PI controller separation parameter setting method and device

Abstract

The invention discloses a PI controller separation parameter setting method and device, and the method is based on a phase margin method, is suitable for a self-balancing object, and comprises a pure delay link, a high-order inertia link and a lagged first-order inertia link. The core innovation of the method is as follows: PI controller parameters in the method are only related to the steady-state gain of a controlled object and are only related to a time scale (a time constant T and delay time), and decoupling is related to T / . The method provides a more flexible and convenient parameter setting approach for complex industrial process control. The device comprises an identification module which is used for identifying parameters of a transfer function of a controlled object by adopting a response curve method; the processing module is used for obtaining the transfer function of the controlled object after the parameters of the transfer function of the controlled object are identified; the calculation module is used for calculating a phase margin; the setting module obtains the proportional gain and the integral time constant of the PI controller according to the adjustable parameters; the invention discloses a PI controller separation parameter setting method.

Description

Technical Field

[0001] This application relates to the field of automation technology, and in particular to a PI controller. Separation parameter tuning method. Background Technology

[0002] In the field of industrial automatic control, proportional-integral (PI) controllers are widely used in various control systems due to their simple structure and good robustness. However, for controlled objects containing pure delay elements, high-order inertial elements, and first-order inertial elements with hysteresis, traditional PI controller parameter tuning methods, such as the trial-and-error method, have obvious shortcomings. This method often relies on experience, the tuning process is time-consuming, and it is difficult to balance system stability, speed, and accuracy. Under complex controlled objects, it is prone to problems such as large overshoot and long settling time.

[0003] Classic PI controller parameter tuning methods, such as the Ziegler-Nichols (ZN) method and the Cohen-Coon (CC) method, involve controlling the gain parameters of the controlled object. With time parameters (time constant) Lag time The proportional gain of the controller is not independently affected. and points time Instead, they are intertwined and jointly affect the controller parameters, which means that adjusting one parameter will disrupt the original control effect of another parameter, increasing the difficulty and uncertainty of debugging.

[0004] Therefore, there is an urgent need for a separate parameter tuning technique for PI controllers for self-balancing controlled objects (pure delay elements, higher-order inertial elements, and first-order inertial elements with hysteresis). Summary of the Invention

[0005] This application provides a PI controller. A separate parameter tuning method and device are proposed to solve the problems of traditional PI controller parameter tuning methods, which are time-consuming and difficult to balance system stability, speed and accuracy. Under complex controlled objects, they are prone to problems such as large overshoot and long settling time.

[0006] A first aspect of this application provides a PI controller. The separation parameter tuning method includes the following steps: S1: Using the response curve method, the transfer function of the controlled object is... The parameters to be identified include: steady-state gain. K Inertial time constant T and delay time ; S2: Transfer function to the controlled object After the parameters are identified, the transfer function of the controlled object is obtained as follows: , in, steady-state gain of the controlled object ， The time constant of the inertial element 、 The order of the inertial element ， For delay time; The PI controller transfer function is: , in, For the proportional gain of the PI controller, The integral time constant of the PI controller; The open-loop transfer function of the system is: , S3: Calculate the phase margin: , in, For the phase margin, This refers to the open-loop phase of the system. S4: Based on adjustable parameters , Find the proportional gain of the PI controller. Integration time constant .

[0007] PI controller The method for tuning the separation parameters is as follows:

[0008] in, It is an adjustable parameter. , For phase margin, This is the system's time scale.

[0009] According to one embodiment of this application, when the When the time interval is reached, the transfer function of the pure delay element is: The calculation shows that: .

[0010] According to one embodiment of this application, when the At that time, the transfer function of the higher-order inertial element is The calculation shows that: .

[0011] According to one embodiment of this application, when the At that time, the transfer function of the first-order inertial element with hysteresis is The calculation shows that: .

[0012] According to one embodiment of this application, the phase margin .

[0013] According to one embodiment of this application, the The range is .

[0014] According to one embodiment of this application, the The At that time, by the aforementioned Calculate .

[0015] According to one embodiment of this application, when the The At that time, by the aforementioned Calculate .

[0016] According to one embodiment of this application, in S1, a two-point method is used to extract key feature points of the system step response curve to achieve efficient identification of the core parameters of the object.

[0017] A second aspect of this application provides a PI controller. The separation parameter tuning device includes: The identification module is used to identify the transfer function of the controlled object using the response curve method. The parameters to be identified include: steady-state gain. K Inertial time constant T and delay time ; The processing module is used to pass functions to the controlled object. After the parameters are identified, the transfer function of the controlled object is obtained as follows: , in, steady-state gain of the controlled object ， The time constant of the inertial element 、 The order of the inertial element ， For delay time; The PI controller transfer function is: , in, For the proportional gain of the PI controller, The integral time constant of the PI controller; The open-loop transfer function of the system is: , The calculation module is used to calculate the phase margin. , in, For the phase margin, This refers to the open-loop phase of the system. The tuning module is used to adjust the adjustable parameters. , Find the proportional gain of the PI controller. Integration time constant .

[0018] PI controller The method for tuning the separation parameters is as follows:

[0019] in, It is an adjustable parameter. , For phase margin, This is the system's time scale.

[0020] According to one embodiment of this application, in S1, a two-point method is used to extract key feature points of the system step response curve to achieve efficient identification of the core parameters of the object.

[0021] This application discloses a proportional-integral (PI) controller. α - β Separate parameter tuning technique. This technique is based on the phase margin method and is applicable to self-balancing objects, including pure delay elements, higher-order inertial elements, and first-order inertial elements with hysteresis. Its core innovation lies in the PI controller parameters in this method. Only related to the steady-state gain of the controlled object Related, Only related to time scale (time constant) T and delay time Related, decoupling and T / This technology provides a more flexible and convenient parameter tuning approach for complex industrial process control. It solves the problems of traditional PI controller parameter tuning methods, which are time-consuming and struggle to balance system stability, speed, and accuracy, and are prone to large overshoot and long settling times under complex controlled objects.

[0022] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0023] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 A PI controller provided according to an embodiment of this application Separation parameter tuning method , The step response curve of the system at time; Figure 2 A PI controller provided according to an embodiment of this application Separation parameter tuning method , The step response curve of the system at time; Figure 3 A PI controller provided according to an embodiment of this application A schematic diagram of the separation parameter tuning device. Detailed Implementation

[0024] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0025] The PI controller of this application embodiment is described below with reference to the accompanying drawings. A method and apparatus for separate parameter tuning. Addressing the limitations of traditional PI controller parameter tuning methods mentioned in the background section, which are time-consuming and struggle to balance system stability, speed, and accuracy, this application provides a PI controller... The separate parameter tuning method, based on the phase margin method, is applicable to self-balancing objects, including pure delay elements, higher-order inertial elements, and first-order inertial elements with hysteresis. Its core innovation lies in the PI controller parameters... Only related to the steady-state gain of the controlled object Related, Only related to time scale (time constant) T and delay time Related, decoupling and T / This technology provides a more flexible and convenient parameter tuning approach for complex industrial process control. It solves the problems of traditional PI controller parameter tuning methods, which are time-consuming and struggle to balance system stability, speed, and accuracy, and are prone to large overshoot and long settling times under complex controlled objects.

[0026] Specifically, the embodiments of this application provide a PI controller. The separation parameter tuning method includes the following steps: S1: Using the response curve method, the transfer function of the controlled object is applied. The parameters to be identified include: steady-state gain. K Inertial time constant T and delay time .

[0027] In some embodiments, in S1, a two-point method is used to extract key feature points from the system step response curve to achieve efficient identification of the core parameters of the object.

[0028] S2: Transfer function to the controlled object After the parameters are identified, the transfer function of the controlled object is obtained as follows: , in, steady-state gain of the controlled object ， The time constant of the inertial element 、 The order of the inertial element ， For delay time; The PI controller transfer function is: , in, For the proportional gain of the PI controller, The integral time constant of the PI controller; The open-loop transfer function of the system is: .

[0029] In some embodiments, when When the time interval is reached, the transfer function of the pure delay element is: The calculation shows that: .

[0030] In other embodiments, when At that time, the transfer function of the higher-order inertial element is The calculation shows that: .

[0031] In some embodiments, when At that time, the transfer function of the first-order inertial element with hysteresis is The calculation shows that: .

[0032] S3: Calculate the phase margin: , in, For phase margin, This represents the open-loop phase of the system.

[0033] In some embodiments, phase margin Preferred .

[0034] S4: Based on adjustable parameters , Find the proportional gain of the PI controller. Integration time constant .

[0035] PI controller The method for tuning the separation parameters is as follows:

[0036] in, It is an adjustable parameter. , For phase margin, This is the system's time scale.

[0037] In some embodiments, The range is Preferred or .

[0038] In other embodiments, , At that time, by Calculate .

[0039] In some embodiments, when , At that time, by Calculate ; The following describes a PI controller. The specific implementation method of the separation parameter tuning method is described in detail.

[0040] (1) The transfer function of the controlled object is ,in, The steady-state gain of the controlled object, The time constant of the inertial element、 The order of the inertial element ， This is the delay time. The PI controller transfer function is: ,in, For the proportional gain of the PI controller, Let be the integral time constant of the PI controller. Then, the open-loop transfer function of the system is: .

[0041] (2) When When the time interval is reached, the transfer function of the pure delay element is: The open-loop transfer function of the system is The frequency characteristics of this system are: .

[0042] Cutoff frequency of open-loop transfer function satisfy:

[0043] PI controller based on phase margin (PM) method α - β Separation parameter tuning method, system phase margin for:

[0044] make ,

[0045] Therefore, there is , ,in .

[0046] System phase margin requirements Preferred Table 1 shows the situation at this time. and The calculation results.

[0047] Table 1

[0048] (3) When At that time, the transfer function of the higher-order inertial element is The open-loop transfer function of the system is The frequency characteristics of this system are:

[0049] Cutoff frequency of open-loop transfer function satisfy:

[0050] The product of the integral time constant and the cutoff frequency is calculated. for:

[0051] As n approaches infinity We can obtain:

[0052] System phase margin for:

[0053] Therefore:

[0054] make , Therefore, there is , ,in .

[0055] (4) When At that time, the transfer function of the first-order inertial element with hysteresis is The open-loop transfer function of the system is .

[0056] Cutoff frequency of open-loop transfer function satisfy:

[0057] The product of the integral time constant and the cutoff frequency is calculated. for:

[0058] make when hour, We can obtain:

[0059] System phase margin for:

[0060] Therefore:

[0061] make , Therefore, there is , ,in .

[0062] Example 1: The controlled object transfer function is ,when When the time interval is reached, the transfer function of the pure delay element is: ,when , At that time, a PI controller was used. , After calculation , Its step response curve is as follows Figure 1 As shown. The settling time is 46.5s, and the overshoot is 6.3%.

[0063] when At that time, the transfer function of the higher-order inertial element is ,when , , At that time, a PI controller was used. , After calculation , Its step response curve is as follows Figure 1 As shown. The settling time is 62.5s, and the overshoot is 5.3%.

[0064] when At that time, the transfer function of the first-order inertial element with hysteresis is ,when , , At that time, a PI controller was used. , After calculation , Its step response curve is as follows Figure 1 As shown, its settling time is 36.8s and its overshoot is 5%.

[0065] Example 2: The controlled object transfer function is ,when When the time interval is reached, the transfer function of the pure delay element is: ,when , At that time, a PI controller was used. , After calculation , Its step response curve is as follows Figure 2 As shown. The settling time is 44.0 s, and the overshoot is 7.8%.

[0066] when At that time, the transfer function of the higher-order inertial element is ,when , , At that time, a PI controller was used. , After calculation , Its step response curve is as follows Figure 2 As shown. The settling time is 58.1 s, and the overshoot is 5.4%.

[0067] when At that time, the transfer function of the first-order inertial element with hysteresis is ,when , , At that time, a PI controller was used. , After calculation , Its step response curve is as follows Figure 2 As shown, the settling time is 33.1 s and the overshoot is 6.3%.

[0068] Figure 1 and Figure 2 The comparison revealed that, When the value is small (0.25), the settling time is long and the overshoot is small; A larger value (0.3) results in a shorter adjustment time and a larger overshoot. The appropriate value can be selected based on the specific circumstances. The value of .

[0069] The PI controller proposed according to the embodiments of this application The separate parameter tuning method, based on the phase margin method, is applicable to self-balancing objects, including pure delay elements, higher-order inertial elements, and first-order inertial elements with hysteresis. Its core innovation lies in the PI controller parameters... Only related to the steady-state gain of the controlled object Related, Only related to time scale (time constant) T and delay time Related, decoupling and T / This technology provides a more flexible and convenient parameter tuning approach for complex industrial process control. It solves the problems of traditional PI controller parameter tuning methods, which are time-consuming and struggle to balance system stability, speed, and accuracy, and are prone to large overshoot and long settling times under complex controlled objects.

[0070] Next, referring to the accompanying drawings, a PI controller according to an embodiment of this application is described. Separation parameter tuning device.

[0071] Figure 3 This is the PI controller in the embodiments of this application. A schematic diagram of the separation parameter tuning device.

[0072] like Figure 3 As shown, the PI controller The separation parameter setting device 10 includes: an identification module 100, a processing module 200, a calculation module 300, and a setting module 400.

[0073] Specifically, the identification module 100 is used to identify the transfer function of the controlled object using the response curve method. The parameters to be identified include: steady-state gain. K Inertial time constant T and delay time .

[0074] Processing module 200 is used to pass functions to the controlled object. After the parameters are identified, the transfer function of the controlled object is obtained as follows: , in, steady-state gain of the controlled object ， The time constant of the inertial element 、 The order of the inertial element ， For delay time; The PI controller transfer function is: , in, For the proportional gain of the PI controller, The integral time constant of the PI controller; The open-loop transfer function of the system is: .

[0075] Calculation module 300 is used to calculate the phase margin: , in, For the phase margin, This represents the open-loop phase of the system.

[0076] Tuning module 400 is used to adjust parameters. , Find the proportional gain of the PI controller. Integration time constant .

[0077] PI controller The method for tuning the separation parameters is as follows:

[0078] in, It is an adjustable parameter. , For phase margin, This is the system's time scale.

[0079] It should be noted that the aforementioned PI controller The explanation of the separation parameter tuning method embodiment also applies to the PI controller of this embodiment. The separation parameter tuning device will not be described in detail here.

[0080] The PI controller proposed according to the embodiments of this application The separate parameter tuning device, based on the phase margin method, is applicable to self-balancing objects, including pure delay elements, higher-order inertial elements, and first-order inertial elements with hysteresis. Its core innovation lies in the PI controller parameters... Only related to the steady-state gain of the controlled object Related, Only related to time scale (time constant) T and delay time Related, decoupling and T / This technology provides a more flexible and convenient parameter tuning approach for complex industrial process control. It solves the problems of traditional PI controller parameter tuning methods, which are time-consuming and struggle to balance system stability, speed, and accuracy, and are prone to large overshoot and long settling times under complex controlled objects.

[0081] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0082] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0083] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

Claims

1. A PI controller Separation parameter setting method characterized by, The method comprises the following steps: S1: Using the response curve method, the transfer function of the controlled object is applied. The parameters to be identified include: steady-state gain. K Inertial time constant T and delay time ; S2: complete identification on parameters of the controlled object transfer function After the identification on parameters of the controlled object transfer function is completed, the controlled object transfer function is obtained as ， wherein, Kp is the steady state gain of the controlled object ， Ti is the time constant of the inertia loop 、 N is the order of the inertia loop ， T is the delay time; The PI controller transfer function is: ， wherein, Kp is a PI controller proportional gain, Ki is a PI controller integral time constant; The open loop transfer function of the system is: ， S3: Calculate the phase margin: ， wherein, is the phase margin for the system, is the open loop phase of the system; S4: The PI controller proportional gain , , integral time constant , are calculated as a function of the adjustable parameters . PI controller The separation parameter setting method is: wherein is an adjustable parameter, , is a phase margin, is a system time scale.

2. The PI controller of claim 1 Separation parameter setting method characterized by When the transfer function of the pure delay element is , it is calculated that .

3. The PI controller of claim 1 Separation parameter setting method characterized by When the transfer function of the high-order inertia link is , it is calculated that .

4. The PI controller of claim 1 Separation parameter setting method characterized by When the transfer function of the first order inertia link with hysteresis is , it is calculated that: .

5. The PI controller of claim 1 Separation parameter setting method characterized by The phase margin .

6. The PI controller of claim 1 Separation parameter setting method characterized by The ranging from .

7. The PI controller of claim 1 Separation parameter setting method characterized by The , the time, by the , calculated .

8. The PI controller of claim 1 Separation parameter setting method characterized by When the , the time, by the , calculated .

9. The PI controller of claim 1 Separation parameter setting method characterized by In the S1, by extracting the key feature points of the system step response curve, the efficient identification of the object core parameters is realized by using the two-point method.

10. A PI controller Separation parameter setting device characterized by, Comprise: The identification module is used to identify the transfer function of the controlled object using the response curve method. The parameters to be identified include: steady-state gain. K Inertial time constant T and delay time ; a processing module for obtaining the controlled object transfer function after identifying parameters of the controlled object transfer function ​ ， wherein, Kp is the proportional gain of the controlled object ， Ti is the time constant of the inertia link 、 N is the order of the inertia link ， T is the delay time; The PI controller transfer function is: ， wherein, Kp is a PI controller proportional gain, Ki is a PI controller integral time constant; The open loop transfer function of the system is: ， The calculation module is used for calculating the phase margin: ， wherein, is the phase margin for the system, is the open loop phase of the system; a tuning module for deriving the PI controller proportional gain , , integral time constant , from the adjustable parameters . PI controller The separation parameter setting method is: wherein is an adjustable parameter, , is a phase margin, is a system time scale.

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