Resistance furnace temperature control method based on IMC-PID feedforward decoupling

Abstract

The invention particularly relates to a resistance furnace temperature control method based on IMC-PID feedforward decoupling. The method comprises the steps that temperature curves of a first temperature interval and a second temperature interval which are coupled in a resistance furnace are collected; constructing a mathematical model of the system based on the temperature curve; based on the mathematical model of the system, establishing a feed-forward decoupling compensator by adopting a feed-forward compensation decoupling method; the system is decoupled through a feedforward decoupling compensator, and a decoupled mathematical model is obtained; and an IMC-PID controller is adopted to control the decoupled mathematical model, and independent temperature control over the first temperature interval and the second temperature interval is achieved. The method is simple and easy to implement, and can eliminate the condition of temperature interval coupling under the condition that a mathematical model is not accurate, so that the temperatures of the two temperature intervals are accurately controlled.

Description

Technical Field

[0001] The present invention belongs to the technical field of resistance furnace temperature control, and particularly relates to a resistance furnace temperature control method based on IMC-PID feedforward decoupling. Background Art

[0002] A resistance furnace is a commonly used electric heating device in industrial production and is widely used in industries such as metallurgy, machinery, and building materials. This resistance furnace has two temperature ranges, and the increase in temperature in one temperature range will inevitably affect the temperature in the other temperature range. Eliminating the temperature influence between these two temperature ranges is decoupling control. Only when the resistance furnace can control the temperature accurately can it adapt to the processing of various metal parts during the heat treatment process. A resistance furnace is a non-linear, pure-delay, large-inertia, and strongly coupled object, which has various characteristics (non-linearity, delay, inertia, coupling) that may exist in the controlled object during the control process. It is difficult to establish an accurate mathematical model. Traditional PID cannot eliminate the temperature influence between the two temperature ranges, thus bringing great uncertainty to temperature control and seriously affecting product quality. In view of the strong coupling of the system and the difficulty in establishing an accurate mathematical model, the present invention proposes a simple and easy-to-implement resistance furnace temperature control method based on IMC-PID feedforward decoupling, which can eliminate coupling and achieve precise control of the temperatures in the two temperature ranges even when the model is inaccurate.

[0003] In the prior art, people have studied the decoupling control of resistance furnaces through various control algorithms, such as adaptive decoupling, fuzzy decoupling, neural network decoupling, etc. The algorithms of the prior art are too complex and have a large amount of calculation, making it difficult to be popularized and applied in actual production. In addition, the mathematical model of the system is inaccurate, which affects the decoupling effect.

[0004] The invention patent with the patent number CN 110032226 A discloses a fuzzy control system and control method for the temperature of a resistance furnace, which achieves a better control effect on the temperature of the resistance furnace. This control method is for the control of a single-loop temperature and does not involve the decoupling control between multiple loops. In addition, the intelligent control method is too complicated and the calculation amount increases, which is not conducive to the rapid and simple control of the system.

[0005] Aiming at the coupling phenomenon in the resistance furnace system and the inability to achieve precise control of the temperatures in the two temperature ranges, the present invention proposes a control method based on IMC-PID feedforward decoupling. By using this control method in the system, the multivariable control system is changed into a single-variable control system, eliminating the coupling between the two temperature ranges and improving the control accuracy. Summary of the Invention

[0006] According to the technical problems existing in the resistance furnace temperature control system in the above-mentioned prior art, such as strong coupling, inaccurate mathematical model, difficulty in eliminating the coupling influence by traditional PID control, and complex and large computational amount of the existing decoupling algorithms, a resistance furnace temperature control method based on IMC-PID feedforward decoupling is provided. The present invention mainly uses a technical solution combining a PID controller based on the feedforward compensation decoupling method and the internal model idea, so as to achieve the effects of eliminating the coupling influence between two temperature ranges, improving the control accuracy, simplifying the algorithm complexity, reducing the computational amount, and enhancing the system robustness.

[0007] The technical means adopted by the present invention are as follows:

[0008] A resistance furnace temperature control method based on IMC-PID feedforward decoupling, the steps include:

[0009] S101. Collect the temperature curves of the first temperature range and the second temperature range in the resistance furnace, and there is coupling between the first temperature range and the second temperature range;

[0010] S102. Based on the temperature curves of the first temperature range and the second temperature range, construct a first transfer function for the first temperature range, a second transfer function for the second temperature range, a third transfer function for the influence of the second temperature range on the first temperature range, and a fourth transfer function for the influence of the first temperature range on the second temperature range. Based on the first transfer function, the second transfer function, the third transfer function, and the fourth transfer function, establish a mathematical model of the system;

[0011] S103. Based on the mathematical model of the system, adopt the feedforward compensation decoupling method to establish a feedforward decoupling compensator, and the feedforward decoupling compensator includes a first feedforward decoupling compensator and a second feedforward decoupling compensator;

[0012] S104. Decouple the mathematical model of the system through the first feedforward decoupling compensator and the second feedforward decoupling compensator to obtain the decoupled mathematical model of the system. Based on the decoupled mathematical model of the system, generate the decoupled first temperature range and the decoupled second temperature range;

[0013] S105. Establish an IMC-PID controller, and use the IMC-PID controller to control the decoupled first temperature range and the decoupled second temperature range to achieve independent temperature control of the first temperature range and the second temperature range.

[0014] Further, the mathematical model of the system is:

[0015]

[0016] Wherein, G(s) is the mathematical model of the system, G 11(s) is the first transfer function, G 22 (s) is the second transfer function, G 12 (s) is the third transfer function, G 21 (s) is the fourth transfer function, K 11 is the amplification coefficient corresponding to the first transfer function, K 22 is the amplification coefficient corresponding to the second transfer function, K 12 is the amplification coefficient corresponding to the third transfer function, K 21 is the amplification coefficient corresponding to the fourth transfer function, θ 11 is the lag time corresponding to the first transfer function, θ 22 is the lag time corresponding to the second transfer function, θ 12 is the lag time corresponding to the third transfer function, θ 21 is the lag time corresponding to the fourth transfer function, T 11 is the time constant corresponding to the first transfer function, T 22 is the time constant corresponding to the second transfer function, T 12 is the time constant corresponding to the third transfer function, T 21 is the time constant corresponding to the fourth transfer function, and s is the Laplace operator.

[0017] Furthermore, the calculation formula of the first feedforward decoupling compensator is:

[0018]

[0019] where, P 12 (s) is the transfer function of the first feedforward decoupling compensator, G 11 (s) is the first transfer function, G 12 (s) is the third transfer function,

[0020] The calculation formula of the second feedforward decoupling compensator is:

[0021]

[0022] where, P 21 (s) is the transfer function of the second feedforward decoupling compensator, G 21 (s) is the fourth transfer function, G 22 (s) is the second transfer function.

[0023] Furthermore, the decoupled mathematical model is:

[0024]

[0025] where, G’(s) is the transfer function of the decoupled system, G’ 11 (s) is the decoupled first transfer function, G’22 (s) is the decoupled second transfer function, T’ 11 is the time constant corresponding to the decoupled first transfer function, T’ 22 is the time constant corresponding to the decoupled second transfer function, θ’ 11 is the dead time corresponding to the decoupled first transfer function, θ’ 22 is the dead time corresponding to the decoupled second transfer function, K’ 11 is the magnification factor corresponding to the decoupled first transfer function, K’ 22 is the magnification factor corresponding to the decoupled second transfer function, s is the Laplace operator.

[0026] Furthermore, the transfer function between the decoupled first temperature range and the decoupled second temperature range is:

[0027]

[0028] where G”(s) is the transfer function between the decoupled first temperature range and the decoupled second temperature range, K is the magnification factor corresponding to the transfer function, T is the time constant corresponding to the transfer function, θ is the dead time corresponding to the transfer function, s is the Laplace operator,

[0029] Taking the first-order Pade approximation for the time-delay term, the expression formula for the time-delay term is:

[0030]

[0031] where θ is the dead time corresponding to the transfer function, s is the Laplace operator.

[0032] Furthermore, the transfer function of the IMC-PID controller is:

[0033]

[0034] where G c1 (s) is the transfer function of the IMC-PID controller, K P is the proportionality coefficient, T I is the integral time constant, s is the Laplace operator, T D is the derivative time constant,

[0035] The PID parameters are tuned by the following formula:

[0036]

[0037] T I = T + θ / 2

[0038]

[0039] Among them, K P is the proportionality coefficient, T is the time constant corresponding to the transfer function, λ is the filter parameter, K is the amplification coefficient corresponding to the transfer function, T I is the integral time constant, θ is the lag time, T D is the differential time constant.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. The control method based on IMC-PID feedforward decoupling provided by the present invention, by combining with a simplified feedforward compensator and internal model control (IMC), effectively eliminates the coupling influence between two temperature ranges of the resistance furnace, transforms the multivariable control system into a single-variable control system, solves the technical problem of difficultly eliminating the coupling influence between temperature ranges in the resistance furnace system, and improves the control accuracy.

[0042] 2. The resistance furnace temperature control method based on IMC-PID feedforward decoupling provided by the present invention, by combining with a simplified IMC-PID controller structure, realizes reducing the algorithm complexity, reducing the calculation amount and facilitating rapid deployment in the industrial field.

[0043] 3. The resistance furnace temperature control method based on IMC-PID feedforward decoupling provided by the present invention, by combining with an internal model control (IMC) filter, realizes maintaining good decoupling and stable control even under the condition of uncertain or mismatched model parameters.

[0044] For the above reasons, the present invention can be widely promoted in the fields such as resistance furnace temperature control. Brief Description of the Drawings

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0046] Figure 1 is the flowchart of the resistance furnace temperature control method based on IMC-PID feedforward decoupling provided by the present invention.

[0047] Figure 2 is the structure diagram of the IMC-PID feedforward decoupling control system provided by the present invention.

[0048] Figure 3 is the structural block diagram of the IMC control provided by the present invention.

[0049] Figure 4It is a schematic structural diagram of the resistance furnace provided by the present invention.

[0050] Figure 5 It is the response curve after decoupling of the system when the gain, time constant, and dead time of the system provided by the present invention are all increased by 20% due to model mismatch, and the decoupling response curve when the model is exactly matched. Specific embodiments

[0051] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0052] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that such used data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0053] As Figure 4 shown, in the resistance furnace system, there is coupling in two temperature ranges. The temperature in one temperature range will inevitably affect the temperature in the other temperature range. The temperatures of the two temperature ranges are measured separately by sensors.

[0054] Aiming at the coupling phenomenon in the resistance furnace system and being unable to achieve precise control of the temperatures in the two temperature ranges, a control method based on IMC-PID feedforward decoupling is proposed. By using this control method in the system, the multivariable control system is changed into a single-variable control system, the coupling between the two temperature ranges is eliminated, and the control accuracy is improved.

[0055] As Figures 1-3 shown, the present invention provides a resistance furnace temperature control method based on IMC-PID feedforward decoupling. Figure 1 Among them, R1(s) is the set temperature of the first temperature range, R2(s) is the set temperature of the second temperature range, Y1(s) is the output temperature value of the first temperature range, and Y2(s) is the output temperature value of the first temperature range.

[0056] The specific steps include:

[0057] S101. Collect the temperature curves of the first temperature range and the second temperature range in the resistance furnace. There is coupling between the first temperature range and the second temperature range.

[0058] S102. Based on the temperature curves of the first temperature range and the second temperature range, construct a first transfer function for the first temperature range, a second transfer function for the second temperature range, a third transfer function for the influence of the second temperature range on the first temperature range, and a fourth transfer function for the influence of the first temperature range on the second temperature range. Based on the first transfer function, the second transfer function, the third transfer function, and the fourth transfer function, establish a mathematical model of the system.

[0059] Specifically, a mathematical model with double inputs and double outputs for the two temperature ranges.

[0060] The calculation formula of the actual temperature module is:

[0061]

[0062] Among them, G(s) is the mathematical model of the system, G 11 (s) is the first transfer function, G 22 (s) is the second transfer function, G 12 (s) is the third transfer function, G 21 (s) is the fourth transfer function, K 11 is the amplification coefficient corresponding to the first transfer function, K 22 is the amplification coefficient corresponding to the second transfer function, K 12 is the amplification coefficient corresponding to the third transfer function, K 21 is the amplification coefficient corresponding to the fourth transfer function, θ 11 is the lag time corresponding to the first transfer function, θ 22 is the lag time corresponding to the second transfer function, θ 12 is the lag time corresponding to the third transfer function, θ 21 is the lag time corresponding to the fourth transfer function, T 11 is the time constant corresponding to the first transfer function, T 22 is the time constant corresponding to the second transfer function, T 12 is the time constant corresponding to the third transfer function, T 21 is the time constant corresponding to the fourth transfer function, and s is the Laplace operator.

[0063] S103. Based on the mathematical model of the system, adopt the feedforward compensation decoupling method to establish a feedforward decoupling compensator. The feedforward decoupling compensator includes a first feedforward decoupling compensator and a second feedforward decoupling compensator.

[0064] Specifically, the calculation formula for the first feedforward decoupling compensator is as follows:

[0065]

[0066] where P 12 (s) is the transfer function of the first feedforward decoupling compensator, G 12 (s) is the third transfer function, and G 11 (s) is the first transfer function.

[0067] The calculation formula for the second feedforward decoupling compensator is as follows:

[0068]

[0069] where P 21 (s) is the transfer function of the second feedforward decoupling compensator, G 21 (s) is the fourth transfer function, and G 22 (s) is the second transfer function.

[0070] S104. Decouple the mathematical model of the system through the first feedforward decoupling compensator and the second feedforward decoupling compensator to obtain the decoupled mathematical model of the system. Based on the decoupled mathematical model of the system, generate the decoupled first temperature range and the decoupled second temperature range.

[0071] Specifically, the calculation formula for the decoupled temperature module is as follows:

[0072]

[0073] where G’(s) is the transfer function of the decoupled system, G’ 11 (s) is the decoupled first transfer function, G’ 22 (s) is the decoupled second transfer function, T’ 11 is the time constant corresponding to the decoupled first transfer function, T’ 22 is the time constant corresponding to the decoupled second transfer function, θ’ 11 is the lag time corresponding to the decoupled first transfer function, θ’ 22 is the lag time corresponding to the decoupled second transfer function, K’ 11 is the amplification factor corresponding to the decoupled first transfer function, K’ 22 is the amplification factor corresponding to the decoupled second transfer function, and s is the Laplace operator.

[0074] S105. Establish an IMC-PID controller and use the IMC-PID controller to control the decoupled first temperature range and the decoupled second temperature range to achieve independent temperature control of the first temperature range and the second temperature range.

[0075] Specifically, the transfer function between the decoupled first temperature range and the decoupled second temperature range is as follows:

[0076]

[0077] Among them, G”(s) is the transfer function between the decoupled first temperature range and the decoupled second temperature range, K is the amplification coefficient corresponding to the transfer function, T is the time constant corresponding to the transfer function, θ is the lag time corresponding to the transfer function, and s is the Laplace operator.

[0078] Taking the first-order Pade approximation for the time-delay term, the expression formula for the time-delay term is:

[0079]

[0080] Among them, θ is the lag time corresponding to the transfer function, and s is the Laplace operator.

[0081] The transfer function of the IMC-PID controller is:

[0082]

[0083] Among them, G c1 (s) is the transfer function of the IMC-PID controller, K P is the proportional coefficient, T I is the integral time constant, s is the Laplace operator, and T D is the differential time constant.

[0084] The PID parameters are tuned through the following formula:

[0085]

[0086] T I = T + θ / 2

[0087]

[0088] Among them, K P is the proportional coefficient, T is the time constant corresponding to the transfer function, λ is the filter parameter, K is the amplification coefficient corresponding to the transfer function, T I is the integral time constant, θ is the lag time, and T D is the differential time constant.

[0089] The advantage of the IMC controller is that it has an adjustable filter parameter λ, which determines the response speed of the system.

[0090] As Figure 3 shown, G IMC(s) Internal model controller, Gp(s) is the transfer function of the actual model, G d (s) is the transfer function of the disturbance channel, and Gm(s) is the transfer function of the internal model. In order to transform it into the form of IMC-PID control, the current equivalent diagram of the internal model controller is drawn to facilitate the calculation of K p , K i , K d .

[0091] As Figure 5 shown, it can be seen that even if the model is inaccurate, the IMC-PID feedforward decoupling control can eliminate the mutual influence between the two temperature ranges and achieve precise control of the temperatures in the two temperature ranges.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A temperature control method for a resistance furnace based on IMC-PID feedforward decoupling, characterized in that the steps Including: S101. Collect the temperature curves of the first temperature range and the second temperature range in the resistance furnace, where there is coupling between the first temperature range and the second temperature range; S102. Based on the temperature curves of the first temperature range and the second temperature range, construct a first transfer function for the first temperature range, a second transfer function for the second temperature range, a third transfer function for the influence of the second temperature range on the first temperature range, and a fourth transfer function for the influence of the first temperature range on the second temperature range. Based on the first transfer function, the second transfer function, the third transfer function, and the fourth transfer function, establish a mathematical model of the system; S103. Based on the mathematical model of the system, use the feedforward compensation decoupling method to establish a feedforward decoupling compensator, where the feedforward decoupling compensator includes a first feedforward decoupling compensator and a second feedforward decoupling compensator; S104. Decouple the mathematical model of the system through the first feedforward decoupling compensator and the second feedforward decoupling compensator to obtain the decoupled mathematical model of the system. Based on the decoupled mathematical model of the system, generate the decoupled first temperature range and the decoupled second temperature range; S105. Establish an IMC-PID controller, and use the IMC-PID controller to control the decoupled first temperature range and the decoupled second temperature range to achieve independent temperature control of the first temperature range and the second temperature range.

2. The temperature control method of the resistance furnace based on IMC-PID feedforward decoupling according to claim 1, wherein, The mathematical model of the system is: Among them, G(s) is the mathematical model of the system, G 11 (s) is the first transfer function, G 22 (s) is the second transfer function, G 12 (s) is the third transfer function, G 21 (s) is the fourth transfer function, K 11 is the amplification coefficient corresponding to the first transfer function, K 22 is the amplification coefficient corresponding to the second transfer function, K 12 is the amplification coefficient corresponding to the third transfer function, K 21 is the amplification coefficient corresponding to the fourth transfer function, θ 11 is the lag time corresponding to the first transfer function, θ 22 is the lag time corresponding to the second transfer function, θ 12 is the lag time corresponding to the third transfer function, θ 21 is the lag time corresponding to the fourth transfer function, T 11 is the time constant corresponding to the first transfer function, T 22 is the time constant corresponding to the second transfer function, T 12 is the time constant corresponding to the third transfer function, T 21 is the time constant corresponding to the fourth transfer function, and s is the Laplace operator.

3. The temperature control method of the resistance furnace based on IMC-PID feedforward decoupling according to claim 1, characterized in that The calculation formula of the first feedforward decoupling compensator is: where, P 12 (s) is the transfer function of the first feedforward decoupling compensator, G 11 (s) is the first transfer function, G 12 (s) is the third transfer function, The calculation formula of the second feedforward decoupling compensator is: Among them, P 21 (s) is the transfer function of the second feedforward decoupling compensator, G 21 (s) is the fourth transfer function, G 22 (s) is the second transfer function.

4. The temperature control method of the resistance furnace based on IMC-PID feedforward decoupling according to claim 1, characterized in that The decoupled mathematical model is: Among them, G’(s) is the transfer function of the decoupled system, G’ 11 (s) is the first transfer function after decoupling, G’ 22 is the second transfer function after decoupling, T’ 11 is the time constant corresponding to the first transfer function after decoupling, T’ 22 is the time constant corresponding to the second transfer function after decoupling, θ’ 11 is the lag time corresponding to the first transfer function after decoupling, θ’ 22 is the lag time corresponding to the second transfer function after decoupling, K’ 11 is the magnification factor corresponding to the first transfer function after decoupling, K’ 22 is the magnification factor corresponding to the second transfer function after decoupling, and s is the Laplace operator.

5. The temperature control method of the resistance furnace based on IMC-PID feedforward decoupling according to claim 1, wherein The transfer function between the decoupled first temperature range and the decoupled second temperature range is: Where, G”(s) is the transfer function between the decoupled first temperature range and the decoupled second temperature range, K is the amplification coefficient corresponding to the transfer function, T is the time constant corresponding to the transfer function, θ is the lag time corresponding to the transfer function, and s is the Laplace operator. Take the first-order Pade approximation for the time-delay term, and the expression formula of the time-delay term is: Where, θ is the lag time corresponding to the transfer function, and s is the Laplace operator.

6. The temperature control method of the resistance furnace based on IMC-PID feedforward decoupling according to claim 1, characterized in that The transfer function of the IMC-PID controller is: Among them, G c1 (s) is the transfer function of the IMC-PID controller, K P is the proportionality coefficient, T I is the integral time constant, s is the Laplace operator, T D is the derivative time constant, The PID parameters are tuned through the following formula: T I = T + θ / 2 Among them, K P is the proportionality coefficient, T is the time constant corresponding to the transfer function, λ is the filter parameter, K is the amplification coefficient corresponding to the transfer function, T I is the integral time constant, θ is the lag time, T D is the differential time constant.

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