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

Abstract

The invention discloses a heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID, comprising the following steps: step 1, designing an internal model control structure; step 2, designing an improved two-degree-of-freedom internal model control structure; 3. The controller design and tuning of the stable process. This method improves the two-degree-of-freedom internal model control structure. By adding a weighting factor to the parameters of the setpoint tracking controller, it is convenient for online tuning and achieves good setpoint tracking. For the first-order and second-order delay processes, different The equivalent design of the controller in the form of a PID controller can simply and conveniently obtain the various tuning parameters of the controller, and can make the system satisfy both good tracking performance and interference suppression performance, and the control requirements of the system can also be guaranteed.

Description

A heating furnace temperature control method based on a 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 technique

In the actual control process, the PID controller has a high utilization rate in the industrial production process, but with the increasing requirements for the control accuracy and safe operation of the product, the ordinary PID controller often cannot meet the requirements. For the process of model uncertainty/mismatch with time delay, the control method designed is often complicated, and it cannot take into account the set point tracking characteristics and anti-interference characteristics at the same time. Therefore, a new two-degree-of-freedom internal model PID control method is studied. Necessary.

SUMMARY OF THE INVENTION

The purpose of the invention is to solve the problems of the traditional two-degree-of-freedom internal model control method in industrial process production, such as large time delay, insufficient control accuracy, complex controller design, model uncertainty/mismatch, etc. The heating furnace temperature control method of internal mold PID. Based on the design of the internal model control structure, this method designs a new two-degree-of-freedom internal-model control structure, using an accurate time delay approximation method, by choosing complementary sensitivity functions and traditional two-degree-of-freedom internal model control Structural equivalence yields two controllers with two degrees of freedom. Then, the parameters of the set point tracking controller are passed through the weighting factor to facilitate tuning and achieve better set point tracking control. Finally, through the equivalent design of the controller in the form of different PID controllers for the first-order and second-order time-delay processes, the tuning parameters of the controller can be obtained simply and conveniently. Compared with some traditional methods, the new two-degree-of-freedom internal model PID control method proposed in this application can simultaneously achieve good setpoint tracking and interference suppression performance, and the design is simple and targeted, and the control accuracy is very high. big improvement.

The steps of the method of the present invention include:

Step 1. Design the internal model control structure. The specific steps are:

1.1 According to the traditional internal model control structure design structure in Figure 1, G(s) represents the controlled process object, M(s) represents the process model, G _IMC (s) represents the internal model controller; r represents The input of the control system; y is the output of the control system; d is the disturbance signal.

1.2 The closed-loop transfer function of the system output:

1.3 If the model is accurate, that is, when G(s)=M(s):

y=G _IMC (s)G(s)r+[1-G _IMC (s)M(s)]d

It can be known that the set point tracking characteristics and the anti-jamming rejection characteristics are related to _GIMC (s).

1.4 In order to overcome the model mismatch uncertainty and other problems and make the actual controller realize the problem, the internal model is used to control the design process, and the process model is decomposed into:

M(s)=M ₊ (s)M _- (s)

where M ₊ (s) is the irreversible part of the process model and M _- (s) is the reversible part of the process model.

1.5 Select the internal model controller G _IMC (s) as the reciprocal of the reversible part, namely:

1.6 In order to make the internal model controller suitable and achievable, an internal model control low-pass filter is added. The low-pass filter transfer function is used to stabilize the controller. The designed internal model control filter form is:

where λ is the tuning parameter, and r is chosen to be large enough to meet the appropriate IMC controller;

1.7 Through steps 1.5 to 1.6, the internal model controller is:

1.8 The time delay part e ^-θs is approximated by choosing the following form:

1.9 Through the structural transformation, the structure of Fig. 1 is equivalently transformed into the classical feedback control structure shown in Fig. 2.

1.10 According to the equivalence relation, we can get the design of the controller C(s):

Step 2, the design of the improved two-degree-of-freedom internal model control structure, the specific steps are:

2.1 The two-degree-of-freedom internal model control structure is shown in Figure 3. Q ₁ (s) and Q ₂ (s) constitute a two-degree-of-freedom internal model controller.

2.2 The relationship between the output of the control system and the disturbance can be calculated from Figure 3:

2.3 The complementary sensitivity function t(s) between the input and output of the process is:

2.4 The controller Q ₂ (s) can be obtained from the above formula:

2.5 Then, further obtain the relationship between output and interference:

2.6 Choose the form of complementary sensitivity:

t(s)=G ⁺ (s)h(s)

λ₂为待整定参数。in,

λ ₂ is a parameter to be adjusted.

2.7 The controller _Q2 (s) can be obtained in the form:

2.8 The two-DOF internal model control structure diagram in Fig. 3 is equivalently converted into the traditional two-DOF internal model control structure in Fig. 4, C ₁ (s) and C ₂ (s) constitute a two-degree-of-freedom controller.

2.9 According to the equivalence relation, we can get:

C ₁ (s)=Q ₂ (s)

2.10 By calculation, we can get:

Step 3. Controller design and tuning of the stabilization process, specifically:

3.1 Consider first the choice of the value of λ ₂ , that is, the design of Q ₂ (s). In order to achieve better control effect, we adjust λ to achieve the set point tracking characteristics required by the system.

3.2 When choosing λ ₂ , the weighting factor μ is added on the basis of the original C ₂ (s). Consider the design of the setpoint controller as follows:

Among them, 0≤μ≤1. The choice of μ can be tuned online within [0,1] based on the setpoint response until the desired setpoint response is achieved.

3.3 Consider a first-order process model:

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 in the following form:

3.5 The design method of step 2 can obtain the controller:

Rewrite as follows:

3.6 Apply the internal model feedback controller to the PID controller structure:

Among them, K _c , T _i , T _d correspond to the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the PID controller, respectively.

3.7 Through the approximation of the corresponding internal model controller and PID controller, it can be obtained:

C _PID (s) = C ₁ (s)

which is:

其中，3.8 To simplify the calculation, let

in,

m(s)=0.5Tθ ² s ³ +(Tθ+0.5θ ² )s ² +(T+θ)s+1

n(s)=K[0.5λ ₂ θ ² s ² +(λ ₂ +0.5θ ² )s+(λ ₂ +θ)]

Then you can get:

K _c =W'(0)

T _i =W ^-1 (0)

3.9 According to the McLaughlin expansion sequence, each tuning parameter can be obtained as:

T _i =K(λ ₂ +θ)

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:

Among them, T ₁ and T ₂ are process model time constants.

3.12 Implement the PID parameters by reducing the controller form to that of a PID controller in series with a lead-lag filter of the following equation:

3.13 By calculation and simplification, we can get:

3.14 Therefore, the various parameters of the controller can be obtained:

a=0; b=0.5θ ² ; c=θ; d=0

3.15 After the PID parameters are obtained, further fine-tuning may sometimes be required to obtain a perfect controller.

The invention proposes a heating furnace temperature control method based on a novel two-degree-of-freedom internal model PID. This method improves the two-degree-of-freedom internal model control structure. By adding a weighting factor to the parameters of the setpoint tracking controller, it is convenient for online tuning and achieves good setpoint tracking. For the first-order and second-order delay processes, different The equivalent design of the controller in the form of a PID controller can simply and conveniently obtain the various tuning parameters of the controller, and can make the system satisfy both good tracking performance and interference suppression performance, and the control requirements of the system can also be guaranteed.

Description of drawings

Figure 1 is a block diagram of the internal model control;

Figure 2 is a block diagram of a classic feedback control;

Figure 3 is a block diagram of an improved two-degree-of-freedom internal model control structure;

Figure 4 is a classic two-degree-of-freedom control block diagram;

Detailed ways

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

Take the actual industrial heating furnace temperature control as an example:

1. According to the first-order plus time-delay process model of the heating furnace, design a two-degree-of-freedom internal model PID controller. The specific steps are:

1.1 First, consider the input and output temperature data of the heating process of the industrial heating furnace, and establish the transfer function transfer function of the first-order plus time delay process model of the heating furnace, as shown in the following formula:

Among them, G(s) is the model of the heating process of the furnace, K is the process gain coefficient; T is the process time constant; θ is the delay time.

1.2 In the two-degree-of-freedom control structure, the internal model control filter h(s) is reasonably designed in the following form:

1.3 According to the design method of the improved two-degree-of-freedom internal model control structure, the controller can be obtained:

Rewrite as follows:

1.4 Apply the internal model feedback controller to the PID controller structure:

Among them, K _c , T _i , T _d correspond to the proportional gain coefficient and integral gain coefficient of the PID controller, respectively

and differential gain factor.

1.5 Through the approximation of the corresponding internal model controller and PID controller, it can be obtained:

C _PID (s) = C ₁ (s)

which is:

其中，1.6 To simplify the calculation, let

in,

m(s)=0.5Tθ ² s ³ +(Tθ+0.5θ ² )s ² +(T+θ)s+1

n(s)=K[0.5λ ₂ θ ² s ² +(λ ₂ +0.5θ ² )s+(λ ₂ +θ)]

Then you can get:

K _c =W'(0)

T _i =W ^-1 (0)

1.7 According to the McLaughlin expansion sequence, each tuning parameter can be obtained as:

T _i =K(λ ₂ +θ)

1.8 After obtaining the PID parameters, further fine-tuning may sometimes be required to obtain the perfect controller for the furnace.

2. According to the second-order plus time-delay process model of the heating furnace, design a two-degree-of-freedom internal model PID controller. The specific steps are:

2.1 Consider the input and output temperature data of the heating process of the industrial heating furnace, and establish the transfer function of the second-order plus time-delay process model of the heating furnace, as shown in the following formula:

Among them, T ₁ and T ₂ are the time constants of the heating process model of the heating furnace.

2.2 The PID parameters are realized by reducing the controller form to the form of a PID controller in series with a lead-lag filter of the following equation:

2.3 Through calculation and simplification, we can get:

2.4 Therefore, the various parameters of the controller can be obtained:

a=0; b=0.5θ ² ; c=θ; d=0

2.5 After obtaining the PID parameters, further fine-tuning may sometimes be required to obtain a perfect controller for 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 model_IMC(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:

1.3 when the model is accurate, i.e. g(s) ═ m(s):

y＝G_IMC(s)G(s)r+[1-G_IMC(s)M(s)]d

the set point tracking characteristic and the interference rejection characteristic are in accordance with G_IMC(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 G_IMC(s) as the reciprocal of the reversible moiety, i.e.:

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:

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:

1.8 time delay section e^-θsThe following form approximation was chosen:

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:

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:

2.3 the complementary sensitivity function t(s) between the inputs and outputs of the process is:

2.4 the controller Q can be obtained from the above equation₂(s)：

2.5 then, the relationship between output and interference is further obtained:

2.6 selection of complementary sensitivity formats:

t(s)＝G⁺(s)h(s)

wherein,

λ₂is a parameter to be set;

2.7 obtaining the controller Q₂Form(s):

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)

2.10 by calculation, one can obtain:

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:

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:

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:

3.5 the design method of step 2 can obtain a controller:

the following is rewritten:

3.6 apply the internal model feedback controller to the PID controller structure:

wherein, K_c，T_i，T_dProportional 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:

C_PID(s)＝C₁(s)

namely:

3.8 to simplify the calculation, let

Wherein,

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:

K_c＝W'(0)

T_i＝W^-1(0)

3.9 obtaining each setting parameter according to the Meglalin spreading sequence as follows:

T_i＝K(λ₂+θ)

3.10 after obtaining the PID parameters, further fine tuning to obtain a controller;

3.11 consider the second order delay process model:

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:

3.13 by calculation and simplification, one can get:

3.14 obtaining various parameters of the controller:

a＝0；b＝0.5θ²；c＝θ；d＝0

T_i＝T₁+T₂；

3.15 after obtaining the PID parameters, further fine tuning the obtained controller.

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