CN114815922A - GPC and GPIO-based electric heating furnace temperature anti-interference control method - Google Patents

GPC and GPIO-based electric heating furnace temperature anti-interference control method Download PDF

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CN114815922A
CN114815922A CN202210315849.2A CN202210315849A CN114815922A CN 114815922 A CN114815922 A CN 114815922A CN 202210315849 A CN202210315849 A CN 202210315849A CN 114815922 A CN114815922 A CN 114815922A
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electric heating
heating furnace
control system
gpio
temperature control
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CN114815922B (en
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黄文聪
王浩源
胡宇博
余文锦
周菲菲
常雨芳
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Hubei University of Technology
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D23/00Control of temperature
    • G05D23/19Control of temperature characterised by the use of electric means
    • G05D23/20Control of temperature characterised by the use of electric means with sensing elements having variation of electric or magnetic properties with change of temperature

Abstract

The invention relates to a control technology of an electric heating furnace temperature control system, in particular to an electric heating furnace temperature anti-interference control method based on GPC and GPIO, which comprises the following steps: collecting and identifying operation data of the electric heating furnace temperature control system, wherein the operation data comprises a set temperature and a water supply temperature; carrying out system modeling on the electric heating furnace temperature control system through the acquired data to obtain a transfer function of the electric heating furnace temperature control system, and obtaining a state space model of the system according to the transfer function; designing a Generalized Proportional Integral Observer (GPIO) based on a transfer function of an electric heating furnace temperature control system; a prediction model based on GPIO vertical generalized prediction control; a Generalized Predictive Controller (GPC) is established to adjust the set temperature. The control method has the advantages of high precision, high adjusting speed, small overshoot, good anti-interference capability and robustness, and can effectively overcome lumped disturbance in the temperature control system of the electric heating furnace, so that the temperature is stabilized near a set value, and the fluctuation range is small.

Description

GPC and GPIO-based electric heating furnace temperature anti-interference control method
Technical Field
The invention relates to a control technology of an electric heating furnace temperature control system, in particular to a composite anti-interference control method of the electric heating furnace temperature control system.
Background
Along with the deterioration of ecological environment, the attention degree of China on environmental protection and pollution emission is continuously improved, and the traditional coal-fired and oil-fired furnace with larger pollution is gradually replaced by a clean and safe electric heating furnace. An electric heating furnace is used as a typical temperature control system, can convert electric energy into heat energy, and is widely applied to the fields of chemicals, textiles, plastics, rubber, food processing and the like. However, the temperature control system of the electric heating furnace with the characteristics of time-varying property, large inertia, large time lag and the like has difficulty in meeting the control requirements of the traditional PID control method.
Disclosure of Invention
The technical problem of the invention is mainly solved by the following technical scheme:
an electric heating furnace temperature anti-interference control method based on GPC and GPIO is characterized by comprising the following steps:
collecting and identifying operation data of the electric heating furnace temperature control system, wherein the operation data comprises a set temperature and a water supply temperature;
carrying out system modeling on the electric heating furnace temperature control system through the acquired data to obtain a transfer function of the electric heating furnace temperature control system, and obtaining a state space model of the system according to the transfer function;
designing a Generalized Proportional Integral Observer (GPIO) based on a transfer function of an electric heating furnace temperature control system;
a prediction model based on GPIO vertical generalized prediction control;
a Generalized Predictive Controller (GPC) is established to adjust the set temperature.
In the above mentioned anti-interference control method for temperature of electric heating furnace based on GPC and GPIO, the heat transfer of electric heating furnace comprises
Executing a component heat generation stage: is a first-order inertia element, and its transfer function is expressed as
Figure BDA0003568971830000021
Wherein k and ψ are constants;
the heat transfer stage of the electric heating furnace: for energy transfer of electric heating furnaces, electric heatingThe furnace energy transfer is expressed as
Figure BDA0003568971830000022
wherein ,Q1 For performing element heating, Q 2 Is heat loss; from the formula of specific heat capacity Q ═ MC Δ T
Figure BDA0003568971830000023
M is the mass of the electric heating wire, C is the specific heat capacity in the furnace, and T is the temperature in the furnace;
from the convective heat transfer rate equation Φ ═ α a (T-T) w ) Will Q 2 Is approximately Q 2 ≈αA(T-T w ) (ii) a Wherein alpha and A are convection heat transfer coefficient of the electric heating furnace and contact surface area of the furnace wall and the external environment, and T w Is the external ambient temperature;
combining electrothermal furnace energy transfer expressions and Q 2 Expression, get
Figure BDA0003568971830000024
Subjecting it to Ralsberg transformation, i.e. Q 1 (s)-αAT(s)=MCsT(s);
From the above formula, the transfer function of the heat transfer stage of the electric heating furnace is obtained as
Figure BDA0003568971830000025
Combining the transfer functions of the two stages, the transfer function of the temperature control system of the electric heating furnace is expressed as
Figure BDA0003568971830000026
The temperature control system model of the electric heating furnace is a second-order time lag system
Figure BDA0003568971830000027
in the formula ,
Figure BDA0003568971830000028
e -τs is a systemA time delay link;
obtaining a state space equation of the electric heating furnace temperature control system according to the transfer function G(s):
Figure BDA0003568971830000029
where ξ (t) is the lumped perturbation of the system; u (t-tau) is the input delay link of the system.
In the above anti-interference control method for the temperature of the electric heating furnace based on GPC and GPIO, the state space equation of the temperature control system of the electric heating furnace is systematically expanded:
Figure BDA0003568971830000031
wherein
Figure BDA0003568971830000032
And satisfy
Figure BDA0003568971830000033
For the system state space equation after the upper extension, 4-order GPIO is constructed as follows:
Figure BDA0003568971830000034
wherein ,l1 、l 2 、l 3 、l 4 Is the adjustment parameter of the observer;
subtracting the above two equations to obtain:
Figure BDA0003568971830000035
wherein ,
Figure BDA0003568971830000036
the above equation can be regarded as a high-dimensional input/output system, and can be written as:
Figure BDA0003568971830000037
the eigen equation for matrix a is then:
p(λ)=λ 4 +k 4 λ 3 +k 3 λ 2 +k 2 λ+k 1
selecting a suitable k 1 、k 2 、k 3 、k 4 The characteristic root of the matrix A is configured on the left half plane far away from the virtual axis, and the upper system can be obtained
Figure BDA0003568971830000038
The input and the output are bounded and stable; thus, when
Figure BDA0003568971830000041
The error e asymptotically approaches zero over time.
In the anti-interference control method for the temperature of the electric heating furnace based on GPC and GPIO, a controlled autoregressive integrated moving average (CARIMA) is used as a prediction model, and a controlled system is discretized to obtain
Figure BDA0003568971830000042
The CARIMA model was obtained as:
Figure BDA0003568971830000043
in the formula ,
Figure BDA0003568971830000044
u (k) and xi (k) respectively represent white noise sequences with zero average values of output, input and observed after GPIO; the transfer function of the electric heating furnace temperature control system is A (z) -1 )、B(z -1) and C(z-1 ):
Figure BDA0003568971830000045
The following objective function was used:
Figure BDA0003568971830000046
wherein n is the maximum prediction length, m is the control length, and λ (j) is the weighting coefficient;
Figure BDA0003568971830000047
w (k + j) is an expected output sequence value, wherein the output sequence value is observed by the GPIO; to predict the leading j-step output, a look-less-graph (dioadapt) equation is introduced to predict the leading j-step output:
Figure BDA0003568971830000048
in the formula ,
Figure BDA0003568971830000049
combining the charpy equation with the CARIMA model equation
Figure BDA00035689718300000410
Rewriting the above formula into vector form, i.e.
y=Gu+Fy(k)+HΔu(k-1)+E
in the formula ,
Figure BDA0003568971830000051
let wT be [ w (k +1), … w (k + j) ], the objective function is expressed as
J=(y-w) T (y-w)+λu T u;
Substituting the expression of y into the objective function J to calculate the minimum value of J, namely when
Figure BDA0003568971830000052
Then, get
Figure BDA0003568971830000053
The optimum control law of GPC is:
Figure BDA0003568971830000054
in the formula ,pT Is (G) T G+λI) -1 G T The first row of (2).
Has the advantages that: compared with the prior art, the invention has the following beneficial effects: 1. the proposed composite anti-interference control method estimates the lumped interference of the system through GPIO and feeds the estimated lumped interference back to a forward channel for interference compensation. A prediction model obtained after system lumped disturbance is eliminated, a generalized prediction controller is designed, GPC (phase-shift graphics) is established through the model, rolling optimization and feedback correction are carried out, and the response speed and the control precision of the system are improved. 2. Simulation results show that the provided composite control method has high precision, high adjusting speed, small overshoot, good anti-interference capability and robustness, and can effectively overcome lumped disturbance in the temperature control system of the electric heating furnace, so that the temperature is stabilized near a set value, and the fluctuation range is small.
Drawings
FIG. 1 is a flow chart of the method steps of the present invention.
FIG. 2 is a heat transfer diagram of the temperature control system of the electric heating furnace according to the present invention.
Fig. 3 is a structural diagram of a temperature control system of the electric heating furnace.
FIG. 4 is a graph comparing the effect of the present invention method with that of the conventional PID method.
Detailed Description
The invention will be further described in detail with reference to the following drawings and specific examples, which are not intended to limit the invention, but are for clear understanding.
The attached drawings are shown in figure 1, and the composite control method of the temperature control system of the electric heating furnace comprises the following steps:
(1) collecting and identifying operation data of the electric heating furnace temperature control system, wherein the operation data comprises a set temperature and a water supply temperature;
(2) carrying out system modeling on the electric heating furnace temperature control system through the acquired data to obtain a transfer function of the electric heating furnace temperature control system, and obtaining a state space model of the system according to the transfer function;
mathematical modeling is carried out based on a heat transfer model of an electric heating furnace temperature control system, and the attached drawing is shown in figure 2:
wherein I is the input of the execution element, Q 1 For performing element heating, Q 2 Heat is lost. Based on the heat transfer relationship of the electric heating furnace temperature control system, the heat transfer of the electric heating furnace is divided into two stages, namely an execution element heat generation stage and an electric heating furnace heat transfer stage. Wherein G is 1 For performing element heat-generating phases, G 2 Is the heat transfer stage of the electric heating furnace.
The heat generation stage of the execution element can be regarded as a first-order inertia link, so
Figure BDA0003568971830000061
The heat transfer stage of the electric heating furnace is the energy transfer of the electric heating furnace, and the energy transfer of the electric heating furnace can be expressed as
Figure BDA0003568971830000062
From the formula of specific heat capacity Q ═ MC Δ T
Figure BDA0003568971830000063
M is the mass of the electric heating wire, C is the specific heat capacity in the furnace, and T is the temperature in the furnace. The heat loss is mainly realized by two heat transfer modes of heat radiation and heat convection, but the heat radiation energy of the temperature control system of the electric heating furnace is very small and can be ignored. Therefore, the convection heat transfer rate equation phi is defined as alpha A (T-T) w ) Will Q 2 Is approximately Q 2 ≈αA(T-T w ). Wherein alpha and A are convection heat transfer coefficient of the electric heating furnace and contact surface area of the furnace wall and the external environment, and T w Is the outside ambient temperature.
Combining electrothermal furnace energy transfer expressions and Q 2 Expression, can obtain
Figure BDA0003568971830000064
Subjecting it to Ralsberg transformation, i.e. Q 1 (s)-αAT(s)=MCsT(s)。
From the above formula, the transfer function of the heat transfer stage of the electric heating furnace is obtained as
Figure BDA0003568971830000071
Combining the transfer functions of the two stages, the transfer function of the temperature control system of the electric heating furnace is expressed as
Figure BDA0003568971830000072
The temperature control system model of the electric heating furnace is a second-order time lag system
Figure BDA0003568971830000073
in the formula ,
Figure BDA0003568971830000074
e -τs is a system delay link.
Obtaining a state space equation of the electric heating furnace temperature control system according to the transfer function G(s):
Figure BDA0003568971830000075
the attached drawing is shown in fig. 3, which is a composite control block diagram of the electric heating furnace temperature control system of the invention, and the composite control block diagram comprises the following steps:
(3) designing a Generalized Proportional Integral Observer (GPIO) based on a transfer function of an electric heating furnace temperature control system;
carrying out system expansion on the state space equation of the electric heating furnace temperature control system:
Figure BDA0003568971830000076
wherein
Figure BDA0003568971830000077
And satisfy
Figure BDA0003568971830000078
For the system state space equation after the upper extension, a 4-order GPI observer is constructed as follows:
Figure BDA0003568971830000079
wherein ,l1 、l 2 、l 3 、l 4 Is the adjustment parameter of the observer.
Subtracting the above two equations can obtain:
Figure BDA0003568971830000081
the above equation can be regarded as a high-dimensional input/output system, and can be written as:
Figure BDA0003568971830000082
the eigen equation for matrix a is then:
p(λ)=λ 4 +k 4 λ 3 +k 3 λ 2 +k 2 λ+k 1
selecting a suitable k 1 、k 2 、k 3 、k 4 The characteristic root of the matrix A is configured on the left half plane far away from the virtual axis, and the upper system can be obtained
Figure BDA0003568971830000083
It is the input-output bounded stability. Thus, when
Figure BDA0003568971830000084
The error e asymptotically approaches zero over time.
(4) Establishing a prediction model of generalized predictive control based on GPIO;
(5) a Generalized Predictive Controller (GPC) is established to adjust the set temperature.
The controlled system is discretized by adopting a controlled autoregressive integral moving average model (CARIMA) as a prediction model
Figure BDA0003568971830000085
The CARIMA model can be obtained as follows:
Figure BDA0003568971830000086
in the formula ,
Figure BDA0003568971830000087
u (k) and ξ (k) represent the output observed by the GPIO, the system actual input, and the white noise sequence with the mean value zero, respectively; the transfer function of the temperature control system of the electric heating furnace is A (z) -1 )、B(z -1) and C(z-1 ):
Figure BDA0003568971830000088
The following objective function was used:
Figure BDA0003568971830000089
where n is the maximum prediction length, m is the control length, and λ (j) is the weighting factor.
Figure BDA0003568971830000091
To output the sequence value, ω (k + j) is the expected output sequence value. According to the prediction theory, in order to predict the output of the leading j steps, a loss of pattern (Dioaphanine) equation is introduced to predict the output of the leading j steps:
Figure BDA0003568971830000092
in the formula ,
Figure BDA0003568971830000093
combining the charpy equation with the CARIMA model equation
Figure BDA0003568971830000094
Rewriting the above formula into vector form, i.e.
y=Gu+Fy(k)+HΔu(k-1)+E
in the formula ,
Figure BDA0003568971830000095
let w T =[w(k+1),…w(k+j)]Then the objective function can be expressed as
J=(y-w) T (y-w)+λu T u。
Substituting the expression of y into the objective function J to calculate the minimum value of J, namely when
Figure BDA0003568971830000096
Then, get
u=(G T G+λI) -1 G T [w-Fy(k)-HΔu(k-1)]
The optimal control law of CPC is
Figure BDA0003568971830000097
in the formula ,pT Is (G) T G+λI) -1 G T The first row of (2).
The attached figure is shown in fig. 4, which shows that the composite control method provided by the invention has the advantages of high tracking speed, small overshoot and strong capacity of resisting disturbance amount by comparing the composite control method with the traditional PID control method.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (4)

1. An electric heating furnace temperature anti-interference control method based on GPC and GPIO is characterized by comprising the following steps:
collecting and identifying operation data of the electric heating furnace temperature control system, wherein the operation data comprises a set temperature and a water supply temperature;
carrying out system modeling on the electric heating furnace temperature control system through the acquired data to obtain a transfer function of the electric heating furnace temperature control system, and obtaining a state space model of the system according to the transfer function;
designing a Generalized Proportional Integral Observer (GPIO) based on a transfer function of an electric heating furnace temperature control system;
a prediction model based on GPIO vertical generalized prediction control;
a Generalized Predictive Controller (GPC) is established to adjust the set temperature.
2. The GPC and GPIO-based temperature anti-interference control method of claim 1, wherein electrothermal furnace heat transfer comprises
Executing a component heat generation stage: is a first-order inertia element, and its transfer function is expressed as
Figure FDA0003568971820000011
Wherein k and ψ are constants;
the heat transfer stage of the electric heating furnace: for electrothermal furnace energy transfer, the electrothermal furnace energy transfer is expressed as
Figure FDA0003568971820000012
wherein ,Q1 For performing element heating, Q 2 Is heat loss; from the formula of specific heat capacity Q ═ MC Δ T
Figure FDA0003568971820000013
M is the mass of the electric heating wire, C is the specific heat capacity in the furnace, and T is the temperature in the furnace;
from the convective heat transfer rate equation Φ ═ α a (T-T) w ) Will Q 2 Is approximately Q 2 ≈αA(T-T w ) (ii) a Wherein alpha and A are convection heat transfer coefficient of the electric heating furnace and contact surface area of the furnace wall and the external environment, and T w Is the external ambient temperature;
combining electrothermal furnace energy transfer expressions and Q 2 Expression, get
Figure FDA0003568971820000014
Subjecting it to Ralsberg transformation, i.e. Q 1 (s)-αAT(s)=MCsT(s);
From the above formula, the transfer function of the heat transfer stage of the electric heating furnace is obtained as
Figure FDA0003568971820000015
Combining the transfer functions of the two stages, the transfer function of the temperature control system of the electric heating furnace is expressed as
Figure FDA0003568971820000021
The temperature control system model of the electric heating furnace is a second-order time lag system
Figure FDA0003568971820000022
in the formula ,
Figure FDA0003568971820000023
a system delay link is adopted;
obtaining a state space equation of the electric heating furnace temperature control system according to the transfer function G(s):
Figure FDA0003568971820000024
where ξ (t) is the lumped perturbation of the system; u (t-tau) is the input delay link of the system.
3. The method for the anti-interference control of the temperature of the electric heating furnace based on GPC and GPIO as claimed in claim 1, wherein the state space equation of the electric heating furnace temperature control system is systematically expanded:
Figure FDA0003568971820000025
wherein
Figure FDA0003568971820000026
And satisfy
Figure FDA0003568971820000027
For the system state space equation after the upper extension, 4-order GPIO is constructed as follows:
Figure FDA0003568971820000028
wherein ,l1 、l 2 、l 3 、l 4 Is the adjustment parameter of the observer;
subtracting the above two equations to obtain:
Figure FDA0003568971820000029
wherein ,
Figure FDA0003568971820000031
the above equation can be regarded as a high-dimensional input/output system, and can be written as:
Figure FDA0003568971820000032
the eigen equation for matrix a is then:
p(λ)=λ 4 +k 4 λ 3 +k 3 λ 2 +k 2 λ+k 1
selecting a suitable k 1 、k 2 、k 3 、k 4 The characteristic root of the matrix A is configured on the left half plane far away from the virtual axis, and the upper system can be obtained
Figure FDA00035689718200000310
The input and the output are bounded and stable; thus, when
Figure FDA0003568971820000033
The error e asymptotically approaches zero over time.
4. The method as claimed in claim 1, wherein a controlled autoregressive integrated moving average (CARIMA) model is used as a prediction model to discretize a controlled system into a discrete value
Figure FDA0003568971820000034
The CARIMA model was obtained as:
Figure FDA0003568971820000035
in the formula ,
Figure FDA0003568971820000036
u (k) and xi (k) respectively represent white noise sequences with zero average values of output, input and observed after GPIO; the transfer function of the temperature control system of the electric heating furnace is A (z) -1 )、B(z -1) and C(z-1 ):
Figure FDA0003568971820000037
The following objective function was used:
Figure FDA0003568971820000038
wherein n is the maximum prediction length, m is the control length, and λ (j) is the weighting coefficient;
Figure FDA0003568971820000039
w (k + j) is an expected output sequence value, wherein the output sequence value is observed by the GPIO; to predict the leading j-step output, a look-less-graph (dioadapt) equation is introduced to predict the leading j-step output:
Figure FDA0003568971820000041
in the formula ,
Figure FDA0003568971820000042
combining the equation of the lost-hairplay map with the equation of the CARIMA model
Figure FDA0003568971820000043
Rewriting the above formula into vector form, i.e.
y=Gu+Fy(k)+HΔu(k-1)+E
in the formula ,
Figure FDA0003568971820000044
let w T =[w(k+1),…w(k+j)]Then the objective function is expressed as
J=(y-w) T (y-w)+λu T u;
Substituting the expression of yInto the objective function J, the minimum value of J is calculated, i.e. when
Figure FDA0003568971820000045
Then, get
Figure FDA0003568971820000046
The optimum control law of GPC is:
Figure FDA0003568971820000047
in the formula ,pT Is (G) T G+λI) -1 G T The first row of (2).
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