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CN113325696B - Single neuron PID and model prediction combined hybrid control method applied to crosslinked cable production equipment - Google Patents

Single neuron PID and model prediction combined hybrid control method applied to crosslinked cable production equipment Download PDF

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CN113325696B
CN113325696B CN202110608695.1A CN202110608695A CN113325696B CN 113325696 B CN113325696 B CN 113325696B CN 202110608695 A CN202110608695 A CN 202110608695A CN 113325696 B CN113325696 B CN 113325696B
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郜峰利
宿刚
刘浩
乔君丰
齐文斌
王向超
徐信
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Baicheng Fujia Technology Co ltd
Jilin University
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Jilin University
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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

Hybrid control method for combining single neuron PID and model prediction applied to crosslinked cable production equipment
Technical Field
The invention relates to a temperature control method, in particular to a hybrid control method combining single neuron PID and model prediction applied to crosslinked cable production equipment.
Background
In general, if an accurate model of the system is known, control of the system is very easy, but accurate modeling of the temperature system is very difficult. Based on the situation, at present, the main methods applied to temperature control include methods such as PID control, fuzzy logic control, neural network control and the like, and the expected control effect can be achieved only by adjusting parameters without involving system modeling. The PID control is most widely applied, and has the advantages of simple principle, easy realization, wide application range, direct and effective performance and the like. However, when facing some systems with certain requirements on control accuracy, the PID method has a general control effect; fuzzy logic control is to make a fuzzy table by professionals, to carry out table look-up reasoning on different states of the system to infer corresponding control strategies, which is very suitable for systems only working in certain specific states, but has the defect that the making of a good fuzzy table generally needs to be obtained by professional technicians through experience accumulation and continuous tests of long-time field operation; the neural network control is an emerging intelligent control method in recent years, has good adaptability and good control quality for a nonlinear time-varying system, a time-delay system and a complex system which is difficult to model, and has the defects that a large amount of data needs to be subjected to real-time operation processing, a processor has higher performance requirements, the development difficulty is higher, and a large amount of actual data training is needed.
The single neuron PID controller is based on a PID controller, and combines adaptability of neural network control and self-learning property thereof, a better control effect can be generated when a system with an unknown system model is controlled than when the system is controlled by using the PID controller alone, which is proved in recent literatures, a Hebb learning rule is generally used for a learning rule of the single neuron PID controller, a proper learning rule needs to be selected according to the system property in the aspect of rule selection, but a better effect can be achieved in the learning mode by selecting the single neuron PID control learning rule, and no related literature is explored in the aspect at present.
Disclosure of Invention
Aiming at the problem of single learning rule selection in the existing single neuron PID technology, the invention provides a single neuron PID learning method combined with a model predictive control Method (MPC), and the method can realize good control effect on a constant temperature control system. The method incorporates the control concept of MPC to make specific adjustments to PID parameters. The method uses a simple and effective modeling method for the temperature system, obtains the future approximate change trend of the system by analyzing the model, and correspondingly adjusts the PID parameters by using the principle of the minimum sum of squares of errors in a period of time in the future as a rule, thereby making up the blindness in the selection of learning rules and improving the control precision of the system.
A single neuron PID and model prediction combined hybrid control method applied to crosslinked cable production equipment comprises the following specific steps:
step 1: establishing a temperature system model;
the temperature system model used was:
Figure BDA0003094656310000021
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, AiOutputting a corresponding weighting coefficient for the ith historical system before the sampling time, wherein the initial value is set as follows: a. the1(0)＝A2(0)＝A3(0)＝…A7(0)＝0，A8(0)＝A9(0)＝A10(0) 0.33; u (k) is the system history input at the kth sampling instant, Bi(k) Inputting corresponding weighting coefficients for the ith historical system ahead of the sampling time, and setting the initial value as B1(0)＝B2(0)＝…＝B10(0) After that, the model is corrected so that a is abovei、BiThe initial value of (A) can be finely adjusted;
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 feedbacki(k)，Bi(k) 1,2, … 10; the increment of each sampling time adjustment is as follows: delta Ai，ΔBi；
ΔAi＝ZAi*EF(k)*C(k-i)
ΔBi＝ZBi*EF(k)*U(k-i)
The above ZAi，ZBiLearning rate parameters to be adjusted according to system conditions, wherein ZA1＝ZA2＝ZA3＝…ZA7＝0，ZB9＝ZB100; the rest learning rate parameters need to be adjusted according to the actual condition of the system; eF(k) The error value of the sampling moment is; wherein,
EF(k)＝C(k)-Y(k)；
Therefore, the model parameters corrected at this time are as follows:
Ai(k)＝Ai(k-1)+ΔAi
Bi(k)＝Bi(k-1)+ΔBi
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:
Figure BDA0003094656310000031
wherein,
EY(k+i)＝R-Y(k+i)
by a proportionality coefficient K to PIDPIntegral coefficient KIDifferential coefficient KDPartial differentiation to obtain three pre-parameters for single neuron PID
Figure BDA0003094656310000032
The increments of (c) are as follows:
Figure BDA0003094656310000033
Figure BDA0003094656310000034
Figure BDA0003094656310000035
wherein R is a system output set value, ZP、ZI、ZDLearning rate parameters which need to be adjusted according to the actual condition of the system;
obtaining an adjusted PID pre-parameter:
Figure BDA0003094656310000036
Figure BDA0003094656310000037
Figure BDA0003094656310000038
and 4, step 4: PID output;
three pre-parameters for PID in step 3
Figure BDA0003094656310000039
Carrying out normalization processing to obtain proportion coefficient K of PIDPIntegral coefficient KIDifferential coefficient KD：
Figure BDA00030946563100000310
Figure BDA00030946563100000311
Figure BDA00030946563100000312
Obtaining the input U (k) finally given to the system by the sampling time controller:
U(k)＝KP(k)*E(k)+KI(k)*EI(k)+KD(k)*ED(k)
wherein
E(k)＝R-C(k)
Figure BDA0003094656310000041
ED(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 systemI(k) In that respect And (5) giving an output U (k) to the system, completing the operation required to be executed by the sampling, and returning to the step 2 for circular execution.
Compared with the prior art, the invention has the following advantages:
1. the adjustment process contains system future information, and the interference on the controller caused by the time-lag characteristic of the temperature system is pertinently reduced;
2. the sum of the squares of the errors in a period of time in the future is used as an adjustment basis, so that the control effect is more stable;
3. due to the fact that PID parameters are dynamically adjusted, the anti-interference capability is strong, and the method has strong robustness.
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FIG. 1 is a functional block diagram of a hybrid control method of single neuron PID combined with model prediction for a cross-linked cable manufacturing apparatus according to the present invention;
FIG. 2 is a predictive model diagram of a single neuron PID and model predictive combined hybrid control method for a crosslinked cable manufacturing apparatus according to the present invention;
FIG. 3 is a learning basis graph of a hybrid control method for combining single neuron PID and model prediction applied to a crosslinked cable manufacturing apparatus according to the present invention;
fig. 4 is a system diagram attached to the hybrid control method combining single neuron PID and model prediction applied to the crosslinked cable production apparatus according to the present invention.
Detailed Description
The scheme of the invention is further explained in the following by combining the attached drawings.
The block diagram of the temperature control system according to the present invention is shown in fig. 4:
the model of the main control screen adopted by the invention is Siemens SIMATIC HMI, the controller is Siemens PLC300, and the WINCC7.3 version is used as configuration software for the control screen to control and monitor the production process.
The complete control process for one time is as follows:
inputting a set temperature R through a main control screen; reading a temperature signal C (k) of the thermocouple by the controller; and obtaining output U (k) by the control method, controlling a heating signal and a cooling signal according to the size of the U (k), and feeding the heating signal and the cooling signal to a heating tile and a circulating water cooling valve arranged on the extruder to finish primary control.
The specific implementation object of this embodiment is a cross-linked cable production line extruder, the parameters used in this embodiment are applicable to this system, and may also be used as references for other temperature systems, and the specific implementation needs to be adjusted appropriately according to the actual operating conditions. The realization mode is realized by programming a microcontroller, the output of the system is sampled once every 1 second, a learning algorithm and a PID algorithm are executed at the same time, the output quantity of the time is calculated and then output to the system, and the output value U ranges from-1000 to + 1000.
Initialization: the initial values are set as follows: a. the 1＝A2＝A3＝…A7＝0，A8＝A9＝A10＝0.33；B1＝B2＝…＝B10＝0；K＝30。KP＝30、KI＝1、KD＝100；
Figure BDA0003094656310000051
The parameters are set as follows: ZA1＝ZA2＝ZA3＝…ZA7＝0，ZA8＝ZA9＝ZA10＝10-4，ZB1＝ZB2＝ZB3＝…ZB8＝10-7，ZB9＝ZB10＝0。ZP＝1、ZI＝10-3、ZD＝0.1；
The operations performed for each sampling are as follows:
step 1: using temperature models
Figure BDA0003094656310000052
And historical data, wherein C (k-i) and U (k-i), i is 1,2 and 3 … 10, the predicted system output y (k) at the sampling time is calculated, the system output is sampled to obtain an output actual value C (k), and the difference between the output actual value C (k) and the predicted value y (k) is:
EF(k)＝C(k)-Y(k)
and 2, step: model delta Δ A was calculated using the following formulai，ΔBi，i＝1,2,3…10。
ΔAi＝ZAi*EF(k)*C(k-i)
ΔBi＝ZBi*EF(k)*U(k-i)
Update all A's with the above incrementi，Bi，i＝1,2,3…10。
Ai(k)＝Ai(k-1)+ΔAi
Bi(k)＝Bi(k-1)+ΔBi
And 3, step 3: and calculating prediction data.
The following data were calculated:
E(k)＝R-C(k)
Figure BDA0003094656310000061
ED(k)＝E(k)-E(k-1)
U(k)＝KP*E(k)+KI*EI(k)+KD*ED(k)
adding anti-integral saturation if EI(k)>200, then EI(k) 200 parts of a total weight; if E isI(k)<200, then EI(k) -200. While limiting the output size, if U (k)>1000, then u (k) is 1000; if U (k)<-1000, then u (k) ═ 1000.
Using the updated weighting parameter A in step 2i(k)，Bi(k) Substituting the model predicted value Y (k) into the actual system output c (k) in step 1 to find Y (k +1), where i is 1,2,3 … 10, and u (k), Y (k) of the data are substituted into the model formula in step 1;
the following data continues to be calculated:
EY(k+1)＝R-Y(k+1)
EYI(k+1)＝EI(k)+EY(k+1)
EYD(k+1)＝EY(k+1)-E(k)
UY(k+1)＝KP*EY(k+1)+KI*EYI(k+1)+KD*EYD(k+1)
likewise, add anti-integral saturation if EYI(k+i)>200, then EYI(k +1) ═ 200; if E isYI(k+1)<200, then EYI(k+1)＝-200。
While limiting the output size if UY(k+i)>1000, then UY(k + i) 1000; if U is presentY(k+i)<1000, then UY(k+i)＝-1000。
Using the updated weighting parameter A in step 2i(k)，Bi(k) Substituting the model predicted value Y (k +1) instead of the actual system output c (k)) into the model formula in step 1 to obtain Y (k +2), where i is 1,2,3 … 10, and u (k) and Y (k +1) of the data;
By iterating the above process, Y (k + i), U can be calculatedY(k+i)，EY(k+i)，EYI(k+i)，EYD(k+i)，i＝1,2,3…10。
And 4, step 4: calculating out
Figure BDA0003094656310000062
Firstly, the method is simplified to obtain:
Figure BDA0003094656310000063
Figure BDA0003094656310000064
when i is 2,3 … 10. The following formula is provided:
Figure BDA0003094656310000071
Figure BDA0003094656310000072
can be calculated one by one through the formula
Figure BDA0003094656310000073
And 5: computing
Figure BDA0003094656310000074
Firstly, the method is simplified to obtain:
Figure BDA0003094656310000075
Figure BDA0003094656310000076
when i is 2,3 … 10. The following formula is provided:
Figure BDA0003094656310000077
Figure BDA0003094656310000078
can be calculated one by one through the formula
Figure BDA0003094656310000079
Step 6: computing
Figure BDA00030946563100000710
Firstly, the method is simplified to obtain:
Figure BDA00030946563100000711
Figure BDA00030946563100000712
when i is 2,3 … 10. The following formula is provided:
Figure BDA00030946563100000713
Figure BDA00030946563100000714
can be calculated one by one through the formula
Figure BDA00030946563100000715
And 7: computing
Figure BDA00030946563100000716
Increment of (2)
Figure BDA00030946563100000717
And then updated to be adjusted
Figure BDA00030946563100000718
Figure BDA0003094656310000081
Can be derived by derivation
Figure BDA0003094656310000082
Substituting the data obtained by calculation in the steps 3 and 4 into the formula to obtain
Figure BDA0003094656310000083
ZPTo learn the rate.
And 8: computing
Figure BDA0003094656310000084
Increment of (2)
Figure BDA0003094656310000085
And then updated to be adjusted
Figure BDA0003094656310000086
Figure BDA0003094656310000087
Can be derived by derivation
Figure BDA0003094656310000088
Substituting the data obtained by calculation in the steps 3 and 4 into the formula to obtain
Figure BDA0003094656310000089
ZITo learn the rate.
And step 9: computing
Figure BDA00030946563100000810
Increment of (2)
Figure BDA00030946563100000811
And then updated to be adjusted
Figure BDA00030946563100000812
Figure BDA00030946563100000813
Can be derived by derivation
Figure BDA00030946563100000814
Substituting the data obtained by calculation in the steps 3 and 4 into the formula to obtain
Figure BDA00030946563100000815
ZDTo learn the rate.
Step 10: substituting the data obtained by updating in the step 9 into the following formula to update the KP、KI、KD。
Figure BDA00030946563100000816
Figure BDA00030946563100000817
Figure BDA00030946563100000818
Step 11: and calculating the final output of the current sampling through the following formula and the data in the step 3 and the step 10.
U(k)＝KP*E(k)+KI*EI(k)+KD*ED(k)
Limit output size, if u (k) >1000, 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:
Figure FDA0003657508640000011
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, AiOutputting 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, Bi(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;
real-time correction in step 1 by using system real output as feedbackModel parameter Ai(k)，Bi(k) 1, 2, … 10; the increment of each sampling time adjustment is as follows: delta Ai，ΔBi；
ΔAi＝ZAi*EF(k)*C(k-i)
ΔBi＝ZBi*EF(k)*U(k-i)；
The above ZAi，ZBiIn order to learn the rate parameters that need to be adjusted according to the actual conditions of the system,
EF(k) the error value of the sampling moment is; wherein,
EF(k)＝C(k)-Y(k)；
therefore, the model parameters corrected at this time are as follows:
Ai(k)＝Ai(k-1)+ΔAi
Bi(k)＝Bi(k-1)+ΔBi；
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:
Figure FDA0003657508640000021
wherein,
EY(k-1)＝R-Y(k-1)
by proportional coefficient K to PIDPIntegral coefficient KIDifferential coefficient KDPartial differentiation to obtain three pre-parameters for single neuron PID
Figure FDA0003657508640000022
The increments of (c) are as follows:
Figure FDA0003657508640000023
Figure FDA0003657508640000024
Figure FDA0003657508640000025
wherein R is a system output set value, ZP、ZI、ZDLearning rate parameters which need to be adjusted according to the actual condition of the system;
obtaining an adjusted PID pre-parameter:
Figure FDA0003657508640000026
Figure FDA0003657508640000027
Figure FDA0003657508640000028
and 4, step 4: PID output;
three pre-parameters for PID in step 3
Figure FDA0003657508640000029
Carrying out normalization processing to obtain proportion coefficient K of PIDPIntegral coefficient KIDifferential coefficient KD：
Figure FDA00036575086400000210
Figure FDA00036575086400000211
Figure FDA00036575086400000212
Obtaining the input U (k) finally given to the system by the sampling time controller:
U(k)＝KP(k)*E(k)+KI(k)*EI(k)+KD(k)*ED(k)；
wherein
E(k)＝R-C(k)
Figure FDA0003657508640000031
ED(k)＝E(k)-E(k-1)；
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 systemI(k) (ii) a 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 set 1＝ZA2＝ZA3＝…ZA7＝0，ZB9＝ZB10＝0。
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