficient K_DPartial differentiation to obtain three pre-parameters for single neuron PID

The increments of (c) are as follows:

wherein R is a system output set value, Z_P、Z_I、Z_DLearning rate parameters which need to be adjusted according to the actual condition of the system;

obtaining an adjusted PID pre-parameter:

and 4, step 4: PID output;

three pre-parameters for PID in step 3

Carrying out normalization processing to obtain proportion coefficient K of PID_PIntegral coefficient K_IDifferential coefficient K_D：

Obtaining the input U (K) finally given to the system by the sampling time controller:

U(k)＝K_P(k)*E(k)+K_I(k)*E_I(k)+K_D(k)*E_D(k)

wherein

E(k)＝R-C(k)

E_D(k)＝E(k)-E(k-1)

And K is a PID gain parameter which needs to be adjusted according to the actual condition of the system. In addition, due to the control of the temperature system, the E is limited by properly adding integral saturation according to the actual condition of the system_I(k) In that respect And (5) giving an output U (k) to the system, finishing the operation required to be executed by the sampling, and returning to the step 2 for circular execution.

2. The hybrid control method of the combination of the single neuron PID and the model prediction applied to the crosslinked cable manufacturing apparatus according to claim 1, wherein the initial values in the step 1 are set as follows: a. the₁(0)＝A₂(0)＝A₃(0)＝…A₇(0)＝0，A₈(0)＝A₉(0)＝A₁₀(0)＝0.33；B₁(0)＝B₂(0)＝…＝B₁₀(0)＝0。

3. The hybrid control method of combining single neuron PID and model prediction for a crosslinked cable manufacturing apparatus according to claim 1, wherein in step 2, ZA is set₁＝ZA₂＝ZA₃＝…ZA₇＝0，ZB₉＝ZB₁₀＝0。

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