CN109557810B - Heating furnace temperature control method based on novel two-degree-of-freedom internal model PID - Google Patents

Heating furnace temperature control method based on novel two-degree-of-freedom internal model PID Download PDF

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CN109557810B
CN109557810B CN201811448501.0A CN201811448501A CN109557810B CN 109557810 B CN109557810 B CN 109557810B CN 201811448501 A CN201811448501 A CN 201811448501A CN 109557810 B CN109557810 B CN 109557810B
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张日东
李孜伟
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Hangzhou Dianzi University
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Abstract

The invention discloses a heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID, which comprises the following steps: step 1, designing an internal mold control structure; step 2, designing an improved two-degree-of-freedom internal mold control structure; and 3, designing and setting a controller in the stabilizing process. The method improves a two-degree-of-freedom internal model control structure, facilitates on-line setting and achieves good set point tracking by adding weighting factors to parameters of a set point tracking controller, simply and conveniently obtains each setting parameter of the controller by adopting equivalent design of the controller in different PID controller forms aiming at a first-order time lag process and a second-order time lag process, and can ensure that a system simultaneously meets good tracking performance and interference suppression performance and the control requirement of the system can be ensured.

Description

Heating furnace temperature control method based on novel two-degree-of-freedom internal model PID
Technical Field
The invention belongs to the technical field of automation, and relates to a heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID.
Background
In the actual control process, the PID controller has high utilization rate in the industrial production process, but with the higher and higher requirements on the control precision and safe operation of products, the common PID controller can not meet the requirements. For the uncertain/unmatched process of a model with time lag, the designed control method is often complex, and the set point tracking characteristic and the anti-interference characteristic cannot be considered simultaneously, so that the research of a novel two-degree-of-freedom internal model PID control method is necessary.
Disclosure of Invention
The invention aims to provide a heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID, aiming at the problems of large time lag, insufficient control precision, complex controller design, uncertain/unmatched model and the like in industrial process production of the traditional two-degree-of-freedom internal model control method. The method designs a new two-degree-of-freedom internal model control structure on the basis of the internal model control structure design, adopts an accurate time delay approximation method, and obtains two controllers with two degrees of freedom by selecting a complementary sensitivity function and equivalent to the traditional two-degree-of-freedom internal model control structure. And then, parameters of the set point tracking controller are conveniently set and better set point tracking control is achieved through weighting factors. Finally, each setting parameter of the controller is simply and conveniently obtained through equivalent design of the controller in different PID controller forms aiming at the first-order time lag process and the second-order time lag process. Compared with the traditional methods, the novel two-degree-of-freedom internal model PID control method can simultaneously realize good set point tracking and interference suppression performance, is simple in design and has pertinence, and the control precision is greatly improved.
The method comprises the following steps:
step 1, designing an internal mold control structure, which comprises the following specific steps:
1.1 the conventional internal model control structure design structure according to fig. 1, wherein G(s) represents the controlled process object of the controlled process, m(s) represents the process model, G(s) represents the process modelIMC(s) represents an internal model controller; r represents an input of the control system; y represents the output of the control system; d represents an interference signal.
1.2 closed loop transfer function of system output:
Figure BDA0001885289560000021
1.3 if the model is accurate, i.e. g(s) ═ m(s):
y＝GIMC(s)G(s)r+[1-GIMC(s)M(s)]d
it will be appreciated that the set point tracking characteristic and the interference rejection characteristic are associated with GIMC(s) are related.
1.4 in order to overcome the problems of model mismatch uncertainty and the like and realize the problem of an actual controller, the design process is controlled by an internal model, and the process model is decomposed into:
M(s)＝M+(s)M-(s)
wherein M is+(s) is the irreversible part of the process model, M-(s) is the reversible part of the process model.
1.5 selection internal model controller GIMC(s) as the reciprocal of the reversible moiety, i.e.:
Figure BDA0001885289560000022
1.6 in order to make the internal model controller suitable and realizable, add an internal model control low-pass filter, the low-pass filter transfer function is used to make the controller stable, the form of the designed internal model control filter is:
Figure BDA0001885289560000023
where λ is the tuning parameter, r is chosen large enough to be adequate for the IMC controller to be suitable;
1.7 through steps 1.5 to 1.6, the internal model controller is:
Figure BDA0001885289560000024
1.8 time delay section e-θsThe following form approximation was chosen:
Figure BDA0001885289560000025
1.9 through structure conversion, the structure of the figure 1 is equivalently transformed into a classical feedback control structure as shown in figure 2.
1.10 according to the equivalence relation, we can obtain the design of the controller C(s):
Figure BDA0001885289560000026
step 2, designing an improved two-degree-of-freedom internal mold control structure, which comprises the following specific steps:
the 2.1 two-degree-of-freedom internal model control structure is shown in fig. 3. Q1(s) and Q2(s) constitutes a two-degree-of-freedom internal model controller.
2.2 from FIG. 3, the relationship between control system output and disturbance can be calculated:
Figure BDA0001885289560000031
2.3 the complementary sensitivity function t(s) between the inputs and outputs of the process is:
Figure BDA0001885289560000032
2.4 the controller Q can be obtained from the above equation2(s)：
Figure BDA0001885289560000033
2.5 then, the relationship between output and interference is further obtained:
Figure BDA0001885289560000034
2.6 selection of complementary sensitivity formats:
t(s)＝G+(s)h(s)
wherein the content of the first and second substances,
Figure BDA0001885289560000035
λ2is a parameter to be set.
2.7 controller Q can be obtained2Form(s):
Figure BDA0001885289560000036
2.8 equivalently converting the two-degree-of-freedom internal model control structure chart of FIG. 3 into the traditional two-degree-of-freedom internal model control structure chart of FIG. 4, C1(s) and C2(s) constitutes a two degree of freedom controller.
2.9 according to the equivalence relation, can get:
C1(s)＝Q2(s)
Figure BDA0001885289560000037
2.10 by calculation, one can obtain:
Figure BDA0001885289560000038
Figure BDA0001885289560000041
step 3, designing and setting a controller in the stabilization process, which comprises the following steps:
3.1 first consider selecting λ2Of (2), i.e. for Q2(s) designing. To achieve better control, we adjust λ again to achieve the desired set point tracking characteristic of the system.
3.2 at selection λ2When it is in original C2The weighting factor mu is added on the basis of(s). Consider the design of the setpoint controller as follows:
Figure BDA0001885289560000042
wherein, mu is more than or equal to 0 and less than or equal to 1. The selection of μ can be tuned online within 0,1 according to the setpoint response until the desired setpoint response is reached.
3.3 consider the first order process model:
Figure BDA0001885289560000043
where K is the process gain, T is the process time constant, and θ is the delay time.
3.4 in the two-degree-of-freedom control structure, the internal model control filter h(s) is reasonably designed into the following form:
Figure BDA0001885289560000044
3.5 the design method of step 2 can obtain a controller:
Figure BDA0001885289560000045
the following is rewritten:
Figure BDA0001885289560000046
3.6 apply the internal model feedback controller to the PID controller structure:
Figure BDA0001885289560000047
wherein, Kc，Ti，TdCorresponding to the proportional gain factor, the integral gain factor and the differential gain factor of the PID controller, respectively.
3.7 by approximation of the corresponding internal model controller and PID controller, one can obtain:
CPID(s)＝C1(s)
namely:
Figure BDA0001885289560000051
3.8 to simplify the calculation, let
Figure BDA0001885289560000052
Wherein the content of the first and second substances,
m(s)＝0.5Tθ2s3+(Tθ+0.5θ2)s2+(T+θ)s+1
n(s)＝K[0.5λ2θ2s2+(λ2+0.5θ2)s+(λ2+θ)]
then, one can obtain:
Kc＝W'(0)
Ti＝W-1(0)
Figure BDA0001885289560000053
3.9 obtaining each setting parameter according to the Meglalin spreading sequence as follows:
Ti＝K(λ2+θ)
Figure BDA0001885289560000054
Figure BDA0001885289560000055
3.10 after obtaining the PID parameters, further fine tuning may sometimes be required to obtain a perfect controller.
3.11 consider the second order delay process model:
Figure BDA0001885289560000056
wherein, T1、T2Is the process model time constant.
3.12 the PID parameters are implemented by reducing the controller form to that of a PID controller in series with a lead-lag filter of the formula:
Figure BDA0001885289560000061
3.13 by calculation and simplification, one can get:
Figure BDA0001885289560000062
3.14 thus, the various parameters of the controller can be obtained:
a＝0；b＝0.5θ2；c＝θ；d＝0
Figure BDA0001885289560000063
Figure BDA0001885289560000064
3.15 after obtaining the PID parameters, further fine tuning may sometimes be required to obtain a perfect controller.
The invention provides a heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID. The method improves a two-degree-of-freedom internal model control structure, facilitates on-line setting and achieves good set point tracking by adding weighting factors to parameters of a set point tracking controller, simply and conveniently obtains each setting parameter of the controller by adopting equivalent design of the controller in different PID controller forms aiming at a first-order time lag process and a second-order time lag process, and can ensure that a system simultaneously meets good tracking performance and interference suppression performance and the control requirement of the system can be ensured.
Drawings
FIG. 1 is a block diagram of an internal model control;
FIG. 2 is a block diagram of a classical feedback control;
FIG. 3 is a block diagram of an improved two-degree-of-freedom internal model control architecture;
FIG. 4 is a block diagram of a classical two degree of freedom control;
Detailed Description
The invention will be further explained with reference to the drawings.
Taking the temperature control of an actual industrial heating furnace as an example:
1. designing a two-degree-of-freedom internal model PID controller according to a first-order time-delay process model of a heating furnace, and specifically comprising the following steps:
1.1, firstly, considering input and output temperature data of the heating process of the industrial heating furnace, and establishing a first-order time-delay process model transfer function of the heating furnace, which is shown as the following formula:
Figure BDA0001885289560000071
wherein G(s) is a model of the heating process of the furnace, and K is a process gain coefficient; t is the process time constant; θ represents a delay time.
1.2 in the two-degree-of-freedom control structure, the internal model control filter h(s) is reasonably designed into the following form:
Figure BDA0001885289560000072
1.3 the controller can be obtained according to the improved design method of the two-degree-of-freedom internal model control structure:
Figure BDA0001885289560000073
the following is rewritten:
Figure BDA0001885289560000074
1.4 apply the internal model feedback controller in the PID controller structure:
Figure BDA0001885289560000075
wherein, Kc，Ti，TdProportional gain coefficient and integral gain coefficient corresponding to PID controller respectively
And a differential gain factor.
1.5 by approximation of the corresponding internal model controller and PID controller, one can obtain:
CPID(s)＝C1(s)
namely:
Figure BDA0001885289560000076
1.6 to simplify the calculation, let
Figure BDA0001885289560000081
Wherein the content of the first and second substances,
m(s)＝0.5Tθ2s3+(Tθ+0.5θ2)s2+(T+θ)s+1
n(s)＝K[0.5λ2θ2s2+(λ2+0.5θ2)s+(λ2+θ)]
then, one can obtain:
Kc＝W'(0)
Ti＝W-1(0)
Figure BDA0001885289560000082
1.7 obtaining each setting parameter according to the Meglalin spreading sequence as follows:
Ti＝K(λ2+θ)
Figure BDA0001885289560000083
Figure BDA0001885289560000084
1.8 after obtaining the PID parameters, further fine tuning may sometimes be required to obtain a perfect controller action on the furnace.
2. Designing a two-degree-of-freedom internal model PID controller according to a second-order time-delay process model of a heating furnace, and specifically comprising the following steps:
2.1, considering input and output temperature data of the heating process of the industrial heating furnace, establishing a transfer function of a second-order time-delay process model of the heating furnace, wherein the transfer function is shown as the following formula:
Figure BDA0001885289560000085
wherein, T1、T2Is the time constant of the heating process model of the heating furnace.
2.2 the PID parameters are implemented by reducing the controller form to that of a PID controller in series with a lead-lag filter of the following formula:
Figure BDA0001885289560000086
2.3 by calculation and simplification, one can obtain:
Figure BDA0001885289560000091
2.4 thus, the various parameters of the controller can be obtained:
a＝0；b＝0.5θ2；c＝θ；d＝0
Figure BDA0001885289560000092
Figure BDA0001885289560000093
2.5 after obtaining the PID parameters, further fine tuning may sometimes be required to obtain a perfect controller action on the furnace.

Claims (1)

1. A heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID comprises the following steps:
step 1, designing an internal mold control structure;
step 2, designing an improved two-degree-of-freedom internal mold control structure;
step 3, designing and setting a controller in the stabilization process;
the step 1 is as follows:
1.1 designing the structure according to the traditional internal model control structure, G(s) represents the controlled process object of the controlled process, M(s) represents the process model, G(s) represents the process modelIMC(s) represents an internal model controller; r represents an input of the control system; y represents the output of the control system; d represents an interference signal;
1.2 closed loop transfer function of system output:
Figure FDA0003075323120000011
1.3 when the model is accurate, i.e. g(s) ═ m(s):
y＝GIMC(s)G(s)r+[1-GIMC(s)M(s)]d
the set point tracking characteristic and the interference rejection characteristic are in accordance with GIMC(s) correlating;
1.4 the design process is controlled by an internal model, and the process model is decomposed into:
M(s)＝M+(s)M-(s)
wherein M is+(s) is the irreversible part of the process model, M-(s) is a reversible part of the process model;
1.5 selection internal model controller GIMC(s) as the reciprocal of the reversible moiety, i.e.:
Figure FDA0003075323120000012
1.6 adding an internal model control low-pass filter, wherein the transfer function of the low-pass filter is used for stabilizing the controller, and the designed internal model control low-pass filter is in the form of:
Figure FDA0003075323120000013
where λ is the tuning parameter, r is chosen large enough to be adequate for the IMC controller to be suitable;
1.7 through steps 1.5 to 1.6, the internal model controller is:
Figure FDA0003075323120000014
1.8 time delay section e-θsThe following form approximation was chosen:
Figure FDA0003075323120000021
1.9 converting the structure into a classical feedback control structure through structure conversion;
1.10 according to the equivalence relation, the design of the controller C(s) is obtained:
Figure FDA0003075323120000022
the step 2 is as follows:
2.1 design of two-degree-of-freedom inner mold control Structure, Q1(s) and Q2(s) forming a two-degree-of-freedom internal model controller;
2.2 calculate the relationship between the control system output and the interference:
Figure FDA0003075323120000023
2.3 the complementary sensitivity function t(s) between the inputs and outputs of the process is:
Figure FDA0003075323120000024
2.4 the controller Q can be obtained from the above equation2(s)：
Figure FDA0003075323120000025
2.5 then, the relationship between output and interference is further obtained:
Figure FDA0003075323120000026
2.6 selection of complementary sensitivity formats:
t(s)＝G+(s)h(s)
wherein the content of the first and second substances,
Figure FDA0003075323120000027
λ2is a parameter to be set;
2.7 obtaining the controller Q2Form(s):
Figure FDA0003075323120000028
2.8 converting the two-degree-of-freedom internal mold control structure into a traditional two-degree-of-freedom internal mold control structure, C1(s) and C2(s) constitutes a two degree of freedom controller;
2.9 according to the equivalence relation, can get:
C1(s)＝Q2(s)
Figure FDA0003075323120000031
2.10 by calculation, one can obtain:
Figure FDA0003075323120000032
Figure FDA0003075323120000033
the specific process of the step 3 is as follows:
3.1 first consider selecting λ2Of (2), i.e. for Q2(s) designing; adjusting λ to achieve a desired set point tracking characteristic of the system;
3.2 at selection λ2When it is in original C2(s) adding a weighting factor mu; consider the design of the setpoint controller as follows:
Figure FDA0003075323120000034
wherein mu is more than or equal to 0 and less than or equal to 1; mu is selected to be adjusted online in [0,1] according to the response of the set point until the required set point response is reached;
3.3 consider the first order process model:
Figure FDA0003075323120000035
where K is the process gain, T is the process time constant, θ is the delay time;
3.4 in the two-degree-of-freedom control structure, the internal model control low-pass filter h(s) is reasonably designed into the following form:
Figure FDA0003075323120000036
3.5 the design method of step 2 can obtain a controller:
Figure FDA0003075323120000037
the following is rewritten:
Figure FDA0003075323120000041
3.6 apply the internal model feedback controller to the PID controller structure:
Figure FDA0003075323120000042
wherein, Kc，Ti，TdProportional gain coefficient, integral gain coefficient and differential gain coefficient corresponding to PID controller respectively;
3.7 by approximation of the corresponding internal model controller and PID controller, one can obtain:
CPID(s)＝C1(s)
namely:
Figure FDA0003075323120000043
3.8 to simplify the calculation, let
Figure FDA0003075323120000044
Wherein the content of the first and second substances,
m(s)＝0.5Tθ2s3+(Tθ+0.5θ2)s2+(T+θ)s+1
n(s)＝K[0.5λ2θ2s2+(λ2+0.5θ2)s+(λ2+θ)]
then, one can obtain:
Kc＝W'(0)
Ti＝W-1(0)
Figure FDA0003075323120000045
3.9 obtaining each setting parameter according to the Meglalin spreading sequence as follows:
Ti＝K(λ2+θ)
Figure FDA0003075323120000046
Figure FDA0003075323120000047
3.10 after obtaining the PID parameters, further fine tuning to obtain a controller;
3.11 consider the second order delay process model:
Figure FDA0003075323120000051
wherein, T1、T2Is the process model time constant;
3.12 the PID parameters are implemented by reducing the controller form to that of a PID controller in series with a lead-lag filter of the formula:
Figure FDA0003075323120000052
3.13 by calculation and simplification, one can get:
Figure FDA0003075323120000053
3.14 obtaining various parameters of the controller:
a＝0；b＝0.5θ2；c＝θ；d＝0
Figure FDA0003075323120000054
Figure FDA0003075323120000055
Ti＝T1+T2；
Figure FDA0003075323120000056
3.15 after obtaining the PID parameters, further fine tuning the obtained controller.
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