A control system PI parameter engineering tuning method based on Bode diagram

Abstract

The invention discloses a control system PI parameter engineering setting method based on a Bode diagram, comprising the following steps: a first step: establishing a mathematical model of a control object system and drawing a system Bode diagram; a second step: finding the cutoff frequency of the control object system and the gain corresponding to the optimal phase margin in the Bode diagram; a third step: finding the frequency point where the optimal phase margin Pm=45° of the control object system is located and the corresponding gain in the Bode diagram; and a fourth step: calculating and setting PI link control parameters Kp and Ki / Ti. The control system PI parameter engineering setting method based on a Bode diagram proposed by the invention can be seen from a current closed-loop step response curve that the control performance of the original system can be improved by matching the PI parameters of the optimal phase margin PM=45° on the Bode diagram; the method is intuitive, simple and worthy of promotion.

Description

Technical Field

[0001] The invention belongs to the technical field of control systems based on Bode diagrams, and in particular relates to a control system PI parameter engineering setting method based on Bode diagrams. Background Art

[0002] In control systems, the classic control method PID is widely used and very effective, but the setting of control parameters in the PID control link has always been a headache for engineers. The reason is that on the one hand, it is necessary to master the operating mechanism and control model of the control object, and on the other hand, it requires professional knowledge of automatic control principles. Therefore, in the actual application process, the operating parameters of the PID control link are divided into two camps. One is to perform theoretical calculations based on the control model of the entire control system, and the other is to use the "trial and error method" in actual engineering, manually adjust the three parameters of PID, and judge whether the PID parameters are appropriate based on the response results of the system. The theoretical calculation of PID parameters involves many fields and requires rich on-site control experience. The "trial and error method" has a long debugging process and may not be adjusted well. Summary of the invention

[0003] The purpose of the present invention is to provide a control system PI parameter engineering tuning method based on the Bode diagram. The system frequency characteristics are analyzed through the Bode diagram of the control system, and the phase and gain corresponding to the optimal phase margin of the control system are found in the diagram; by matching the appropriate PI proportional parameter Kp, the gain at the frequency point where the optimal phase margin of the control system is located is adjusted to 1 (lossless gain); through the Bode diagram of the PI control link, the frequency with the least impact on the optimal phase margin is matched, and the integral time Ti of the response is calculated based on this, and then the PI integral parameter Ki is obtained.

[0004] To achieve the above object, the present invention provides the following technical solution: a control system PI parameter engineering tuning method based on Bode diagram, step 1: establish a mathematical model of the control object system and draw the system Bode diagram; obtain the stator winding parameters L and R of the permanent magnet synchronous motor and establish a mathematical model; the model can be established through matlab or simulink, or by handwriting mathematical formulas:

[0005]

[0006] Simple programming modeling in MATLAB, drawing Bode diagrams;

[0007]

[0008] In Matlab, simply write the following to complete the rational linear lag link model;

[0009] Gdly2=tf([Td^2-6*Td 12],[Td^26*Td 12]);

[0010] The mathematical model of the permanent magnet synchronous motor current loop under PWM pulse control is:

[0011]

[0012] In Matlab, simply write the following to complete the mathematical model of the permanent magnet synchronous motor current loop under PWM pulse control, and draw the Bode diagram for comparison;

[0013] Gobj_a3=Gobj*Gdly2

[0014] hl=bodeplot(Gobj_a3,'r-',Gobj,'g--');

[0015] Step 2: Find the cutoff frequency of the controlled object system and the gain corresponding to the optimal phase margin in the Bode diagram; find the phase φ of the object system and obtain the current phase margin Pm=180+φ by passing the amplitude in the Bode diagram of the controlled object system through the frequency point where 0dB is located; Pm=45° is considered the best in theory and engineering. If Pm is too large, it is necessary to correct it by connecting a PID link in series in the object system to make the phase margin of the object system around the optimal Pm;

[0016] Step 3: Find the frequency point and corresponding gain where the optimal phase margin Pm = 45° of the controlled system is located in the Bode diagram;

[0017] Simple programming in matlab to find the frequency of Pm; adjust the frequency Freq in the code below, and check the corresponding phase value phase in the Bode diagram of the controlled system in real time. When phase == -135°, the search for Pm is completed; at this time, the mag value is the gain corresponding to the optimal phase margin of the controlled system;

[0018] Frequency characteristics of %PM=45°

[0019] Fpm=834.6;%Hz

[0020] [mag,phase,rads]=bode(Gobj_a3,Fpm*2*pi);

[0021] Observing the Bode plot, we know that the frequency of Pm = 45° is 834.6 Hz, the corresponding angular frequency is ω = 132.8 rad / s, and the corresponding amplitude gain is -5.27 dB;

[0022] Step 4: Calculate and adjust the PI link control parameters Kp, Ki / Ti;

[0023] In order to achieve the best phase margin of the permanent magnet synchronous motor current loop, the gain at the frequency point corresponding to the current Pm of the control object should be adjusted by 1 (0dB) by adjusting the PI parameters, and the current phase should not be greatly affected, so as to improve the stability of the rapid response of the control object system;

[0024] The gain corresponding to Pm in the Bode diagram of the control object system is -5.27dB. The proportional parameter Kp is calculated by the following formula:

[0025] 20lg(K p )=5.27

[0026] K can be calculated p =1.834;

[0027] K p =1.834 is equivalent to adding 5.27dB gain to the control system, so that the gain of the control system at the Pm frequency is adjusted to 0dB, that is, the amplitude gain is 1;

[0028] Observe the control curve in the Bode diagram of the PI link. When τ i When ω=20, the phase lag caused by the PI controller is only 2.86°, which has little effect on the phase margin of the controlled system. This value can be selected to calculate the integral time. Then the integral parameter Ki is obtained as

[0029]

[0030] The system Bode diagram of the controlled object after adding the PI controller.

[0031] Preferably, considering the hysteresis effect of the control pulse PWM of the converter power device IGBT, the following rational formula can be used to replace the actual pulse hysteresis link:

[0032]

[0033] Preferably, in the theoretical linear hysteresis link model of step 1, Td is the time value of 1.5 PMW pulse locking response.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: a control system PI parameter engineering setting method based on a Bode diagram proposed by the present invention can be seen from the current closed-loop step response curve, by matching the PI parameters of the optimal phase margin PM=45° on the Bode diagram, the control performance of the original system can be improved; this method is intuitive, simple, and worthy of promotion. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1The Bode diagram of the current loop of the 3.5MW permanent magnet synchronous motor of the present invention;

[0036] Figure 2 The Bode diagram of the current loop of a 3.5MW permanent magnet synchronous motor under the influence of the 1.5*TPWM cycle hysteresis of the present invention;

[0037] Figure 3 is the Bode diagram of the PI control loop of the present invention;

[0038] Figure 4 The Bode diagram of the current loop of the 3.5MW permanent magnet synchronous motor after the PI control link of the present invention is corrected;

[0039] Figure 5 This is a corrected 3.5MW permanent magnet synchronous motor current closed-loop step response curve diagram of the present invention;

[0040] Figure 6 This is a current closed-loop step response curve diagram of a 3.5MW permanent magnet synchronous motor after correction by the present invention;

[0041] Figure 7 This is the current closed-loop impulse response curve of the 3.5MW permanent magnet synchronous motor after correction by the present invention. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] See also Figures 1 to 7 ,The first step: establish the mathematical model of the control object system and draw the system Bode diagram; take the permanent magnet synchronous motor current loop control in a 3MW wind turbine as an example.

[0044] Obtain the stator winding parameters L and R of the permanent magnet synchronous motor and establish a mathematical model. The model can be established through matlab or simulink, or by handwriting mathematical formulas:

[0045]

[0046] Simple programming modeling in Matlab, drawing the Bode diagram as shown in Figure (1).

[0047]

[0048] Considering the hysteresis effect of the control pulse PWM of the converter power device IGBT, the following rational formula can be used to replace the actual pulse hysteresis link:

[0049]

[0050] The rational linear hysteresis link model is simply written in Matlab as follows, where Td is the time value of the 1.5 PMW pulse locking response.

[0051] Gdly2=tf([Td^2-6*Td 12],[Td^26*Td 12]);

[0052] The mathematical model of the permanent magnet synchronous motor current loop under PWM pulse control is:

[0053]

[0054] In Matlab, simply write the following to complete the mathematical model of the permanent magnet synchronous motor current loop under PWM pulse control, and draw the Bode diagram comparison Figure 2 .

[0055] Gobj_a3=Gobj*Gdly2

[0056] hl=bodeplot(Gobj_a3,'r-',Gobj,'g--');

[0057] Step 2: Find the cutoff frequency and gain corresponding to the optimal phase margin of the controlled system in the Bode diagram.

[0058] Bode diagram of the control object system Figure 2 The amplitude in the object system crosses the frequency point where 0dB is located, and the phase φ of the object system is found and the current phase margin Pm=180+φ is obtained. In theory and engineering, Pm=45° is considered the best. If Pm is too large, it is necessary to calibrate it by connecting a PID link in series in the object system to make the phase margin of the object system around the optimal Pm.

[0059] In the bird diagram Figure 2 The phase φ at the cutoff frequency of the motor is found to be -114°, and the current phase margin Pm=66° is too large, indicating that the motor current loop control system needs to be optimized.

[0060] Step 3: Find the frequency point and corresponding gain where the optimal phase margin Pm=45° of the controlled system is located in the Bode diagram.

[0061] Simple programming in matlab to find the frequency of Pm. Adjust the frequency Freq in the code below and check the corresponding phase value phase in the Bode diagram of the controlled system in real time. When phase == -135°, the search for Pm is complete. At this time, the mag value is the gain corresponding to the optimal phase margin of the controlled system.

[0062] Frequency characteristics of %PM=45°

[0063] Fpm=834.6;%Hz

[0064] [mag,phase,rads]=bode(Gobj_a3,Fpm*2*pi);

[0065] Observing Bird Figure 2 It is known that the frequency of Pm=45° is 834.6Hz, the corresponding angular frequency is ω=132.8rad / s, and the corresponding amplitude gain is -5.27dB.

[0066] Step 4: Calculate and adjust the PI link control parameters Kp, Ki / Ti.

[0067] Figure 3 The Bode diagram is Kp = 1, Ti = 0.001s. In order to realize the optimal phase margin of the above 3.5MW permanent magnet synchronous motor current loop, it is necessary to adjust the PI parameters, adjust the gain at the frequency point corresponding to the current Pm of the control object by 1 (0dB), and have little effect on the current phase, so as to improve the stability of the rapid response of the control object system.

[0068] Bode diagram of the controlled system Figure 2 The gain corresponding to Pm is -5.27dB, and the proportional parameter Kp is calculated by the following formula:

[0069] 20lg(Kp)=5.27 (4)

[0070] K can be calculated p =1.834.

[0071] K p =1.834 is equivalent to adding 5.27dB of gain to the control system, so that the gain of the control system at the Pm frequency is adjusted to 0dB, that is, the amplitude gain is 1.

[0072] Observe the Bode plot of the PI link Figure 3 In the control curve, when τ i When ω=20, the phase lag caused by the PI controller is only 2.86°, which has little effect on the phase margin of the controlled system. This value can be selected to calculate the integral time. Then the integral parameter Ki is obtained as

[0073]

[0074] After adding the PI controller, the system Bode diagram of the controlled object is as follows: Figure 4 .

[0075] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A control system PI parameter engineering tuning method based on Bode diagram, characterized by: Step 1: Establish a mathematical model of the control object system and draw the system Bode diagram; obtain the stator winding parameters L and R of the permanent magnet synchronous motor and establish a mathematical model; the model is established through MATLAB: Programming modeling in MATLAB and drawing Bode diagrams; Simply write a rational linear lag link model in matlab; The mathematical model of the permanent magnet synchronous motor current loop under PWM pulse control is: Simply write the mathematical model of the permanent magnet synchronous motor current loop under PWM pulse control in Matlab, and draw the Bode diagram for comparison; Step 2: Find the cutoff frequency of the controlled system and the gain corresponding to the optimal phase margin in the Bode diagram; find the phase φ of the controlled system and obtain the current phase margin Pm=180+φ by passing the amplitude in the Bode diagram of the controlled system through the frequency point where 0dB is located; Pm=45° is the best in theory and engineering. If Pm is too large, it is necessary to calibrate it by connecting a PID link in series in the controlled system to make the phase margin of the controlled system around the optimal Pm; Step 3: Find the frequency point and corresponding gain of the optimal phase margin Pm=45° of the controlled system in the Bode diagram; Program in matlab to find the frequency of Pm; adjust the frequency in matlab and check the corresponding phase value phase in the Bode diagram of the control object system in real time. When phase=-135°, the search for Pm is completed; Observing the Bode diagram, we know that the frequency of Pm=45° is 834.6Hz, and the corresponding angular frequency is , the corresponding amplitude gain is -5.27dB; Step 4: Calculate and adjust the PI link control parameters Kp, Ki / Ti; The gain corresponding to Pm in the Bode diagram of the control object system is -5.27dB. The proportional parameter Kp is calculated by the following formula: Calculated ; This is equivalent to adding 5.27dB of gain to the control system, so that the gain of the control system at the Pm frequency is adjusted to 0dB, that is, the amplitude gain is 1; Observe the control curve in the Bode diagram of the PI link. When , the phase lag caused by the PI controller is only 2.86°, which has little effect on the phase margin of the controlled system. This value is selected to calculate the integral time , and then the integral parameter Ki is obtained as The system Bode diagram of the controlled object after adding the PI controller.

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