CN114740709A - Bode diagram-based control system PI parameter engineering setting method - Google Patents
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Abstract
The invention discloses a Bode diagram-based control system PI parameter engineering setting method, which comprises the following steps: establishing a mathematical model of a control object system, drawing a system bode diagram, and a second step: finding out the gain corresponding to the cut-off frequency and the optimal phase margin of the control object system in the Bode diagram; the third step: finding a frequency point and a corresponding gain where the optimal phase margin Pm of the control object system is 45 degrees in the Berde diagram, and the fourth step: calculating and setting PI link control parameters Kp, Ki/Ti; the Bode diagram-based control system PI parameter engineering setting method can be seen from a current closed loop step response curve, and the control performance of a plateau system can be improved by matching PI parameters with the optimal phase angle margin PM (phase angle) of 45 degrees on the Bode diagram; the method is visual and simple and is worthy of popularization.
Description
Technical Field
The invention belongs to the technical field of control systems based on Bode diagrams, and particularly relates to a PI parameter engineering setting method of a control system based on the Bode diagrams.
Background
In a control system, the classical control mode PID is widely applied and is very effective, but the setting of control parameters in a PID control link always causes great headache for engineering personnel because on one hand, the operation mechanism and the control model of a control object need to be mastered, and on the other hand, professional knowledge of the automatic control principle is also needed. In the practical application process, the operation parameters of the PID control link are divided into two groups, firstly, theoretical calculation is carried out according to the control model of the whole control system, secondly, a trial and error method is adopted in the practical engineering, three parameters of the PID are manually adjusted, and whether the PID parameters are proper or not is judged according to the response result of the system. The theoretical calculation of PID parameters relates to a plurality of fields, needs abundant field control experience, and has long debugging process of a trial and error method and possible poor debugging.
Disclosure of Invention
The invention aims to provide a Bode diagram-based PI parameter engineering setting method for a control system, which analyzes the frequency characteristic of the system through the Bode diagram of the control system and finds out the phase and gain corresponding to the optimal phase angle margin of the control system in the diagram; adjusting the gain of the frequency point where the optimal phase angle margin of the control system is located to be 1 (lossless gain) by matching with a proper PI proportional parameter Kp; matching the frequency with the minimum influence on the optimal phase angle margin through a Berde diagram of a PI control link, and calculating the response integral time Ti according to the frequency to further obtain a PI integral parameter Ki.
In order to achieve the purpose, the invention provides the following technical scheme: a method for adjusting PI parameter engineering of a control system based on a Bode diagram comprises the following steps: establishing a mathematical model of a control object system, and drawing a system Bode diagram; obtaining stator winding parameters L and R of the permanent magnet synchronous motor, and establishing a mathematical model; the model can be established through matlab or simulink, and can also be completed through a handwritten mathematical formula:
simple programming modeling in matlab, and drawing a Bode diagram;
the rational linear hysteresis link model is completed by simply writing in matlab as follows;
Gdly2＝tf([Td^2-6*Td 12],[Td^26*Td 12])；
the mathematical model of the current loop of the permanent magnet synchronous motor under the control of the PWM pulse is as follows:
in matlab, a mathematical model of a current loop of the permanent magnet synchronous motor under PWM pulse control is simply compiled as follows, and Bode diagram comparison is drawn;
Gobj_a3＝Gobj*Gdly2
hl＝bodeplot(Gobj_a3,'r-',Gobj,'g--')；
step two: finding out the gain corresponding to the cut-off frequency and the optimal phase margin of the control object system in the Bode diagram; finding the phase phi of the object system and obtaining the current phase margin Pm which is 180+ phi by controlling the frequency point where the amplitude in the Burde diagram of the object system crosses 0 dB; the optimal Pm is 45 degrees in theory and engineering, if the Pm is too large, a PID link is required to be connected in series in the object system for correction, and the phase margin of the object system is about the optimal Pm;
step three: searching a frequency point where the optimal phase margin Pm of the control object system is 45 degrees and a corresponding gain in the Berde graph;
simple programming in matlab finds the frequency of Pm; adjusting frequency Freq in the code below, and checking a corresponding phase value phase in a control object system Boolean graph in real time, and finishing searching Pm when the phase is-135 degrees; at this time, the mag value is the gain corresponding to the optimal phase margin of the control object system;
frequency characteristic of 45 DEG PM%
Fpm＝834.6；％Hz
[mag,phase,rads]＝bode(Gobj_a3,Fpm*2*pi)；
Observing the bode diagram, the frequency of Pm is 834.6Hz when the Pm is 45 degrees, the corresponding angular frequency is omega 132.8rad/s, and the corresponding amplitude gain is-5.27 dB;
step four: calculating and setting PI link control parameters Kp, Ki/Ti;
in order to realize the current loop of the permanent magnet synchronous motor in the optimal phase margin, the gain of the frequency point corresponding to the current Pm of the control object is adjusted by 1(0dB) by adjusting the PI parameter, and the influence on the current phase is not large, so that the stability of the quick response of the control object system is improved;
the gain corresponding to Pm in the Boolean diagram of the controlled object system is-5.27 dB, and the proportional parameter Kp is calculated by the following formula
20lg(Kp)＝5.27
K can be calculatedp＝1.834；
Kp1.834 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, namely the amplitude gain is 1;
observing the control curve in the bode diagram of the PI link when tauiWhen ω is 20, the phase lag by the PI controller is only 2.86 °, and the influence on the phase margin of the control target system is small, and the integration time can be calculated by this value
Further, an integral parameter Ki of
And after the PI controller is added, controlling the system Bode diagram of the object.
Preferably, in consideration of the hysteresis effect of the control pulse PWM of the converter power device IGBT, the actual pulse hysteresis may be replaced by the following rational equation:
preferably, Td in the rational linear hysteresis loop model of the first step is a time value corresponding to locking of 1.5 PMW pulses
Compared with the prior art, the invention has the beneficial effects that: the Bode diagram-based control system PI parameter engineering setting method can be seen from a current closed loop step response curve, and the control performance of a plateau system can be improved by matching PI parameters with the optimal phase angle margin PM (phase angle) of 45 degrees on the Bode diagram; the method is visual and simple and is worthy of popularization.
Drawings
FIG. 1 is a Bode diagram of a 3.5MW PMSM current loop according to the present invention;
FIG. 2 is a Bode plot of the current loop of a 3.5MW PMSM under the influence of 1.5 × TPWM cycle hysteresis according to the present invention;
FIG. 3 is a PI control loop bode diagram of the present invention;
FIG. 4 is a Bode diagram of a current loop of a 3.5MW PMSM after PI control link correction according to the present invention;
FIG. 5 is a graph of the current closed loop step response of the corrected 3.5MW PMSM of the present invention;
FIG. 6 is a graph of the current closed loop step response of the 3.5MW PMSM after correction according to the present invention;
FIG. 7 is a current closed-loop impulse response curve of the 3.5MW PMSM corrected by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 to 7, the first step is: establishing a mathematical model of a control object system, and drawing a system Bode diagram; take the permanent magnet synchronous motor current loop control in a 3MW wind generator as an example.
And obtaining stator winding parameters L and R of the permanent magnet synchronous motor, and establishing a mathematical model. The model can be established through matlab or simulink, and can also be completed through a handwritten mathematical formula:
simple programming modeling in matlab draws a bode plot as in fig (1).
Considering the hysteresis effect of the control pulse PWM of the converter power device IGBT, the following rational formula can be used for replacing the actual pulse hysteresis link:
the rational linear hysteresis model is completed in matlab by simply programming as follows, where Td is the time value that 1.5 PMW pulses should lock onto.
Gdly2＝tf([Td^2-6*Td 12],[Td^26*Td 12])；
The mathematical model of the current loop of the permanent magnet synchronous motor under the control of the PWM pulse is as follows:
a mathematical model of a permanent magnet synchronous motor current loop under PWM pulse control is simply written in matlab as follows, and a Bode diagram pair is drawn, such as the graph in FIG. 2.
Gobj_a3＝Gobj*Gdly2
hl＝bodeplot(Gobj_a3,'r-',Gobj,'g--')；
The second step is that: and finding the gain corresponding to the cut-off frequency and the optimal phase margin of the control object system in the Bode diagram.
And finding the phase phi of the object system and obtaining the current phase margin Pm which is 180+ phi by controlling the frequency point of the object system Burde diagram in FIG. 2 where the amplitude crosses 0 dB. In theory and engineering, the optimal Pm is 45 degrees, if the Pm is too large, a PID link is connected in series in an object system to correct the Pm, so that the phase margin of the object system is about the optimal Pm.
The phase phi at the cut-off frequency of the motor is found in figure 2, and the current phase margin Pm is larger than 66 degrees, which indicates that the motor current loop control system needs to be optimized.
The third step: and searching a frequency point and a corresponding gain at which the optimal phase margin Pm of the control object system is 45 degrees in the Berde diagram.
Simple programming in matlab looks for the frequency of Pm. Adjusting frequency Freq in the following codes, and looking up corresponding phase value phase in a control object system Booth graph in real time, and finishing searching Pm when the phase is-135 degrees. In this case, the mag value is a gain corresponding to the optimal phase margin of the control target system.
Frequency characteristic of 45 DEG PM%
Fpm＝834.6；％Hz
[mag,phase,rads]＝bode(Gobj_a3,Fpm*2*pi)；
Looking at bode fig. 2, it is known that Pm is 45 ° at 834.6Hz, corresponding to an angular frequency ω of 132.8rad/s, and corresponding to an amplitude gain of-5.27 dB.
The fourth step: and calculating and setting PI link control parameters Kp, Ki/Ti.
Fig. 3 shows a bode diagram of Kp 1 and Ti 0.001 s. In order to realize the current loop of the 3.5MW permanent magnet synchronous motor in the optimal phase margin, the gain of the current Pm of the control object at the corresponding frequency point is adjusted by 1(0dB) by adjusting the PI parameter, and the influence on the current phase is not large, so that the stability of the quick response of the control object system can be improved.
The gain corresponding to Pm in the Burde diagram of the controlled object system in FIG. 2 is-5.27 dB, and the proportional parameter Kp is calculated by the following formula
20lg(Kp)＝5.27 (4)
K can be calculatedp＝1.834。
Kp1.834 corresponds 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, i.e. the amplitude gain is 1.
Observe the control curve in FIG. 3 of Bode diagram of PI element when τ isiWhen ω is 20, the phase lag by the PI controller is only 2.86 °, and the influence on the phase margin of the control target system is small, and the integration time can be calculated by this value
Further, an integral parameter Ki of
After the PI controller is added, the system Bode diagram of the control object is shown in FIG. 4.
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 alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (3)
1. A control system PI parameter engineering setting method based on Bode diagram is characterized in that: the method comprises the following steps: establishing a mathematical model of a control object system, and drawing a system bode diagram; obtaining stator winding parameters L and R of the permanent magnet synchronous motor, and establishing a mathematical model; the model can be established through matlab or simulink, and can also be completed through a handwritten mathematical formula:
simple programming modeling in matlab, and drawing a Bode diagram;
the rational linear hysteresis link model is completed by simply writing in matlab as follows;
Gdly2＝tf([Td^2-6*Td 12],[Td^26*Td 12])；
the mathematical model of the current loop of the permanent magnet synchronous motor under the control of the PWM pulse is as follows:
in matlab, a mathematical model of a current loop of the permanent magnet synchronous motor under PWM pulse control is simply compiled as follows, and Bode diagram comparison is drawn;
Gobj_a3＝Gobj*Gdly2
hl＝bodeplot(Gobj_a3,'r-',Gobj,'g--')；
step two: finding out the gain corresponding to the cut-off frequency and the optimal phase margin of the control object system in the Bode diagram; finding the phase phi of the object system and obtaining the current phase margin Pm which is 180+ phi by controlling the frequency point where the amplitude in the Burde diagram of the object system crosses 0 dB; the optimal Pm is 45 degrees in theory and engineering, if the Pm is too large, a PID link is required to be connected in series in the object system for correction, and the phase margin of the object system is about the optimal Pm;
step three: searching a frequency point where the optimal phase margin Pm of the control object system is 45 degrees and a corresponding gain in the Berde graph;
simple programming in matlab finds the frequency of Pm; adjusting frequency Freq in the code below, and checking a corresponding phase value phase in a control object system Boolean graph in real time, and finishing searching Pm when the phase is-135 degrees; at this time, the mag value is the gain corresponding to the optimal phase margin of the control object system;
frequency characteristic of 45 DEG PM%
Fpm＝834.6；％Hz
[mag,phase,rads]＝bode(Gobj_a3,Fpm*2*pi)；
Observing the bode diagram, the frequency of Pm is 834.6Hz when the Pm is 45 degrees, the corresponding angular frequency is omega 132.8rad/s, and the corresponding amplitude gain is-5.27 dB;
step four: calculating and setting PI link control parameters Kp, Ki/Ti;
in order to realize the current loop of the permanent magnet synchronous motor in the optimal phase margin, the gain of the frequency point corresponding to the current Pm of the control object is adjusted by 1(0dB) by adjusting the PI parameter, and the influence on the current phase is not large, so that the stability of the quick response of the control object system is improved;
the gain corresponding to Pm in the Boolean diagram of the controlled object system is-5.27 dB, and the proportional parameter Kp is calculated by the following formula
20lg(Kp)＝5.27
K can be calculatedp＝1.834；
Kp1.834 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, namely the amplitude gain is 1;
observing the control curve in the Bode diagram of PI link when tau isiWhen ω is 20, the phase lag by the PI controller is only 2.86 °, and the influence on the phase margin of the controlled system is small, and the integration time can be calculated by selecting this value
Further, an integral parameter Ki of
And after the PI controller is added, controlling the system Bode diagram of the object.
2. The bode-plot-based control system PI parameter engineering tuning method of claim 1, wherein: considering the hysteresis effect of the control pulse PWM of the converter power device IGBT, the following rational formula can be used for replacing the actual pulse hysteresis link:
3. the bode-plot-based control system PI parameter engineering tuning method of claim 1, wherein: td in the rational linear hysteresis loop model of the first step is a time value corresponding to locking of 1.5 PMW pulses.
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| JP2001249703A (en) * | 2000-03-07 | 2001-09-14 | Toshiba It & Control Systems Corp | Pid controller |
| WO2018148906A1 (en) * | 2017-02-16 | 2018-08-23 | 深圳市大疆灵眸科技有限公司 | Method of configuring mounting device parameter, device, and mounting device |
| CN109459927A (en) * | 2019-01-16 | 2019-03-12 | 中国科学院光电技术研究所 | PID controller parameter setting method based on neural network |
| CN110737196A (en) * | 2019-10-31 | 2020-01-31 | 中国电子科技集团公司第四十三研究所 | design method of digital power supply loop compensator based on PID α |
| CN112415897A (en) * | 2020-11-30 | 2021-02-26 | 北京罗克维尔斯科技有限公司 | Control system optimization method, device, system, vehicle, medium and equipment |
| US20210124315A1 (en) * | 2018-08-03 | 2021-04-29 | Foshan University | Method For Designing PID Controller (as amended) |
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Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2001249703A (en) * | 2000-03-07 | 2001-09-14 | Toshiba It & Control Systems Corp | Pid controller |
| WO2018148906A1 (en) * | 2017-02-16 | 2018-08-23 | 深圳市大疆灵眸科技有限公司 | Method of configuring mounting device parameter, device, and mounting device |
| US20210124315A1 (en) * | 2018-08-03 | 2021-04-29 | Foshan University | Method For Designing PID Controller (as amended) |
| CN109459927A (en) * | 2019-01-16 | 2019-03-12 | 中国科学院光电技术研究所 | PID controller parameter setting method based on neural network |
| CN110737196A (en) * | 2019-10-31 | 2020-01-31 | 中国电子科技集团公司第四十三研究所 | design method of digital power supply loop compensator based on PID α |
| CN112415897A (en) * | 2020-11-30 | 2021-02-26 | 北京罗克维尔斯科技有限公司 | Control system optimization method, device, system, vehicle, medium and equipment |
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