CN114879505B - Pneumatic regulating valve control method based on quantitative feedback theory - Google Patents

Abstract

The invention relates to a control method of a pneumatic control valve based on quantitative feedback theory, which includes: establishing a mathematical model of a pneumatic control valve system, considering the uncertainty range of system model parameters under actual working conditions to obtain a controlled object template, and designing a robust Stability index and tracking performance index; the model uncertainty and performance index requirements of the pneumatic control valve system are converted into control boundaries in a quantitative way, and the constraints of the controller are obtained; according to the constraints of the controller, the loop forming method is used to obtain A feedback controller that meets the requirements of robustness and a pre-filter that meets the requirements of the tracking performance index. The invention improves the robustness of the pneumatic control valve system by using the known object model and its uncertainty information, so that the control effect of the pneumatic control valve system meets the system performance index requirements when the model parameters change.

Description

Control Method of Pneumatic Control Valve Based on Quantitative Feedback Theory

technical field

The invention relates to the technical field of automatic control, in particular to a control method of a pneumatic regulating valve based on quantitative feedback theory.

Background technique

Pneumatic control valves are indispensable and important equipment in modern industrial process control systems, and their performance will directly affect the entire industrial process. In the actual production process, pneumatic control valves often work in complex environments, and are easily affected by external disturbances and internal equivalent disturbances (including model uncertainty, unmodeled dynamics, etc.). Therefore, the pneumatic control valve system The robust performance requirements of the controller are higher.

At present, the control algorithms used in the pneumatic control valve system mainly include: conventional PID control method and improved control method based on PID. The improved control algorithm based on PID includes fuzzy-PID control, gray predictive fuzzy-PID control, etc. However, the method based on PID control has poor robustness, and cannot satisfy the performance index requirements of the system under external disturbance and model uncertainty, and has strong model dependence. Although the improved control methods based on PID can improve the robustness of the system, they cannot effectively utilize the known object model and its uncertain information.

Contents of the invention

For this reason, the technical problem to be solved by the present invention is to overcome the deficiencies in the prior art, and provide a control method for pneumatic control valves based on quantitative feedback theory, which can improve the robustness of the system and make the system stable when the model parameters change. The control effect meets the system performance index requirements.

In order to solve the above technical problems, the present invention provides a method for controlling a pneumatic control valve based on quantitative feedback theory, which includes the following steps:

Step 1: Establish a mathematical model of the pneumatic control valve system;

Step 2: Considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system, and the robust stability index and track performance metrics;

Step 3: Obtain the compound boundary according to the controlled object template, the robust stability index and the tracking performance index, and obtain the open-loop system response curve when the pneumatic control valve system has no controller according to the compound boundary;

Step 4: Establish a two-degree-of-freedom controller including a feedback controller and a pre-filter, apply the two-degree-of-freedom controller to the pneumatic control valve system, and adjust the two-degree-of-freedom controller until the opening The response curve of the loop system meets the performance requirements, and a pneumatic control valve system that meets the requirements of the robust stability index and the tracking performance index is obtained.

Preferably, the mathematical model of the pneumatic control valve system includes an intelligent positioner module and a valve actuator module,

The intelligent positioner module includes an internal controller, an electrical conversion link, a pneumatic amplification link and a valve position feedback link, and the electrical conversion link and the pneumatic amplification link are modeled as a second-order system;

The valve actuator module includes an airtight air chamber and a valve stem movement link, and the mechanism model of the valve actuator module is divided into an air chamber air pressure conversion link, an air pressure and force conversion link, and a force and valve actuator displacement conversion link;

The transfer function G(s) of the pneumatic regulating valve system=G ₁ (s)G ₂ (s)G ₃ (s)G ₄ (s), wherein G ₁ (s) is the transfer function of the second-order system , G ₂ (s) is the transfer function of the air pressure conversion link in the air chamber, G ₃ (s) is the transfer function of the air pressure and force conversion link, and G ₄ (s) is the force and valve actuator displacement The transfer function of the conversion link.

其中，P₁(s)为智能定位器模块的输出气压，x(s)是阀位输入，K是二阶系统增益，ξ是二阶系统阻尼系数，s是拉普拉斯算子，ω是二阶系统自然振荡频率；As preferably, the transfer function of the second-order system

Among them, P ₁ (s) is the output air pressure of the intelligent positioner module, x (s) is the valve position input, K is the second-order system gain, ξ is the second-order system damping coefficient, s is the Laplacian operator, ω is the natural oscillation frequency of the second-order system;

其中P₂(s)为经拉普拉斯变化后的输出气压P₂，P₁(s)为经拉普拉斯变化后的输入气压P₁，T_v是气动阻容环节时间常数，s是拉普拉斯算子；The transfer function of the air pressure conversion link of the air chamber

Among them, P ₂ (s) is the output air pressure P ₂ changed by Laplace, P ₁ (s) is the input air pressure P ₁ changed by Laplace, T _v is the time constant of the pneumatic resistance-capacitance link, s is the Laplacian operator;

其中F(s)＝P₂(s)·A_D，A_D为气室内膜片的有效面积；The transfer function of the conversion link of the air pressure and force

Among them, F(s)=P ₂ (s)· _AD , where _AD is the effective area of the diaphragm in the gas chamber;

其中x(s)是阀位输入，m为执行机构运动部件的总质量，x为执行机构的输出位移，k为执行机构弹簧的弹性系数，b为执行机构的内摩擦阻尼。The transfer function of the conversion link between the force and valve actuator displacement

Where x(s) is the valve position input, m is the total mass of the moving parts of the actuator, x is the output displacement of the actuator, k is the spring coefficient of the actuator, and b is the internal friction damping of the actuator.

As preferably, considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system, specifically:

Considering the uncertainty range of system model parameters under actual working conditions, the actual expressions of the controlled object templates G ₁ (s), G ₂ (s), G ₃ (s) and G ₄ (s) are obtained, and G ₄ In (s), the mass m of the moving part of the actuator, the spring elastic coefficient k and the internal friction damping b of the actuator are used as uncertain parameters of the pneumatic control valve system;

The range of uncertain parameters m, k and b is obtained through actual measurement, and a value of m, k and b within the range is selected as the nominal parameter of the system, and the transfer function G ₀ (s) of the controlled object is obtained;

和幅值裕度K_M。Select the frequency with greater uncertainty of the controlled object as the frequency array, and set the adjustment time t _s , rise time t _p , overshoot σ, and phase angle margin of the closed-loop system step response according to the dynamic characteristics of the pneumatic control valve system Spend

and amplitude margin K _M .

As preferably, the robust stability index is:

Where s=jω, L(jω)=C(jω)·G ₀ (jω), C(jω) is the feedback controller to be designed, G ₀ (jω)=G ₀ (s).

As preferably, the tracking performance index is:

Among them, D(jω) is the pre-filter to be designed, _Tu (jω) is the upper bound of tracking performance, and T _l (jω) is the lower bound of tracking performance.

Preferably, the composite boundary is obtained according to the controlled object template, the robust stability index and the tracking performance index, specifically:

On the frequency array, the controlled object template is established on the Nichols diagram according to the robust stability index, and a robust stability boundary is established,

On the frequency array, the controlled object template is set up on the Nichols diagram to track the performance boundary according to the tracking performance index,

The robust stability bound and the tracking performance bound are integrated to obtain a composite bound.

As a preference, the adjustment of the two-degree-of-freedom controller until the response curve of the open-loop system meets the performance requirements, so as to obtain a pneumatic control valve system that meets the requirements of the robust stability index and the tracking performance index, specifically:

Adjusting the feedback controller until the response curve of the open-loop system meets the requirements of the robust stability index, and bringing the adjusted feedback controller into the pneumatic control valve system to meet the requirements of the robust stability index Pneumatic control valve system;

Adjust the pre-filter until the response curve of the open-loop system meets the requirements of the tracking performance index, and bring the adjusted pre-filter into the pneumatic control valve system to obtain the pneumatic control valve system that meets the requirements of the tracking performance index. Regulating valve system.

Preferably, the adjustment of the feedback controller until the response curve of the open-loop system meets the requirements of the robust stability index, specifically:

In the pneumatic control valve system with a two-degree-of-freedom controller, by adjusting the gain, zero and pole of the feedback controller, the response curve of the open-loop system satisfies: at the selected frequency point, it is located at the corresponding tracking performance boundary above and does not intersect the robust stability boundary at high frequencies.

Preferably, the pre-filter will be adjusted until the open-loop system response curve meets the requirements of the tracking performance index, specifically:

The two-degree-of-freedom controller is applied to the pneumatic control valve system to obtain the closed-loop system tracking boundary response curve. By adjusting the gain, zero point and pole of the pre-filter, the closed-loop system tracking boundary response curve in the closed-loop response curve The envelope formed by the upper bound and the lower bound is located between the upper bound of tracking performance and the lower bound of tracking performance.

The above technical solution of the present invention has the following advantages compared with the prior art:

The present invention can better deal with the characteristics of the uncertainty of the controlled object through QFT, use the known object model and its uncertainty information to design the controller of the pneumatic control valve system, use the system performance index as the boundary, and use multiple The experimental method is designed so that the controlled objects including uncertainties meet the system performance index requirements, thereby improving the robustness of the pneumatic control valve system, so that the control effect of the pneumatic control valve system is in line with the system performance when the model parameters change. Indicator requirements.

Description of drawings

In order to make the content of the present invention more easily understood, the present invention will be described in further detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a schematic diagram of the modular structure of the pneumatic regulating valve system in the present invention;

Fig. 3 is the open-loop system response curve when the pneumatic regulating valve system without a controller is drawn according to the compound boundary in the embodiment of the present invention;

Fig. 4 is the open-loop system response curve with two degrees of freedom controller in the embodiment of the present invention;

Fig. 5 is the closed-loop system tracking boundary response curve in the embodiment of the present invention;

Fig. 6 is a closed-loop step response curve diagram of the pneumatic control valve system comparing the present invention with the method using PID under the nominal condition in the embodiment of the present invention;

Fig. 7 is the closed-loop step response curve diagram of the pneumatic regulating valve system comparing the present invention with the method using PID when the variation of the parameters of the pneumatic film regulating valve system in the embodiment of the present invention is within the uncertain design range;

Fig. 8 is a closed-loop step response curve diagram of the pneumatic control valve system comparing the present invention with the method using PID in the case of simulating sudden extreme working conditions in the embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.

The invention proposes a controller design method based on Quantitative Feedback Theory (QFT) aiming at the external interference and internal equivalent interference that the pneumatic control valve system receives in the industrial process. As shown in the flow chart of Figure 1, the present invention discloses a method for controlling a pneumatic control valve based on quantitative feedback theory, which includes the following steps:

Step 1: According to the external interference and internal equivalent interference that the pneumatic control valve system receives in the actual industrial engineering, analyze the working process of the pneumatic control valve system, and establish the mathematical model of the pneumatic control valve system.

Step 1-1: As shown in Figure 2, it is a schematic diagram of the modular structure of the pneumatic control valve system. The mathematical model of the pneumatic control valve system divides the system into two modules according to the functional division of the pneumatic control valve, including the intelligent positioner module and a valve actuator module, the intelligent positioner module includes an internal controller, an electrical conversion link, a pneumatic amplification link and a valve position feedback link (displacement sensor in Fig. 2), and the valve position feedback link (displacement sensor ) transfer function is H(s)=1. The electrical conversion link and the pneumatic amplification link are modeled as second-order systems. The valve actuator module includes a closed air chamber and a valve stem movement link, and the mathematical model of the module can be obtained through a mechanism modeling method. The mechanism model of the valve actuator module is divided into the air pressure conversion link of the air chamber, the conversion link of air pressure and force, and the conversion link of force and valve actuator displacement.

其中，P₁(s)为智能定位器模块的输出气压，x(s)是阀位输入，K是二阶系统增益，ξ是二阶系统阻尼系数，s是拉普拉斯算子，ω是二阶系统自然振荡频率。Step 1-2: Establish the transfer function of the second-order system

Among them, P ₁ (s) is the output air pressure of the intelligent positioner module, x (s) is the valve position input, K is the second-order system gain, ξ is the second-order system damping coefficient, s is the Laplacian operator, ω is the natural oscillation frequency of the second-order system.

其中P₂(s)为经拉普拉斯变化后的输出气压P₂，P₁(s)为经拉普拉斯变化后的输入气压P₁，T_v是气动阻容环节时间常数，s是拉普拉斯算子；Step 1-3: Establish the transfer function of the air pressure conversion link of the air chamber

Among them, P ₂ (s) is the output air pressure P ₂ changed by Laplace, P ₁ (s) is the input air pressure P ₁ changed by Laplace, T _v is the time constant of the pneumatic resistance-capacitance link, s is the Laplacian operator;

The derivation process of the transfer function G ₂ (s) is:

The air chamber of the valve actuator module can be approximated as a resistance-capacity link, according to the calculation formula of the elastic modulus under the ideal gas isothermal state:

Among them, K _v , ΔP, ΔV and V are the ideal gas isothermal elastic modulus, the change value of the pressure in the gas chamber, the change value of the gas volume after compression and the volume of the gas before compression.

并根据物料平衡关系式，

变为：make

And according to the material balance relation,

becomes:

Where _Qi is the gas inflow flow rate, _Qo is the gas outflow flow rate and _P2 is the pressure inside the gas chamber.

其中P₁为输入气压，R_v为导气气阻。由于气动薄膜执行机构的气室是封闭的，可知输出流量Q_o＝0。将

代入

中，经整理，并进行增量化处理后可得：When the gas flow rate is not high, there is the following approximate relationship between the gas flow rate and the pressure difference

Among them, P ₁ is the input air pressure, and R _v is the air guide air resistance. Since the air chamber of the pneumatic film actuator is closed, it can be seen that the output flow Q _o =0. Will

substitute

Among them, after sorting and incremental processing, we can get:

Among them, ΔP ₂ is the change of output air pressure, and ΔP ₁ is the change of input air pressure.

In order to simplify the writing of the model, the increment symbol is omitted to obtain:

Where T _v is the time constant of the pneumatic resistance-capacitance link.

进行拉氏变换，可得：For the above first order differential equation

Carrying out the Laplace transform, we can get:

T _v ·sP ₂ (s)+P ₂ (s)=P ₁ (s)

Where s is the Laplacian operator, and P ₂ (s) is P ₂ after Laplacian transformation. From this, the transfer function of the gas pressure conversion link can be obtained:

其中F(s)＝P₂(s)·A_D，A_D为气室内膜片的有效面积。Steps 1-4: Establish the transfer function of the conversion link between air pressure and force

Wherein F(s)=P ₂ (s)· _AD , where _AD is the effective area of the diaphragm in the gas chamber.

The derivation process of the transfer function G ₃ (s) is:

The air pressure and force conversion link is to convert the air pressure in the air chamber into the pulling force of the actuator push rod. The force F(t) is related to the effective area A _D of the diaphragm in the air chamber, which can be expressed as:

F(t)=P ₂ (t)A _D ,

where P ₂ (t) is an expression of the output air pressure changing with time in the time domain.

This link is a proportional link, and the Laplace transform of F(t) is obtained:

F(s)=P ₂ (s) · A _D ,

Converting F(s)=P ₂ (s)· _AD into the form of transfer function, we can get:

其中x(s)是阀位输入，m为执行机构运动部件的总质量，x为执行机构的输出位移，k为执行机构弹簧的弹性系数，b为执行机构的内摩擦阻尼。Steps 1-5: Establish the transfer function of the conversion link between the force and the displacement of the valve actuator

Where x(s) is the valve position input, m is the total mass of the moving parts of the actuator, x is the output displacement of the actuator, k is the spring coefficient of the actuator, and b is the internal friction damping of the actuator.

The derivation process of the transfer function G ₄ (s) is:

The displacement conversion link of the pneumatic film regulating valve can be approximated as a mass-spring-damping system. According to Newton's second law, the system equation of the output force of the air chamber is:

Under the zero initial condition, the Laplace transform is carried out, and the transfer function of the output force of the air chamber and the displacement of the valve stem can be obtained after finishing:

Step 1-6: Establish the transfer function of the pneumatic control valve system G(s)=G ₁ (s)G ₂ (s)G ₃ (s)G ₄ (s), where G ₁ (s) is the second-order system Transfer function, G ₂ (s) is the transfer function of the air pressure conversion link of the air chamber, G ₃ (s) is the transfer function of the conversion link of air pressure and force, G ₄ (s) is the transfer function of the conversion link of force and valve actuator displacement Transfer Function.

Step 2: Considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system, and the robust stability index and tracking performance index are designed under the controlled object template.

Step 2-1: Considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system.

G₃(s)＝65，

将G₄(s)中的执行机构运动部分质量m，弹簧弹性系数k和执行机构内摩擦阻尼b作为气动调节阀系统的不确定参数；Step 2-1-1: Considering the uncertainty range of system model parameters under actual working conditions, obtain the controlled object templates G ₁ (s), G ₂ (s), G ₃ (s) and G ₄ (s) The actual expression, obtained in this example

G ₃ (s)=65,

The mass m of the moving part of the actuator in G ₄ (s), the spring elastic coefficient k and the internal friction damping b of the actuator are used as uncertain parameters of the pneumatic control valve system;

Step 2-1-2: Obtain the range of uncertain parameters m, k and b through actual measurement. In this embodiment, m∈[0.04 0.05]kg, k∈[8 10]N/mm, b∈[0.8 1 ] N/mm. Select a value of m, k and b within the range as the nominal parameter of the system to obtain the transfer function G ₀ (s) of the controlled object; in this embodiment, select m ₀ =0.05kg, k ₀ =10N/mm, b ₀ =1N/mm, get

和幅值裕度K_M。本实施例中选择的频率阵列ω＝[0.01 0.05 0.1 0.5 1 5 10 50100 500 1000]rad/s，设置闭的环系统阶跃响应的调节时间t_s≤2.5s，上升时间t_p≤1.5s，超调量σ≤5％，相角裕度

幅值裕度K_M≥5dB。Step 2-1-3: Select the frequency with greater uncertainty of the controlled object as the frequency array, and set the adjustment time t _s , rise time t _p , super Modulation σ, phase angle margin

and amplitude margin K _M . The frequency array ω=[0.01 0.05 0.1 0.5 1 5 10 50100 500 1000]rad/s selected in this embodiment, the adjustment time t _s of the step response of the closed loop system is set ≤2.5s, and the rise time t _p ≤1.5s , overshoot σ≤5%, phase angle margin

Amplitude margin K _M ≥ 5dB.

Step 2-2: Design robust stability indicators and tracking performance indicators under the template of the controlled object.

Step 2-2-1: Establish a robust stability index as:

Where s=jω, L(jω)=C(jω) G ₀ (jω), C(jω) is the feedback controller to be designed, G ₀ (jω)=G ₀ (s);

The specific robust stability index obtained in this embodiment is:

为49°，满足鲁棒稳定性要求。Can guarantee the minimum amplitude margin K _M of the system is 5.26dB, the minimum phase margin

is 49°, which meets the requirement of robust stability.

Step 2-2-2: Establish tracking performance indicators as:

Among them, D(jω) is the pre-filter to be designed, _Tu (jω) is the upper bound of tracking performance, and T _l (jω) is the lower bound of tracking performance.

跟踪性能的下界

所选择的跟踪性能的上下界，保证了满足该上下界的闭环系统阶跃响应，其超调量不超过5％，上升时间不超过1.5秒，调节时间不超过2.5秒，符合跟踪性能要求。The upper bound of tracking performance in this example

Lower bound on tracking performance

The selected upper and lower bounds of the tracking performance ensure the step response of the closed-loop system meeting the upper and lower bounds. The overshoot does not exceed 5%, the rise time does not exceed 1.5 seconds, and the adjustment time does not exceed 2.5 seconds, which meets the tracking performance requirements.

Quantitative feedback refers to the quantification of performance indicators to generate response boundaries to constrain the controller design. Related indicators also need to input disturbance suppression indicators, output disturbance suppression indicators, sensitivity indicators, etc. When designing a pneumatic control valve controller, this embodiment According to the system performance index requirements, only the robust stability index and the tracking performance index are selected.

Step 3: According to the controlled object template, the robust stability index and the tracking performance index, the composite boundary is obtained, and the open-loop system response curve of the pneumatic control valve system without a controller is obtained according to the composite boundary.

Step 3-1: Obtain the compound boundary according to the controlled object template, robust stability index and tracking performance index.

Step 3-1-1: On the frequency array, the controlled object template is established on the Nichols diagram according to the robust stability index, which is the performance index boundary generation process, and the selected frequency array To generate the boundary at the corresponding frequency, first replace the whole with part to reduce the amount of calculation, and control the design for multiple experiments to ensure that all frequencies meet the requirements.

Step 3-1-2: On the frequency array, the controlled object template is used to establish a tracking performance boundary on the Nichols diagram according to the tracking performance index.

Step 3-1-3: Integrate the robust stability boundary and the tracking performance boundary to obtain a composite boundary.

It can be seen from Figure 3 that when the controller is not designed, the system open-loop frequency response curve does not meet the boundary requirements of the system performance index, the system open-loop frequency curve intersects the robust stability boundary and the corresponding frequency point is not above the tracking performance boundary.

Step 3-2: Obtain the open-loop system response curve of the pneumatic control valve system without a controller according to the composite boundary; the open-loop system response curve of the pneumatic control valve system without a controller drawn according to the composite boundary in this embodiment is shown in Figure 3 shown.

Step 4: Establish a two-degree-of-freedom controller including a feedback controller and a pre-filter, apply the two-degree-of-freedom controller to the pneumatic control valve system, and adjust the two-degree-of-freedom controller until the opening The response curve of the loop system meets the performance requirements, and a pneumatic control valve system that meets the requirements of the robust stability index and the tracking performance index is obtained.

Step 4-1: Use the QFT toolbox and the loop shaping method to build a two-degree-of-freedom controller including a feedback controller and a pre-filter.

Step 4-2: Adjusting the feedback controller until the response curve of the open-loop system meets the requirement of the robust stability index. In this embodiment, in the pneumatic regulating valve system with a two-degree-of-freedom controller as shown in FIG. 4 , the open-loop system response curve L ₀ ( jω) satisfies: the selected frequency point is located above the corresponding tracking performance boundary, and L ₀ (jω) does not intersect the robust stability boundary at high frequencies, then the adjusted feedback controller

Step 4-3: Bring the adjusted feedback controller C(s)=C(jω) into the pneumatic control valve system to obtain a pneumatic control valve system that meets the requirements of the robust stability index. In this embodiment, 0.01-1 in Fig. 4 is left and right through as the tracking performance boundary, that is, 0.01-1 is a low frequency place, and 5-10 in Fig. 4 is a robust stable ellipse, which is a robust stability boundary, that is, 5- 10 is the high frequency. It can be seen from Figure 4 that the response curve of the open-loop system is located above the tracking performance boundary at the selected frequency point and the distance from the boundary is very small, which ensures that the system can meet the tracking performance requirements when designing the pre-filter. At high frequencies, the open-loop system response curve does not intersect the robust stability boundary, thus ensuring the stability of the system.

Step 4-4: Adjusting the pre-filter until the response curve of the open-loop system meets the requirements of the tracking performance index. In this embodiment, the two-degree-of-freedom controller is applied to the pneumatic control valve system to obtain the closed-loop system tracking boundary response curve shown in Figure 5. By adjusting the gain, zero point and pole of the pre-filter, the closed-loop system The envelope formed by the upper bound and the lower bound of the closed-loop response curve in the tracking boundary response curve is located at the upper bound of the tracking performance T _u (s) = T _u (jω) and the lower bound of the tracking performance T _l (s) = T _l (jω); at this time, the adjusted pre-filter

Step 4-5: Bring the adjusted pre-filter D(s)=D(jω) into the pneumatic control valve system to obtain a pneumatic control valve system that meets the requirements of the tracking performance index.

Under the action of the above-mentioned feedback controller C(s) and pre-filter D(s), the pneumatic control valve system meets the requirements of robust stability index and tracking performance index.

The present invention can better deal with the characteristics of the uncertainty of the controlled object through QFT, use the known object model and its uncertainty information to design the controller of the pneumatic control valve system, use the system performance index as the boundary, and use multiple The experimental method is designed so that the controlled objects including uncertainties meet the system performance index requirements, thereby improving the robustness of the pneumatic control valve system, so that the control effect of the pneumatic control valve system is in line with the system performance when the model parameters change. Indicator requirements.

In order to further illustrate the beneficial effects of the present invention, in this embodiment, a comparison will be made between the pneumatic regulating valve system using the present invention and the pneumatic regulating valve system using the PID control method.

First, compare the present invention with the PID method under nominal conditions, and the closed-loop step response curve of the pneumatic control valve system under nominal conditions is shown in FIG. 6 . The closed-loop step response curve (full scale is 50mm) when the given valve position signal is 20mm, the dotted line in Fig. 6 is to use the PID method, and the solid line is to use the present invention. As can be seen from Figure 6, under nominal conditions, the pneumatic control valve system of the present invention has no overshoot (the overshoot (overshoot) is the difference between the instantaneous maximum deviation value Xmax of the regulated quantity and the stable value under the action of a step input. The ratio of the state value X(∞) is generally expressed as a percentage: overshoot = [Xmax—X(∞)]/X(∞)×100%, where the percentage of the maximum instantaneous value exceeding the set value of 20mm is adjusted here), And use PID method to have occurred certain overshoot, it can be seen that the robustness of the present invention is better than PID control method; Simultaneously, when using the present invention, closed-loop system satisfies each performance index requirement in the design process, so the present invention is superior to PID control method.

Next, the present invention is compared with the use of the PID method when the variation of the parameters of the pneumatic membrane regulating valve system is within the uncertain design range. Given the closed-loop step response curve when the valve position signal is 20mm (full scale is 50mm), when the change of the system parameters of the pneumatic film regulating valve is within the uncertain design range, that is, the internal frictional damping of the valve actuator b=0.8N/ mm, and the elastic coefficient k of the spring = 8N/mm, its closed-loop step response curve is shown in Figure 7. At this time, using the closed-loop step response curve of the present invention, the overshoot is less than 5%, the rise time is less than 1.5 seconds, and the adjustment time is less than 2.5 seconds, and the control system still meets the performance index requirements of the system. However, the maximum instantaneous value using the PID method is close to 25mm, and the overshoot of the closed-loop step response curve is (25-20)/20×100%, which is far greater than the 5% required by the system, which does not meet the performance index requirements of the system. The present invention is also superior to the PID control method

Finally, the present invention is contrasted with the use of the PID method in the case of simulations facing sudden extreme operating conditions. Under the actual working condition that the internal frictional damping of the valve actuator and the elastic coefficient of the spring continue to decrease, when the parameters are reduced to b=0.7N/mm, k=7N/mm, the closed-loop step response curve of the system is shown in Figure 8 shown. It can be seen from Figure 8 that the overshoot of the closed-loop step response curve using the PID method has reached 38%, seriously exceeding 5% of the system performance requirements, and its adjustment time has also exceeded 2.5 seconds, seriously exceeding the system performance index requirements; Using the closed-loop step response curve of the present invention, the overshoot is still less than 5%, the rise time is still less than 1.5 seconds, the adjustment time is still less than 2.5 seconds, and the performance index of the pneumatic control valve system still meets the design requirements. As can be seen from the above analysis, in the face of sudden extreme working conditions, that is, when the parameter uncertainty of the system exceeds the design working condition, the closed-loop system of the present invention still has strong robustness, which shows that the actual engineering of the present invention Value.

Through comparative experiments in three cases, it is further illustrated that the present invention can control the pneumatic control valve system well, and has better robustness compared with the traditional control method, so that the pneumatic control valve system can be controlled when the model parameters change. The control effect meets the system performance index requirements.

Those skilled in the art should understand that the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowcharts and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

Apparently, the above-mentioned embodiments are only examples for clear description, and are not intended to limit the implementation. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in various forms can also be made. It is not necessary and impossible to exhaustively list all the implementation manners here. However, the obvious changes or changes derived therefrom are still within the scope of protection of the present invention.

Claims (8)

1. A pneumatic control valve control method based on a quantitative feedback theory is characterized by comprising the following steps:

step 1: establishing a mathematical model of the pneumatic regulating valve system; the mathematical model of the pneumatic regulating valve system comprises an intelligent positioner module and a valve actuator module,

the intelligent locator module comprises an internal controller, an electrical conversion link, a pneumatic amplification link and a valve position feedback link, wherein the electrical conversion link and the pneumatic amplification link are modeled into a second-order system;

the valve actuator module comprises a closed air chamber and a valve rod movement link, and a mechanism model of the valve actuator module is divided into an air chamber air pressure conversion link, an air pressure and force conversion link and a force and valve actuator displacement conversion link;

transfer function G(s) = G of the pneumatically regulated valve system ₁ (s)G ₂ (s)G ₃ (s)G ₄ (s) in which G ₁ (s) is the transfer function of the second order system, G ₂ (s) is a transfer function of the air chamber air pressure conversion link, G ₃ (s) is a transfer function of said conversion element of pressure and force, G ₄ (s) is a transfer function of a conversion link of the force and valve actuator displacement;

transfer function of the second order system

Wherein, P ₁ (s) is the output air pressure of the intelligent locator module, x(s) is the valve position input, K is the second-order system gain, ξ is the second-order system damping coefficient, s is the Laplacian operator, and ω is the second-order system natural oscillation frequency;

transfer function of air chamber air pressure conversion link

Wherein P is ₂ (s) is the output pressure P after Laplace change ₂ ，P ₁ (s) is the input pressure P after Laplace change ₁ ，T _v Is the pneumatic resistance-capacitance link time constant, s is the laplace operator;

transfer function of the conversion link of the air pressure and the force

Wherein F(s) = P ₂ (s)·A _D ，A _D Is the effective area of the diaphragm in the air chamber;

transfer function of the conversion link of the force and the displacement of the valve actuator

Wherein x(s) is valve position input, m is the total mass of the moving parts of the actuating mechanism, x is the output displacement of the actuating mechanism, k is the elastic coefficient of the spring of the actuating mechanism, and b is the internal friction damping of the actuating mechanism;

and 2, step: considering the uncertainty change range of system model parameters under the actual working condition, obtaining a controlled object template under the mathematical model of the pneumatic regulating valve system, and designing a robust stability index and a tracking performance index under the controlled object template;

and 3, step 3: obtaining a composite boundary according to the controlled object template, the robust stability index and the tracking performance index, and obtaining an open-loop system response curve when a pneumatic regulating valve system has no controller according to the composite boundary;

and 4, step 4: establishing a two-degree-of-freedom controller comprising a feedback controller and a pre-filter, acting the two-degree-of-freedom controller into the pneumatic regulating valve system, and regulating the two-degree-of-freedom controller until the response curve of the open-loop system meets the performance requirement to obtain the pneumatic regulating valve system meeting the requirements of robust stability index and tracking performance index.

2. The quantitative feedback theory-based pneumatic control valve control method according to claim 1, wherein: the method comprises the following steps of considering the uncertainty change range of system model parameters under the actual working condition, and obtaining a controlled object template under the mathematical model of the pneumatic regulating valve system, wherein the method specifically comprises the following steps:

the uncertainty change range of the system model parameters under the actual working condition is considered to obtain a controlled object template G ₁ (s)、G ₂ (s)、G ₃ (s) and G ₄ (s) actual expression, G ₄ (s) the mass m of the moving part of the actuating mechanism, the elastic coefficient k of the spring and the friction damping b in the actuating mechanism are used as uncertain parameters of the pneumatic adjusting valve system;

obtaining the range of uncertain parameters m, k and b through actual measurement, selecting one value of m, k and b in the range as the nominal parameter of the system, and obtaining the transfer function G of the controlled object ₀ (s)；

Selecting the frequency with larger uncertainty of the controlled object as a frequency array, and setting the adjusting time t of the step response of the closed-loop system according to the dynamic characteristic requirement of the pneumatic adjusting valve system _s Rising time t _p Overshoot σ, phase angle margin

Sum amplitude margin K _M 。

3. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 2, wherein: the robust stability index is as follows:

wherein s = j ω, L (j ω) = C (j ω) · G ₀ (j ω), C (j ω) is the feedback controller to be designed, G ₀ (jω)＝G ₀ (s)。

4. The quantitative feedback theory-based pneumatic control valve control method according to claim 3, wherein: the tracking performance indexes are as follows:

where D (j ω) is the pre-filter to be designed, T _u (j ω) is an upper bound on tracking performance, T _l (j ω) is the lower bound of tracking performance.

5. The quantitative feedback theory-based pneumatic control valve control method according to claim 2, wherein: obtaining a composite boundary according to the controlled object template, the robust stability index and the tracking performance index, specifically:

establishing a robust stability boundary on the Nichols diagram by using the controlled object template on the frequency array according to the robust stability index,

establishing a tracking performance boundary on the Nichols graph by using the controlled object template on the frequency array according to the tracking performance index,

and integrating the robust stability boundary and the tracking performance boundary to obtain a composite boundary.

6. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 4, wherein: the adjusting the two-degree-of-freedom controller until the response curve of the open-loop system meets the performance requirement to obtain the pneumatic regulating valve system meeting the requirements of robust stability index and tracking performance index specifically comprises the following steps:

adjusting the feedback controller until the response curve of the open loop system meets the requirement of the robust stability index, and bringing the feedback controller obtained by adjustment into the pneumatic regulating valve system to obtain the pneumatic regulating valve system meeting the requirement of the robust stability index;

and adjusting the prefilter until the response curve of the open loop system meets the requirement of the tracking performance index, and bringing the prefilter obtained by adjustment into the pneumatic regulating valve system to obtain the pneumatic regulating valve system meeting the requirement of the tracking performance index.

7. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 6, wherein: the adjusting the feedback controller until the response curve of the open loop system meets the requirement of the robust stability index specifically comprises:

in the pneumatic regulating valve system with the two-degree-of-freedom controller, the response curve of the open-loop system meets the following requirements by adjusting the gain, the zero and the pole of a feedback controller: located above the corresponding tracking performance boundary at the selected frequency points and not intersecting the robust stability boundary at high frequencies.

8. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 6, wherein: the pre-filter is adjusted until the response curve of the open loop system meets the requirement of the tracking performance index, and the method specifically comprises the following steps:

and applying a two-degree-of-freedom controller to a pneumatic regulating valve system to obtain a closed loop system tracking boundary response curve, and enabling an envelope formed by an upper bound and a lower bound of the closed loop response curve in the closed loop system tracking boundary response curve to be positioned between the upper bound and the lower bound of the tracking performance by adjusting the gain, the zero and the pole of a pre-filter.

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