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CN113515037B - Improved PID controller parameter setting method for model-free system - Google Patents

Improved PID controller parameter setting method for model-free system Download PDF

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CN113515037B
CN113515037B CN202110885844.9A CN202110885844A CN113515037B CN 113515037 B CN113515037 B CN 113515037B CN 202110885844 A CN202110885844 A CN 202110885844A CN 113515037 B CN113515037 B CN 113515037B
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pid controller
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CN113515037A (en
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尹子栋
唐斌
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Chengdu Aeronautic Polytechnic
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
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Abstract

The invention provides an improved PID controller parameter setting method without a model system, which belongs to the technical field of industrial control, and comprises the steps of giving the preliminary differential gain of a PID controller and taking the value of the preliminary proportional gain of the PID controller; giving the global scaling factor and the integral gain scaling factor of the PID controller to determine the value of the PID controller parameter of the model-free system; and (3) initially operating the controlled system of the step input signal, and correspondingly adjusting integral gain scaling factors, preliminary differential gain and/or global scaling parameters of the PID controller according to a response error curve and expected transient response overshoot, steady state error and response time of the system to finish parameter setting of the PID controller. The invention is not only suitable for PID controller parameter setting of known/unknown linear system, but also suitable for PID controller parameter setting of unknown nonlinear system.

Description

Improved PID controller parameter setting method for model-free system
Technical Field
The invention belongs to the technical field of industrial control, and particularly relates to an improved PID controller parameter setting method of a model-free system.
Background
For mechanical systems, the dynamics equation generally follows newton's law of motion, and can be described by a second order system, such as an unmanned aerial vehicle/unmanned vehicle control system. However, the mathematical model of the controlled object is generally simplified and linearized, and may be greatly different from the actual product. Moreover, it may also be affected by unknown unmodeled disturbances outside or inside the system. In actual PID controller parameter tuning and controller design, it is necessary to take into account the impact of the unmodeled parts missing due to simplification and linearization on the control system. Meanwhile, the influence of external unknown interference on the controlled object also needs to be considered.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an improved PID controller parameter setting method of a model-free system, which aims to solve the problem of controller parameter setting under the condition that the mathematical model of a controlled object is inaccurate or has stronger nonlinearity.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the scheme provides an improved PID controller parameter setting method of a model-free system, which comprises the following steps:
s1, giving preliminary differential gain of PID controller
Figure GDA0003229351910000011
And taking the preliminary proportional gain of the PID controller according to the preliminary differential gain>
Figure GDA0003229351910000012
Wherein%>
Figure GDA0003229351910000013
S2, giving global scaling factor n of PID controller s And integral gain scaling factor n i Wherein n is s ≥1、
Figure GDA0003229351910000014
S3, according to the preliminary differential gain
Figure GDA0003229351910000021
Preliminary proportional gain->
Figure GDA0003229351910000022
Integral gain scaling factor n i Global scaling factor n s Respectively calculating to obtain differential gain, proportional gain and integral gain of the PID controller;
s4, initially operating the controlled system based on the differential gain, the proportional gain and the integral gain of the PID controller, and checking a response error curve of the controlled system;
s5, combining a response error curve of the controlled system with expected transient response overshoot sigma% and steady state error e of the system s % and response time t r Adjusting the global scaling parameter, the integral gain scaling parameter, the preliminary differential gain and the preliminary proportional gain;
and S6, judging whether the response error curve meets the preset condition according to the adjustment result, if so, finishing the adjustment of the parameters of the PID controller, otherwise, returning to the step S3.
The beneficial effects of the invention are as follows: the invention provides an improved parameter setting method for a second-order system by adopting a PID controller, which is suitable for setting the parameters of the PID controller of a known/unknown linear system and the parameters of the PID controller of an unknown nonlinear system. The uncertainty of the unknown linear or nonlinear modeling part in the system in parameter setting can be rapidly and conveniently dealt with.
Further, in the step S1, the proportional gain of the PID controller is obtained
Figure GDA0003229351910000023
The expression of (2) is as follows:
Figure GDA0003229351910000024
wherein,,
Figure GDA0003229351910000025
represents the preliminary proportional gain of the PID controller, ζ is a dimensionless constant whose initial value can be set to 1 for adjusting the preliminary proportional gain +.>
Figure GDA0003229351910000026
Value of->
Figure GDA0003229351910000027
Representing the preliminary derivative gain of the PID controller.
Still further, the expressions of the differential gain, the proportional gain and the integral gain of the PID controller in the step S2 are as follows:
Figure GDA0003229351910000028
wherein K is p Represents the proportional gain, K, of the PID controller d Represents the differential gain, K, of the PID controller i Indicating the integral gain of the PID controller,
Figure GDA0003229351910000031
represents the preliminary proportional gain of the PID controller, +.>
Figure GDA0003229351910000032
Representing the preliminary differential gain, n, of the PID controller s Representing the global scaling factor of a PID controller, n i Representing the integral gain scaling factor of the PID controller.
The beneficial effects of the above-mentioned further scheme are: the proportional gain, the differential gain and the integral gain of the PID controller are disassembled from the transient response overshoot sigma% expected by the controlled system, and the steady-state error e s % and response time t r Is convenient for the rapid setting of the parameters of the PID controller.
Still further, the step S5 includes the following ways:
the first way is:
when the overshoot sigma% of the response error curve needs to be reduced, the integral gain scaling parameter n is increased i When the overshoot sigma% of the response error curve is to be increased, the integral gain scaling parameter n is reduced i Is a value of (2);
the second way is:
when the steady state error e of the controlled system needs to be reduced s % is then increased by the preliminary differential gain
Figure GDA0003229351910000033
Or global scaling parameter n s When the steady state error e of the controlled system needs to be increased s % is the preliminary differential gain is reduced +.>
Figure GDA0003229351910000034
Or global scaling parameter n s Is based on the value of (1) at the same time of the preliminary proportional gain +.>
Figure GDA0003229351910000035
The expression of (2) adjusts the preliminary proportional gain +.>
Figure GDA0003229351910000036
Wherein ζ=1;
third mode:
when the need is reducedResponse time t of control system r When the preliminary differential gain is increased
Figure GDA0003229351910000037
And/or global scaling parameter n s When the response time t of the controlled system needs to be increased r At the time, the preliminary differential gain is reduced>
Figure GDA0003229351910000038
Value or local scaling parameter n s Is based on the value of (1) at the same time of the preliminary proportional gain +.>
Figure GDA0003229351910000039
The expression of (2) adjusts the preliminary proportional gain +.>
Figure GDA00032293519100000310
Where ζ=1.
The beneficial effects of the above-mentioned further scheme are: the transient response overshoot sigma and steady state error e of the controlled system are defined s % and response time t r And the relation and the adjustment method of the global scaling parameter, the integral gain scaling coefficient, the preliminary differential gain and the preliminary proportional gain realize the rapid setting of the PID controller parameter which accords with the expected response performance of the known/unknown linear/nonlinear controlled system.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of the PID control simulation result of example 1 in the present embodiment.
Fig. 3 is a diagram showing the simulation result of the PID control of example 2 in the present embodiment.
Fig. 4 is a diagram showing the simulation result of the PID control of example 3 in the present embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
Examples
Taking a controlled object as a second-order system and being interfered as an example, the controlled object can be described by using the following mathematical model:
Figure GDA0003229351910000041
wherein f 0 Is a known modeling part of the system, and when using a PID controller, its control law model is as follows:
Figure GDA0003229351910000042
wherein, parameter K p ,K i ,K d Is the key to design PID control laws. Therefore, two problems exist when a PID controller is adopted, 1) the stability of the system is not easy to realize by setting parameters; 2) Obtaining the desired transient control performance and steady state error requires a significant amount of time to perform parameter trial and error. The invention provides a PID parameter rapid setting method for a second-order system as a control object aiming at the problems, which is suitable for setting the parameters of a PID controller of a known/unknown linear system and the parameters of a PID controller of an unknown nonlinear system. As shown in fig. 1, the present invention provides an improved method for setting parameters of a PID controller of a model-free system, which is implemented as follows:
s1, giving preliminary differential gain of PID controller
Figure GDA0003229351910000051
And taking the proportional gain of the PID controller according to the preliminary differential gain>
Figure GDA0003229351910000052
Wherein%>
Figure GDA0003229351910000053
Wherein the proportional gain of the PID controller is taken>
Figure GDA0003229351910000054
The expression of (2) is as follows:
Figure GDA0003229351910000055
wherein,,
Figure GDA0003229351910000056
represents the preliminary proportional gain of the PID controller, ζ is a dimensionless constant whose initial value can be set to 1 for adjusting the preliminary proportional gain +.>
Figure GDA0003229351910000057
Value of->
Figure GDA0003229351910000058
Representing the preliminary differential gain of the PID controller, i.e. taking the preliminary proportional gain +.>
Figure GDA0003229351910000059
About preliminary differential gain->
Figure GDA00032293519100000510
About 1/4 times square.
S2, giving global scaling factor n of PID controller s And integral gain scaling factor n i Wherein n is s ≥1、
Figure GDA00032293519100000511
S3, according to the preliminary differential gain
Figure GDA00032293519100000512
Preliminary proportional gain->
Figure GDA00032293519100000513
Integral gain scaling factor n i Global scaling factor n s And respectively calculating to obtain the differential gain, the proportional gain and the integral gain of the PID controller, wherein the expressions of the differential gain, the proportional gain and the integral gain of the PID controller are as follows:
Figure GDA00032293519100000514
wherein K is p Represents the proportional gain, K, of the PID controller d Represents the differential gain, K, of the PID controller i Indicating the integral gain of the PID controller,
Figure GDA00032293519100000515
represents the preliminary proportional gain of the PID controller, +.>
Figure GDA00032293519100000516
Representing the preliminary differential gain, n, of the PID controller s Representing the global scaling factor of a PID controller, n i Representing an integral gain scaling factor of the PID controller;
s4, initially operating the controlled system based on the differential gain, the proportional gain and the integral gain of the PID controller, and checking a response error curve of the controlled system;
in this embodiment, the controlled system is initially operated, the step response or other response is observed, and the system response error curve is checked.
S5, combining a response error curve of the controlled system with expected transient response overshoot sigma% and steady state error e of the system s % and response time t r Adjusting the global scaling parameter, the integral gain scaling parameter, the preliminary differential gain, and the preliminary proportional gain, comprising:
the first way is:
when the overshoot sigma% of the response error curve needs to be reduced, the integral gain scaling parameter n is increased i When the overshoot sigma% of the response error curve is to be increased, then the value of (2) is decreasedIntegral gain scaling parameter n i Is a value of (2);
the second way is:
when the steady state error e of the controlled system needs to be reduced s % is then increased by the preliminary differential gain
Figure GDA0003229351910000061
Or global scaling parameter n s When the steady state error e of the controlled system needs to be increased s % is the preliminary differential gain is reduced +.>
Figure GDA0003229351910000062
Or global scaling parameter n s Is based on the value of (1) at the same time of the preliminary proportional gain +.>
Figure GDA0003229351910000063
The expression of (2) adjusts the preliminary proportional gain +.>
Figure GDA0003229351910000064
Wherein ζ=1;
third mode:
when the response time t of the controlled system needs to be reduced r When the preliminary differential gain is increased
Figure GDA0003229351910000065
And/or global scaling parameter n s When the response time t of the controlled system needs to be increased r At the time, the preliminary differential gain is reduced>
Figure GDA0003229351910000066
Value or local scaling parameter n s Is based on the value of (1) at the same time of the preliminary proportional gain +.>
Figure GDA0003229351910000067
The expression of (2) adjusts the preliminary proportional gain +.>
Figure GDA0003229351910000068
Where ζ=1.
It should be noted that the above three modes are not separated in succession and can be selected according to the situation.
In this embodiment, the integral gain scaling parameter n is appropriately increased or decreased according to the PID controller parameter value rule i To reduce or increase the system transient response overshoot sigma% of the PID control.
In this embodiment, the preliminary differential gain is appropriately increased or decreased according to the PID controller parameters and the proportional gain value rule
Figure GDA0003229351910000071
Or global scaling parameter n s 1 to reduce or increase steady state error e of the system s ％。
In this embodiment, the preliminary differential gain is appropriately increased or decreased according to the controller parameters and the proportional gain value rule
Figure GDA0003229351910000072
Or global scaling parameter n s 1 to reduce or increase the response time t of the system r 。
And S6, judging whether a response error curve of the controlled system meets preset conditions according to the adjustment result, if so, finishing the adjustment of the parameters of the PID controller, otherwise, returning to the step S3.
In this embodiment, the global scaling parameter, the integral gain scaling parameter, the preliminary differential gain and the preliminary proportional gain are adjusted in step S5, and the adjustment can be performed after the comparison in step S6.
In summary, the method includes disassembling proportional gain, differential gain and integral gain of the PID controller into a combination form of preliminary differential gain, preliminary proportional gain, integral gain scaling factor and global scaling factor, specifically, preliminary differential gain of a given PID controller, and taking the value of the preliminary proportional gain of the PID controller; giving the global scaling factor and the integral gain scaling factor of the PID controller to determine the values of the PID controller parameters (proportional gain, differential gain and integral gain) of the model-free system; controlled system for initially operating step input signal and based on response errorCurve and expected transient response overshoot sigma% and steady state error e of system s % and response time t r And correspondingly adjusting integral gain scaling factors, preliminary differential gains and/or global scaling parameters of the PID controller to finish the parameter setting of the PID controller. The invention is not only suitable for PID controller parameter setting of known/unknown linear system, but also suitable for PID controller parameter setting of unknown nonlinear system.
The invention is further illustrated by the following examples.
Example 1
The second order system mathematical model of a control object is as follows:
Figure GDA0003229351910000073
wherein the unknown interference term is
Figure GDA0003229351910000081
w 2 (t) =1.5 sin (0.5 t). The tuning was performed using the set 5 PID parameters shown in table 1, and the results are shown in fig. 2, and fig. 2 is a diagram showing the simulation results of PID control, wherein fig. 2 (b) is a partial enlarged view of the simulation results of PID control.
TABLE 1
Figure GDA0003229351910000082
Example 2
The second order systematic mathematical model of a control object (unmanned aerial vehicle altitude control taking ground effect into account) is as follows:
Figure GDA0003229351910000083
wherein r=0.20 is the propeller diameter; z r ＝0.32+x 1 Is the ground clearance of the propeller; ρ=8.4 is a pending parameter related to the unmanned structure. The tuning was performed using 6 sets of PID parameters as shown in table 2, the results of which are shown in fig. 3, wherein,FIG. 3 (b) is a partial enlarged view of the simulation result of PID control.
TABLE 2
Figure GDA0003229351910000084
Figure GDA0003229351910000091
Example 3
The second order systematic mathematical model of a control object (unmanned aerial vehicle altitude control taking ground effect into account) is as follows:
Figure GDA0003229351910000092
wherein r=0.20 is the propeller diameter; z r ＝0.32+x 1 Is the ground clearance of the propeller; ρ=8.4 is a pending parameter related to the unmanned structure. Unknown interference term is
Figure GDA0003229351910000093
w 2 (t) =1.5 sin (0.5 t), and the sensor had white noise, and was set using the 6 sets of PID parameters shown in table 3, the result is shown in fig. 4, where fig. 4 (b) is a partial enlarged view of the PID control simulation result.
TABLE 3 Table 3
Figure GDA0003229351910000094
In this embodiment, a second-order system mathematical model of a certain control object (unmanned aerial vehicle altitude control considering ground effect) is as follows:
Figure GDA0003229351910000095
wherein r=0.20 is the propeller diameter; z is Z r ＝0.32+x 1 Is a screw propellerGround clearance height; ρ=8.4 is a pending parameter related to the unmanned structure. Unknown interference term is
Figure GDA0003229351910000101
w 2 (t) =1.5 sin (0.5 t), and the sensor has white noise. If the model is part of the content known, < + >>
Figure GDA0003229351910000102
And the sensor has white noise. Wherein (1)>
Figure GDA0003229351910000103

Claims (4)

1. An improved PID controller parameter tuning method for a model-free system, comprising the steps of:
s1, giving preliminary differential gain of PID controller
Figure FDA0003194069950000011
And taking the preliminary proportional gain of the PID controller according to the preliminary differential gain>
Figure FDA0003194069950000012
Wherein%>
Figure FDA0003194069950000013
S2, giving global scaling factor n of PID controller s And integral gain scaling factor n i Wherein n is s ≥1、
Figure FDA0003194069950000014
S3, according to the preliminary differential gain
Figure FDA0003194069950000015
Preliminary proportional gain->
Figure FDA0003194069950000016
Integral gain scaling factor n i Global scaling factor n s Respectively calculating to obtain differential gain, proportional gain and integral gain of the PID controller;
s4, initially operating the controlled system based on the differential gain, the proportional gain and the integral gain of the PID controller, and checking a response error curve of the controlled system;
s5, combining a response error curve of the controlled system with expected transient response overshoot sigma% and steady state error e of the system s % and response time t r Adjusting the global scaling parameter, the integral gain scaling parameter, the preliminary differential gain and the preliminary proportional gain;
and S6, judging whether a response error curve of the controlled system meets preset conditions according to the adjustment result, if so, finishing the adjustment of the parameters of the PID controller, otherwise, returning to the step S3.
2. The method for tuning parameters of a PID controller of an improved model-free system according to claim 1, wherein in step S1, a preliminary proportional gain of the PID controller is taken
Figure FDA0003194069950000017
The expression of (2) is as follows:
Figure FDA0003194069950000018
wherein,,
Figure FDA0003194069950000019
represents the preliminary proportional gain of the PID controller, ζ is a dimensionless constant whose initial value can be set to 1 for adjusting the preliminary proportional gain +.>
Figure FDA00031940699500000110
Value of->
Figure FDA00031940699500000111
Representing the preliminary derivative gain of the PID controller.
3. The improved model-free system PID controller parameter tuning method according to claim 2, wherein the expression of the differential gain, the proportional gain and the integral gain of the PID controller in step S2 is as follows:
Figure FDA0003194069950000021
wherein K is p Represents the proportional gain, K, of the PID controller d Represents the differential gain, K, of the PID controller i Indicating the integral gain of the PID controller,
Figure FDA0003194069950000022
represents the preliminary proportional gain of the PID controller, +.>
Figure FDA0003194069950000023
Representing the preliminary differential gain, n, of the PID controller s Representing the global scaling factor of a PID controller, n i Representing the integral gain scaling factor of the PID controller.
4. The method for tuning the parameters of a PID controller of an improved model-free system according to claim 3, wherein said step S5 comprises the following steps:
the first way is:
when the transient response overshoot sigma% of the response error curve needs to be reduced, the integral gain scaling parameter n is increased i When the transient response overshoot sigma% of the response error curve needs to be increased, the integral gain scaling parameter n is reduced i Is a value of (2);
the second way is:
when the steady state error e of the controlled system needs to be reduced s % is increased by preliminary differential increaseBenefit (benefit)
Figure FDA0003194069950000024
Or global scaling parameter n s When the steady state error e of the controlled system needs to be increased s % is the preliminary differential gain is reduced +.>
Figure FDA0003194069950000025
Or global scaling parameter n s Is based on the value of (1) at the same time of the preliminary proportional gain +.>
Figure FDA0003194069950000026
The expression of (2) adjusts the preliminary proportional gain +.>
Figure FDA0003194069950000027
Wherein ζ=1;
third mode:
when the response time t of the controlled system needs to be reduced r When the preliminary differential gain is increased
Figure FDA0003194069950000028
And/or global scaling parameter n s When the response time t of the controlled system needs to be increased r At the time, the preliminary differential gain is reduced>
Figure FDA0003194069950000029
Value or local scaling parameter n s Is based on the value of (1) at the same time of the preliminary proportional gain +.>
Figure FDA00031940699500000210
The expression of (2) adjusts the preliminary proportional gain +.>
Figure FDA00031940699500000211
Where ζ=1.
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