Stability margin configuration method for specifiedaccuracy PID control system
Stability margin configuration method for specifiedaccuracy PID control system
 CN 106,527,120 A
 Filed: 12/13/2016
 Published: 03/22/2017
 Est. Priority Date: 12/13/2016
 Status: Active Application
First Claim
1. a kind of collocation method of the PID control system stability margin with designated precision, its feature are comprised the following steps：
 S1, sets up the frequency characteristic model of the frequency characteristic model and PID controller of controlled device；
S2, according to specified crossover frequency ω
_{x}With magnitude margin A_{m}Require, calculate the proportional gain of PID controller；
S3, based on optimizing algorithm, search meets specifies Phase margin Φ
_{m}Cutoff frequency ω
_{c}；
S4, calculates the storage gain K of PID_{i}With differential gain K_{d}。
Chinese PRB Reexamination
Abstract
The present invention discloses a stability margin configuration method for a specifiedaccuracy PID control system. The method comprises the steps of firstly, establishing a frequency characteristics model of a controlled object; secondly, according to a specified openloop crossover frequency and a desired amplitude margin, calculating a proportional gain required by a PID controller; thirdly, according to the definition formula of a phase angle margin, searching an openloop cutoff frequency that meets the desired amplitude margin through the optimizing control algorithm; finally, according to a given formula, calculating the integral gain and the differential gain of the PID controller. Based on above three parameter values of the PID, the specified stability margin of the system is realized. According to the technical scheme of the invention, the difficulty of solving nonlinear equations is avoided through the analytic method. Therefore, the PID parameter setting is realized at the specified stability margin.

2 Citations
One kind being based on cutoff frequency control loop design method  
Patent #
CN 110,032,171 A
Filed 04/23/2019

Current Assignee

A kind of industry controlled process characteristic parameter Fast Identification Method  
Patent #
CN 108,594,676 A
Filed 04/04/2018

Current Assignee

6 Claims

1. a kind of collocation method of the PID control system stability margin with designated precision, its feature are comprised the following steps：

S1, sets up the frequency characteristic model of the frequency characteristic model and PID controller of controlled device； S2, according to specified crossover frequency ω
_{x}With magnitude margin A_{m}Require, calculate the proportional gain of PID controller；S3, based on optimizing algorithm, search meets specifies Phase margin Φ
_{m}Cutoff frequency ω
_{c}；S4, calculates the storage gain K of PID_{i}With differential gain K_{d}。


2. the PID control system stability margin degree collocation method with designated precision according to claim 1, its feature existIn：
 Frequency characteristic G of controlled device_{p}(j ω
) is：G_{p}(j ω
)=u (ω
)+jv (ω
) (1)In formula (1), j is imaginary symbols, and ω
is frequency, real parts of the u (ω
) for the frequency characteristic of controlled device, and v (ω
) is controlledThe imaginary part of the frequency characteristic of object；The frequency characteristic model of PID controller is： G_{c}(j ω
)=K_{p}+X(ω
)j (2)Wherein,For the imaginary part of the frequency characteristic of PID controller, K_{p}、
K_{i}And K_{d}It is expressed as PID controllerProportional gain, storage gain and the differential gain.
 Frequency characteristic G of controlled device_{p}(j ω

3. the PID control system stability margin collocation method with designated precision according to claim 1, its feature existIn：
The crossover frequency specified is ω
_{x}, then meet and specify magnitude margin A_{m}Proportional gain by formula (3) calculate：

4. the PID control system stability margin collocation method with designated precision according to claim 1, its feature existIn：
In step S3, it is intended that Phase margin be Φ
_{m}Meet nonlinear equation (4)：

5. the PID control system stability margin collocation method with designated precision according to claim 4, its feature existIn：

The cutoff frequency ω
of solving precision ε
is met using dichotomizing search_{c}, comprise the following steps：S001;
The region of search [ω
is set_{L} ω
_{R}], interval midpoint is taken for ω
_{c}=0.5 (ω
_{L}+ω
_{R})；S002;
By ω
_{c}Nonlinear equation (4) is updated to, the value on the right of nonlinear equation (4) is calculated；S003;
Judge the absolute value of difference of the value on nonlinear equation (4) left side and the value on the right whether less than default precision ε
；
Such asFruit is less than default precision ε
, based on gained ω
_{c}, then turn to step S4；
S004 is performed otherwise；S004;
If value is worth less than the left side on the right of nonlinear equation (4), ω
is taken_{L}=ω
_{c}；
Conversely, ω
_{R}=ω
_{c}；
Return S001.


6. the PID control system stability margin collocation method with designated precision according to claim 1, its feature existIn：
 The storage gain K of PID controller described in step S4_{i}With differential gain K_{d}Calculated based on formula (6)：
 The storage gain K of PID controller described in step S4_{i}With differential gain K_{d}Calculated based on formula (6)：
Specification(s)