CN114879505A - Pneumatic regulating valve control method based on quantitative feedback theory - Google Patents
Pneumatic regulating valve control method based on quantitative feedback theory Download PDFInfo
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Abstract
The invention relates to a pneumatic control valve control method based on a quantitative feedback theory, which comprises the following steps: establishing a mathematical model of a pneumatic regulating valve system, obtaining a controlled object template by considering the uncertainty change range of system model parameters under the actual working condition, and designing a robust stability index and a tracking performance index; converting the model uncertainty, the performance index requirement and the like of the pneumatic regulating valve system into a control boundary in a quantitative mode to obtain the constraint condition of the controller; and obtaining a feedback controller which meets the robustness requirement and a prefilter which meets the tracking performance index requirement by using a loop forming method according to the constraint conditions of the controller. The invention improves the robustness of the pneumatic regulating valve system by utilizing the known object model and the uncertainty information thereof, so that the control effect of the pneumatic regulating valve system when the model parameters change accords with the performance index requirement of the system.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a pneumatic control valve control method based on a quantitative feedback theory.
Background
Pneumatic control valves are important devices that are essential in modern industrial process control systems, and their performance directly affects the entire industrial process. In the actual production process, the pneumatic regulating valve often works in a complex environment and is easily influenced by external interference and internal equivalent interference (including model uncertainty, unmodeled dynamics and the like), so that the robust performance requirement of the pneumatic regulating valve system controller is high.
At present, the control algorithms applied in the pneumatic regulating valve system mainly include: the control algorithm based on PID improvement comprises fuzzy-PID control, gray prediction fuzzy-PID control and the like. However, the method based on PID control has poor robustness, cannot well meet the performance index requirements of the system under external interference and model uncertainty, and has strong model dependence. Although the control method based on the PID improvement can improve the robustness of the system, the known object model and uncertain information thereof cannot be effectively utilized.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defects in the prior art, and provide a pneumatic control valve control method based on a quantitative feedback theory, which can improve the robustness of the system and enable the control effect of the system to meet the requirements of system performance indexes when the model parameters change.
In order to solve the technical problem, the invention provides a pneumatic control valve control method based on a quantitative feedback theory, which comprises the following steps:
step 1: establishing a mathematical model of the pneumatic regulating valve system;
step 2: 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 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 of the pneumatic regulating valve system without a 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.
Preferably, the mathematical model of the pneumatically regulated valve system, including the intelligent positioner module and the valve actuator module,
the intelligent positioner 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;
a 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 the displacement of the valve actuator.
Preferably, the transfer function of the second order system
Wherein, 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 Laplace 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;
rotation of the air pressure and forceTransfer function of link change
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
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 constant of the actuator spring, and b is the internal friction damping of the actuator.
Preferably, the controlled object template is obtained under the mathematical model of the pneumatic regulating valve system by considering the uncertainty change range of the system model parameters under the actual working condition, and specifically comprises:
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 。
Preferably, the robust stability index is:
wherein s is j ω, L (j ω) is C (j ω) G 0 (j ω), C (j ω) is the feedback controller to be designed, G 0 (jω)＝G 0 (s)。
Preferably, the tracking performance index is:
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.
Preferably, a composite boundary is obtained according to the controlled object template, the robust stability index and the tracking performance index, and 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.
Preferably, 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 the robust stability index and the tracking performance index includes:
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 pre-filter until the response curve of the open-loop system meets the requirement of the tracking performance index, and bringing the pre-filter obtained by adjustment into the pneumatic regulating valve system to obtain the pneumatic regulating valve system meeting the requirement of the tracking performance index.
Preferably, the adjusting the feedback controller until the response curve of the open-loop system meets the requirement of the robust stability index includes:
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.
Preferably, the pre-filter is adjusted until the response curve of the open-loop system meets the requirement of the tracking performance index, specifically:
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 enclosed 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.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the method can better process the characteristic of uncertainty of the controlled object through QFT, utilizes the known object model and the uncertainty information thereof to design the controller of the pneumatic regulating valve system, takes the system performance index as a boundary, and utilizes a multi-test method to design the controlled object containing uncertainty to meet the system performance index requirement, thereby improving the robustness of the pneumatic regulating valve system and leading the control effect of the pneumatic regulating valve system when the model parameter changes to meet the system performance index requirement.
Drawings
In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a modular construction of the pneumatic regulator valve system of the present invention;
FIG. 3 is an open loop system response curve for a pneumatically regulated valve system without a controller plotted against a composite boundary in an embodiment of the present invention;
FIG. 4 is a response curve of an open loop system with a two degree of freedom controller in an embodiment of the present invention;
FIG. 5 is a closed loop system tracking boundary response curve in an embodiment of the present invention;
FIG. 6 is a graph of a closed loop step response of a pneumatically regulated valve system comparing the present invention to a method using a PID at nominal conditions in an embodiment of the present invention;
FIG. 7 is a graph of a closed loop step response of a pneumatic regulator system comparing the present invention to a method using PID when the change in the system parameters of the pneumatic diaphragm regulator valve in an embodiment of the present invention is within an indeterminate design range;
FIG. 8 is a graph of a closed loop step response of a pneumatically regulated valve system comparing the present invention to a method using a PID in simulating the presence of sudden extreme conditions in an embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The invention provides a controller design method based on a Quantitative Feedback Theory (QFT) aiming at the problems of external interference and internal equivalent interference of a pneumatic regulating valve system in an industrial process. As shown in the flow chart of FIG. 1, the invention discloses a pneumatic control valve control method based on a quantitative feedback theory, which comprises the following steps:
step 1: aiming at external interference and internal equivalent interference suffered by the pneumatic regulating valve system in actual industrial engineering, the working process of the pneumatic regulating valve system is analyzed, and a mathematical model of the pneumatic regulating valve system is established.
Step 1-1: fig. 2 is a schematic diagram of a modular structure of a pneumatic regulating valve system, in which a mathematical model of the pneumatic regulating valve system divides the system into two modules according to functional partitions of a pneumatic regulating valve, and the two modules include 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 (a displacement sensor in fig. 2), and a transfer function of the valve position feedback link (the displacement sensor) in this embodiment is h(s) -1. And 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 mathematical model of the module can be obtained through a mechanism modeling method. 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.
Step 1-2: establishing a transfer function of the second order system
Wherein, 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 Laplace operator, and ω is the second-order system natural oscillation frequency.
Step 1-3: establishing a transfer function of the 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 G 2 The derivation process of(s) is:
the air chamber of the valve actuator module can be approximated as a resistance-capacitance link, and the formula is calculated according to the elastic modulus of ideal gas in an isothermal state:
wherein K v And respectively obtaining the isothermal elastic modulus of the ideal gas, the pressure change value in the gas chamber, the change value of the volume of the compressed gas and the volume of the gas before compression by finishing
Order to
And according to the relation formula of the material balance,
the following steps are changed:
wherein Q i For gas inflow rate, Q o Is the gas outflow rate sum P 2 Is the pressure in the air chamber.
At low gas flow rates, the following approximate relationship exists between gas flow and pressure differential
Wherein P is 1 For input of air pressure, R v It is used for guiding air and resisting air. Because the air chamber of the pneumatic membrane actuating mechanism is closed, the output flow Q can be known o 0. Will be provided with
Substitution into
After finishing and increasing the quantity, the method can obtain:
wherein Δ P 2 Is the variation of the output air pressure, Δ P 1 Is the input air pressure variation.
To simplify the writing of the model, omitting the incremental notation, one can get:
wherein T is v Is the time constant of the pneumatic resistance-capacitance link.
For the above first order differential equation
And performing Laplace transformation to obtain:
T v ·sP 2 (s)+P 2 (s)＝P 1 (s)
where s is the Laplace operator, P 2 (s) is P after Laplace change 2 . Therefore, the transfer function of the air chamber air pressure conversion link can be obtained:
step 1-4: establishing a transfer function of the air pressure and force conversion link
Wherein F(s) ═ P 2 (s)·A D ，A D Is the effective area of the diaphragm in the air chamber.
Transfer function G 3 The push-to process of(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 push rod of the actuating mechanism, the force F (t) and the effective area A of the diaphragm in the air chamber D In this regard, it can be expressed as:
F(t)＝P 2 (t)A D ，
wherein P is 2 (t) is a time-varying expression of the output air pressure in the time domain.
The link is a proportion link, and the Laplace transformation is carried out on F (t) to obtain:
F(s)＝P 2 (s)·A D ，
converting F(s) to P 2 (s)·A D Conversion to the form of the transfer function yields:
step 1-5: establishing a transfer function of a conversion link of 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 rate of the actuator spring, and b is the internal friction damping of the actuator.
Transfer function G 4 The push-to process of(s) is:
the displacement conversion link of the pneumatic membrane regulating valve can be approximated to a mass-spring-damping system. The system equation for obtaining the output force of the air chamber according to the Newton's second law is as follows:
under the zero initial condition, performing Laplace transformation, and obtaining a transfer function of the output force of the air chamber and the displacement of the valve rod after finishing:
1-6: establishing a transfer function G(s) G for a pneumatically controlled valve system 1 (s)G 2 (s)G 3 (s)G 4 (s) in which G 1 (s) is the transfer function of a second order system, G 2 (s) is the transfer function of the air-chamber air-pressure conversion link, G 3 (s) is the transfer function of the conversion link between air pressure and force, G 4 (s) is the transfer function of the conversion link of force and valve actuator displacement.
Step 2: and 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.
Step 2-1: and (4) considering the uncertainty change range of the system model parameters under the actual working condition, and obtaining a controlled object template under the mathematical model of the pneumatic regulating valve system.
Step 2-1-1: 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, obtained in this example
G 3 (s)＝65，
Will 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;
step 2-1-2: the ranges of uncertain parameters m, k and b are obtained through actual measurement, and m E is obtained in the embodiment [ 0.040.05 ]]kg，k∈[8 10]N/mm，b∈[0.8 1]N/mm. Selecting one value of m, k and b in the range as a nominal parameter of the system to obtain a transfer function G of the controlled object 0 (s); in this example, m is selected 0 ＝0.05kg，k 0 ＝10N/mm，b 0 1N/mm, to yield
Step 2-1-3: 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 . The frequency array ω ═ 0.010.050.10.51510501005001000 selected in this embodiment]rad/s, setting the adjustment time t of the step response of the closed-loop System s Not more than 2.5s, rise time t p Less than or equal to 1.5s, overshoot sigma less than or equal to 5%, and phase angle margin
Amplitude margin K M ≥5dB。
Step 2-2: and designing a robust stability index and a tracking performance index under a controlled object template.
Step 2-2-1: the robust stability index is established as follows:
wherein s is j ω, L (j ω) is C (j ω) G 0 (j ω), C (j ω) is the feedback controller to be designed, G 0 (jω)＝G 0 (s)；
The specific robust stability indexes obtained in this embodiment are:
can ensure the minimum amplitude margin K of the system M 5.26dB, minimum phase margin
Is 49 deg. and meets the requirement of robust stability.
Step 2-2-2: the tracking performance index is established 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.
Upper bound on tracking performance in this example
Lower bound of tracking performance
The selected upper and lower limits of the tracking performance ensure that the closed loop system step response meeting the upper and lower limits is met, the overshoot is not more than 5%, the rising time is not more than 1.5 seconds, the adjusting time is not more than 2.5 seconds, and the tracking performance requirement is met.
The quantitative feedback means that the performance indexes are quantized to generate a response boundary to constrain the design of the controller, the relevant indexes also need to input disturbance suppression indexes, output disturbance suppression indexes, sensitivity indexes and the like, and when the pneumatic regulating valve controller is designed, only the robust stability index and the tracking performance index are selected according to the requirements of the system performance indexes in the embodiment.
And step 3: and 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 of the pneumatic regulating valve system without the controller according to the composite boundary.
Step 3-1: and obtaining a composite boundary according to the controlled object template, the robust stability index and the tracking performance index.
Step 3-1-1: and 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, which is a performance index boundary generation process, performing boundary generation at a corresponding frequency by using the selected frequency array, reducing the calculated amount by partially replacing the whole, and ensuring that all frequencies meet the requirements by controlling and designing multiple tests.
Step 3-1-2: and establishing a tracking performance boundary of the controlled object template on the Nichols diagram according to the tracking performance index on the frequency array.
Step 3-1-3: and integrating the robust stability boundary and the tracking performance boundary to obtain a composite boundary.
As can be seen from fig. 3, when the controller is not designed, the system open-loop frequency response curve does not meet the boundary requirement of the system performance index, the system open-loop frequency curve intersects the robust stability boundary, and the corresponding frequency point is not located above the tracking performance boundary.
Step 3-2: obtaining an open-loop system response curve of the pneumatic regulating valve system without a controller according to the composite boundary; the open loop system response curve without controller for a pneumatically regulated valve system plotted against the composite boundary in this example is shown in FIG. 3.
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.
Step 4-1: a two degree of freedom controller including a feedback controller and a pre-filter is built using a QFT toolset and a loop shaping method.
Step 4-2: and 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 adjustment valve system with the two-degree-of-freedom controller shown in fig. 4, the response curve L of the open-loop system is made by adjusting the gain, the zero point and the pole point of the feedback controller 0 (j ω) satisfies: located above the corresponding tracking performance boundary at the selected frequency point and L at high frequency 0 (j ω) does not intersect the robust stability boundary, the adjusted feedback controller
Step 4-3: the feedback controller C(s) C (j ω) adjusted at this time is taken into the pneumatic control valve system, and a pneumatic control valve system satisfying the robust stability index requirement is obtained. In this embodiment, 0.01-1 in fig. 4 is a left-right through area as a tracking performance boundary, that is, 0.01-1 is a low frequency area, and 5-10 in fig. 4 is a robust stability ellipse as a robust stability boundary, that is, 5-10 is a high frequency area. As can be seen from fig. 4, the response curve of the open-loop system is located above the boundary of the tracking performance at the selected frequency point and has a small distance from the boundary, so that the system can meet the requirement of the tracking performance when designing the pre-filter. At high frequencies, the open-loop system response curve does not intersect the robust stability boundary, thereby ensuring the stability of the system.
Step 4-4: and adjusting the pre-filter until the response curve of the open-loop system meets the requirement of tracking performance index. In this embodiment, the two-degree-of-freedom controller is applied to the pneumatic adjustment valve system to obtain the tracking boundary response curve of the closed-loop system as shown in fig. 5, and the upper and lower bounds of the closed-loop response curve in the tracking boundary response curve of the closed-loop system are enclosed by adjusting the gain, the zero and the pole of the pre-filterThe envelope is located at the upper tracking performance bound T u (s)＝T u (j ω) and the lower bound T of tracking performance l (s)＝T l (j ω) between; the pre-filter obtained by adjustment at this time
And 4-5: and the prefilter D(s) ═ D (j omega) obtained by adjustment at this time is taken into the pneumatic regulating valve system, so that the pneumatic regulating valve system meeting the requirement of the tracking performance index is obtained.
Under the action of the feedback controller C(s) and the prefilter D(s), the pneumatic regulating valve system meets the requirements of robust stability indexes and tracking performance indexes.
The method can better process the characteristic of uncertainty of the controlled object through QFT, utilizes the known object model and the uncertainty information thereof to design the controller of the pneumatic regulating valve system, takes the system performance index as a boundary, and utilizes a multi-test method to design the controlled object containing uncertainty to meet the system performance index requirement, thereby improving the robustness of the pneumatic regulating valve system and leading the control effect of the pneumatic regulating valve system when the model parameter changes to meet the system performance index requirement.
To further illustrate the advantageous effects of the present invention, the present embodiment will compare the pneumatic regulator valve system using the present invention with the pneumatic regulator valve system using the PID control method.
First, the present invention is compared to the use of the PID method under nominal conditions, where the closed loop step response curve of a pneumatically regulated valve system is shown in FIG. 6. Given a closed loop step response curve (50 mm full scale) at a valve position signal of 20mm, the dashed line in fig. 6 is using the PID method and the solid line is using the invention. As can be seen from fig. 6, in the nominal condition, the pneumatic control valve system of the present invention is used without overshoot (overshoot is the ratio of the instantaneous maximum deviation value Xmax of the modulated quantity to the steady-state value X (∞) under the action of step input, generally expressed in percentage, where the overshoot is [ Xmax-X (∞) ]/X (∞) X100%, where the maximum instantaneous value of the modulation exceeds the set value by 20 mm), and a certain overshoot occurs using the PID method, it can be seen that the robustness of the present invention is superior to the PID control method; meanwhile, when the method is used, the closed-loop system meets the requirements of various performance indexes in the design process, so the method is superior to a PID control method.
The invention is then compared to using a PID method when the change in the pneumatic diaphragm regulator valve system parameters is within an uncertain design range. Given a closed loop step response curve (full scale 50mm) at a valve position signal of 20mm, when the change of the parameters of the pneumatic diaphragm regulating valve system is in an uncertain design range, namely the friction damping b in the valve actuator is 0.8N/mm, and the elastic coefficient k of the spring is 8N/mm, the closed loop step response curve is shown in FIG. 7. At this time, the overshoot of the closed loop step response curve is less than 5%, the rise time is less than 1.5 seconds, and the regulation time is less than 2.5 seconds, so that the control system still meets the performance index requirement of the system. The maximum instantaneous value of the PID method is close to 25mm, the overshoot of the closed-loop step response curve is (25-20)/20 multiplied by 100 percent, which is far larger than 5 percent of the system requirement, and the performance index requirement of the system can not be met. The invention is also superior to the PID control method
Finally, the present invention is compared to using the PID method in the case of simulations facing sudden extreme conditions. Under actual conditions where the friction damping and spring rate of the spring in the valve actuator continues to decrease, the closed loop step response curve of the system is shown in fig. 8 when the parameter is decreased to b-0.7N/mm and k-7N/mm. As can be seen from FIG. 8, the overshoot of the closed loop step response curve using the PID method has reached 38% and seriously exceeded 5% of the system performance requirement, and the regulation time has also exceeded 2.5 seconds and seriously exceeded the system performance index requirement; when the closed loop step response curve of the invention is used, the overshoot is still less than 5%, the rising time is still less than 1.5 seconds, the adjusting time is still less than 2.5 seconds, and the performance index of the pneumatic adjusting valve system still meets the design requirement. The analysis shows that the closed-loop system still has stronger robustness in the case of sudden extreme working conditions, namely when the parameter uncertainty of the system exceeds the design working condition, thereby showing the practical engineering application value of the invention.
Through comparison experiments under three conditions, the method disclosed by the invention can well control the pneumatic regulating valve system, and has better robustness compared with the traditional control method, so that the control effect of the pneumatic regulating valve system when the model parameters change meets the requirement of system performance indexes.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. 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, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.
Claims (10)
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;
step 2: 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 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 pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 1, wherein: the mathematical model of the pneumatic regulating valve system comprises an intelligent positioner module and a valve actuator module,
the intelligent positioner 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;
a 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 the displacement of the valve actuator.
3. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 2, wherein:
transfer function of the second order system
Wherein, 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 Laplace 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
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 constant of the actuator spring, and b is the internal friction damping of the actuator.
4. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 3, 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 。
5. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 4, wherein: the robust stability index is as follows:
where s is j ω and L (j ω) is C (j ω) G 0 (j ω), C (j ω) is the feedback controller to be designed, G 0 (jω)＝G 0 (s)。
6. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 5, wherein: the tracking performance index is 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.
7. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 4, 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.
8. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 6, 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 pre-filter until the response curve of the open-loop system meets the requirement of the tracking performance index, and bringing the pre-filter obtained by adjustment into the pneumatic regulating valve system to obtain the pneumatic regulating valve system meeting the requirement of the tracking performance index.
9. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 8, 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.
10. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 8, 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 enclosed 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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