CN107102556A - A kind of method and apparatus for obtaining pseudo- three ranks inertial element - Google Patents

A kind of method and apparatus for obtaining pseudo- three ranks inertial element Download PDF

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CN107102556A
CN107102556A CN201710494581.2A CN201710494581A CN107102556A CN 107102556 A CN107102556 A CN 107102556A CN 201710494581 A CN201710494581 A CN 201710494581A CN 107102556 A CN107102556 A CN 107102556A
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mrow
msub
mfrac
filter
present count
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李军
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Electric Power Research Institute of Guangdong Power Grid Co Ltd
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Electric Power Research Institute of Guangdong Power Grid Co Ltd
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Abstract

The embodiment of the invention discloses a kind of method and apparatus for obtaining pseudo- three ranks inertial element, during for solving automatic disturbance rejection controller being used for across rank control, there is the technical problem of Immunity Performance decline, the method that the embodiment of the present invention obtains pseudo- three ranks inertial element includes：The present count parameter of inertial object is acquired by various identification Methods；Wave filter is combined to form junction filter successively；Inertial object is in parallel with junction filter progress, pseudo- three ranks inertial element is obtained, the inertial object is converted into the pseudo- three ranks inertial element.

Description

A kind of method and apparatus for obtaining pseudo- three ranks inertial element
Technical field
The present invention relates to process control field, more particularly to a kind of method and apparatus for obtaining pseudo- three ranks inertial element.
Background technology
In process control practices, across rank control is generally existing, for example, lower order controller is used for into High order Plant Control.PID (Proportion integration differentiation) controller belongs to a kind of second order feedback controller, PID There is good control characteristic to second order object.Across rank control is feasible to PID control, for example, (be more than PID for high-order Second order) object control, can be handled by parameter depression of order, by High order Plant Parameter Switch be second order image parameter, can obtain good Good across rank control characteristic.
Automatic disturbance rejection controller ADRC (Active disturbance rejection controller) is used for across rank control System, the problem of there is Immunity Performance decline.For example, the single order ADRC Immunity Performances for being used for High order Plant control will be had into larger journey The decline of degree, this not be one by image parameter depression of order handle can preferably solve the problem of.Reason is：In theory, ADRC exponent number needs are corresponding with the exponent number of control object, and ADRC has excellent disturbance rejection control performance in rank, but across rank The Immunity Performance of control, which has, largely to be declined, and this is the Simple Idea that is determined of paradox of things.For High order Plant ADRC controls, direct solution is exactly to increase ADRC exponent number, but with the increase of ADRC exponent numbers, ADRC structure Also more tend to complicate, for example, three rank above ADRC of construction are just considerably complicated, usual ADRC exponent number is limited in three ranks Within.Therefore, across the rank control theory research to automatic disturbance rejection controller also has more worth discussions.By three rank linear active disturbance rejection controls Device processed is used to be more than the control of three rank inertial objects, and preferable method is exactly that will be greater than three rank inertial objects to be converted to pseudo- three ranks inertia Link.
The content of the invention
The invention provides a kind of method and apparatus for obtaining pseudo- three ranks inertial element, solve three rank linear active disturbance rejection controls When device processed is used for across rank control, there is the technical problem of Immunity Performance decline.
A kind of method for obtaining pseudo- three ranks inertial element provided in an embodiment of the present invention includes step：
S1：By the present count inertia constant of Model Distinguish acquisition inertial object, present count gain, present count exponent number, it is used to Sex object is expressed as formula：
Wherein, IO (s) is the transmission function of inertial object；TαFor the present count inertia constant of inertial object, unit s；KαFor The present count gain of inertial object, unit dimensionless；N is the present count exponent number of inertial object, 3<n<16 unit dimensionless；
S2：Uniform filtering time constant, the first filter gain of first wave filter are set, and the first wave filter is expressed as public affairs Formula：
Wherein, F1 (s) is the transmission function of the first wave filter；TFFor uniform filtering time constant, unit s；KF1For first Filter gain, unit dimensionless；First wave filter is first differential device；
S3：Set second and third, the uniform filtering time constant of four wave filters to present count filter order, second filter Ripple device is expressed as formula to present count filter order：
●
●
●
Wherein, F2 (s) is the transmission function of the second wave filter；F3 (s) is the transmission function of the 3rd wave filter；F4 (s) is The transmission function of 4th wave filter；Fn (s) is the transmission function of present count filter order；N be present count exponent number, unit without Dimension；TFFor uniform filtering time constant, unit s；Second wave filter is filtered to present count filter order for one order inertia Device；
S4：First wave filter to present count filter order is connected, and by the 4th wave filter to present count exponent number The output result of wave filter is sequentially overlapped output, forms junction filter, and junction filter is expressed as formula：
Wherein, F (s) is the transmission function of junction filter；KF1For the first filter gain, unit dimensionless；TFFor system One time constant filter, unit s；N is present count exponent number；
S5：Set the first filter gain to be equal to the present count gain, uniform filtering time constant and be equal to described preset Number inertia constant, by inertial object formation pseudo- three rank inertial element in parallel with junction filter, is expressed as formula：
Wherein, FOIO (s) is the transmission function of pseudo- three ranks inertial element；IO (s) is the transmission function of inertial object；F(s) For the transmission function of junction filter；TαFor present count inertia constant, unit s；KαFor present count gain, unit dimensionless；N is Present count exponent number, unit dimensionless；KF1For the first filter gain, unit dimensionless；TFFor uniform filtering time constant, unit s；
S6：Junction filter is used to control more than three rank linear active disturbance rejections of three rank inertial objects.
A kind of device of the pseudo- three rank inertial elements of acquisition for being provided in the embodiment of the present invention, including predetermined inertial object, Model Distinguish unit, the first digital filter device, the second wave filter to present count filter order, the control of three rank linear active disturbance rejections Device, first wave filter is first differential device, and second wave filter to present count filter order is filtered for one order inertia Ripple device；
First wave filter to present count filter order is connected, and by the second wave filter to present count order filtration The output result of device is sequentially overlapped output, forms junction filter；
By junction filter formation pseudo- three rank inertial element in parallel with inertial object, by the output knot of pseudo- three ranks inertial element Fruit three rank linear active disturbance rejection controllers of input, realize three rank linear active disturbance rejection controllers to the three rank lines more than three rank inertial objects Property Active Disturbance Rejection Control；
First wave filter is expressed as formula：
Wherein, F1 (s) is the transmission function of the first wave filter；TFFor uniform filtering time constant, unit s；KF1For first Filter gain, unit dimensionless；
Second wave filter is expressed as formula to the present count filter order：
●
●
●
Wherein, F2 (s) is the transmission function of the second wave filter；F3 (s) is the transmission function of the 3rd wave filter；F4 (s) is The transmission function of 4th wave filter；Fn (s) is the transmission function of present count filter order；N be present count exponent number, unit without Dimension；TFFor uniform filtering time constant, unit s；
Junction filter is expressed as formula：
Wherein, F (s) is the transmission function of junction filter；KF1For the first filter gain, unit dimensionless；TFFor system One time constant filter, unit s；N is present count exponent number；
Pseudo- three rank inertial elements are expressed as formula：
Wherein, FOIO (s) is the transmission function of pseudo- three ranks inertial element；IO (s) is the transmission function of inertial object；F(s) For the transmission function of junction filter；TαFor present count inertia constant, unit s；KαFor present count gain, unit dimensionless；N is Present count exponent number, unit dimensionless；KF1For the first filter gain, unit dimensionless；TFFor uniform filtering time constant, unit s。
As can be seen from the above technical solutions, the embodiment of the present invention has advantages below：
The present count parameter of inertial object is obtained by various identification Methods；Wave filter is combined to form combination successively Wave filter；Inertial object is in parallel with junction filter progress, pseudo- three ranks inertial element is obtained, pseudo- three ranks inertial element is inputted Three rank linear active disturbance rejection controllers, solve the technical problem that inertial object is converted to pseudo- three ranks inertial element.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing There is the accompanying drawing used required in technology description to be briefly described, it should be apparent that, drawings in the following description are only this Some embodiments of invention, for those of ordinary skill in the art, without having to pay creative labor, may be used also To obtain other accompanying drawings according to these accompanying drawings.
Fig. 1 is median filter combination process schematic diagram of the embodiment of the present invention；
Fig. 2 is junction filter schematic diagram in parallel with inertial object in the embodiment of the present invention；
Fig. 3 is used to be more than three rank inertial objects for a kind of method of the pseudo- three rank inertial elements of acquisition in the embodiment of the present invention Three rank linear active disturbance rejections control schematic diagram；
Fig. 4 be the pseudo- three rank inertial elements of a kind of acquisition in the embodiment of the present invention device be used for five rank inertial objects across Rank controls to be used for across the rank control experiment effect comparison diagram of five rank inertial objects with three rank linear active disturbance rejection controllers.
Embodiment
The embodiments of the invention provide a kind of method and apparatus for obtaining pseudo- three ranks inertial element, for solving three rank lines Property automatic disturbance rejection controller be used for be more than three rank inertial objects control when pseudo- three ranks inertial element acquisition problem.
To enable goal of the invention, feature, the advantage of the present invention more obvious and understandable, below in conjunction with the present invention Accompanying drawing in embodiment, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that disclosed below Embodiment be only a part of embodiment of the invention, and not all embodiment.Based on the embodiment in the present invention, this area All other embodiment that those of ordinary skill is obtained under the premise of creative work is not made, belongs to protection of the present invention Scope.
One of the method for the pseudo- three rank inertial elements of a kind of acquisition provided in Fig. 1-Fig. 3, the embodiment of the present invention is provided Embodiment includes step：
S1：By the present count inertia constant of Model Distinguish acquisition inertial object, present count gain, present count exponent number, it is used to Sex object is expressed as formula：
Wherein, IO (s) is the transmission function of inertial object；TαFor the present count inertia constant of inertial object；KαFor inertia pair The present count gain of elephant；N is the present count exponent number of inertial object；
The present count parameter of inertial object is obtained, the present count of inertial object can be acquired by various identification Methods Parameter.Inertial object is expressed as formula (1):
In formula (1), IO (s) is the transmission function of inertial object；TαFor present count inertia constant, unit s；KαIt is default Number gain, unit dimensionless；N is present count exponent number, unit dimensionless；The present count exponent number n>3, the present count exponent number n Can not be infinitely great, limit the present count exponent number n<16.
S2：Uniform filtering time constant, the first filter gain of first wave filter, the first wave filter expression are set For formula：
Wherein, F1 (s) is the transmission function of first wave filter；TFFor the uniform filtering time constant；KF1For institute State the first filter gain；
First wave filter is set, and the first wave filter is expressed as formula (2):
In formula (2), F1 (s) is the transmission function of first wave filter；TFFor uniform filtering time constant, unit s； KF1For first filter gain, unit dimensionless；The substantially first differential device of first wave filter.
S3：Second wave filter is set to the uniform filtering time constant of present count filter order, second filtering Device is expressed as formula to the present count filter order：
Wherein, Fm (s) is the described second transmission function for arriving the present count filter order；M arrives for described second The numbering of the present count filter order, 2≤m≤n；N is the present count exponent number；TFIt is normal for the uniform filtering time Number；
Second wave filter is set to the present count filter order, formula (3) is expressed as:
In formula (3), F2 (s) is the transmission function of the second wave filter；F3 (s) is the transmission function of the 3rd wave filter；F4 (s) it is the transmission function of the 4th wave filter；Fn (s) is the transmission function of present count filter order；N is the present count rank Number, unit dimensionless；TFFor uniform filtering time constant, unit s；Second wave filter is to the present count order filtration The substantially one order inertia wave filter of device.
S4：First wave filter is connected to the present count filter order, and by the 4th wave filter described in The output result of present count filter order is sequentially overlapped output, forms junction filter, and the junction filter is expressed as Formula：
Wherein, F (s) is the transmission function of the junction filter；KF1For first filter gain；TFFor the system One time constant filter；N is the present count exponent number；
First wave filter is combined to the present count filter order, by first wave filter to institute The series connection of present count filter order is stated, and by the output result of the 4th wave filter to the present count filter order successively Superposition output, forms junction filter, obtains junction filter, is expressed as formula (4):
In formula (4), F (s) is the transmission function of junction filter；KF1For first filter gain, unit is immeasurable Guiding principle；TFFor the uniform filtering time constant, unit s；N is the present count exponent number.
The flow of the junction filter, as shown in Figure 1.
S5：Set first filter gain to be equal to the present count gain, the uniform filtering time constant is set It is equal to the present count inertia constant, the inertial object is in parallel with junction filter progress, obtain pseudo- three ranks inertia Link, the pseudo- three ranks inertial element is expressed as formula：
Wherein, FOIO (s) is the transmission function of the pseudo- three ranks inertial element；IO (s) is the transmission of the inertial object Function；F (s) is the transmission function of the junction filter；TαFor the present count inertia constant；KαFor the present count gain； N is the present count exponent number；KF1For first filter gain；TFFor the uniform filtering time constant.
First filter gain is set to be equal to the present count gain；The uniform filtering time constant is set to be equal to The present count inertia constant；It is expressed as formula (5):
In formula (5), KF1For first filter gain, unit dimensionless；KαFor the present count gain, unit without Dimension；TF1For the uniform filtering time constant, unit s；KαFor the inertia constant, unit s.
The inertial object is in parallel with junction filter progress, obtain pseudo- three ranks inertial element；It is expressed as formula (6):
In formula (6), FOIO (s) is the transmission function of pseudo- three ranks inertial element；IO (s) is the transmission of the inertial object Function；F (s) is the transmission function of the junction filter；TαFor the present count inertia constant, unit s；KαPreset to be described Number gain, unit dimensionless；N is the present count exponent number, unit dimensionless；KF1For first filter gain, unit without Dimension；TFFor the uniform filtering time constant, unit s.
Inertial object is in parallel with junction filter progress, by the output of inertial object with it is outer around transmission Signal averaging and with The output of junction filter carries out add operation, as shown in Figure 2.The inertial object is converted into the pseudo- three ranks inertia rings Section.Junction filter is used to control more than three rank linear active disturbance rejections of three rank inertial objects.
In the present embodiment, the present count parameter of inertial object is acquired by various identification Methods；By wave filter according to Secondary combination forms junction filter；Inertial object is in parallel with junction filter progress, pseudo- three ranks inertial element is obtained, will be described Inertial object is converted to the pseudo- three ranks inertial element, when solving automatic disturbance rejection controller for across rank control, there is anti-interference The technical problem of hydraulic performance decline.
One of the device of the pseudo- three rank inertial elements of a kind of acquisition provided in Fig. 1-Fig. 4, the embodiment of the present invention is provided Embodiment, including five rank inertial objects, Model Distinguish unit, the first digital filter device, the second wave filter to present count exponent number Wave filter, three rank linear active disturbance rejection controllers, first wave filter are first differential device, and second wave filter is default to the Number filter order is one order inertia wave filter；
As shown in figure 1, the first wave filter to present count filter order is connected, and the second wave filter to the is preset The output result of number filter order is sequentially overlapped output, forms junction filter；
As shown in Fig. 2 forming pseudo- three ranks inertial element by junction filter is in parallel with inertial object；
As shown in figure 3, inertial object is in parallel with junction filter progress, the output of inertial object is believed with outer around transmission Number superposition simultaneously carries out add operation with the output of junction filter that the output result of pseudo- three ranks inertial element is inputted into three ranks is linear Automatic disturbance rejection controller；
First wave filter is expressed as formula：
Wherein, F1 (s) is the transmission function of the first wave filter；TFFor uniform filtering time constant, unit s；KF1For first Filter gain, unit dimensionless；
Second wave filter is expressed as formula to the present count filter order：
●
●
●
Wherein, F2 (s) is the transmission function of the second wave filter；F3 (s) is the transmission function of the 3rd wave filter；F4 (s) is The transmission function of 4th wave filter；Fn (s) is the transmission function of present count filter order；N be present count exponent number, unit without Dimension；TFFor uniform filtering time constant, unit s；
Junction filter is expressed as formula：
Wherein, F (s) is the transmission function of junction filter；KF1For the first filter gain, unit dimensionless；TFFor system One time constant filter, unit s；N is present count exponent number；
Pseudo- three rank inertial elements are expressed as formula：
Wherein, FOIO (s) is the transmission function of pseudo- three ranks inertial element；IO (s) is the transmission function of inertial object；F(s) For the transmission function of junction filter；TαFor present count inertia constant, unit s；KαFor present count gain, unit dimensionless；N is Present count exponent number, unit dimensionless；KF1For the first filter gain, unit dimensionless；TFFor uniform filtering time constant, unit s。
As shown in figure 4, the device for obtaining pseudo- three ranks inertial element is used for into across the rank control of five rank inertial objects and with three Rank linear active disturbance rejection controller is used for across the rank control of five rank inertial objects in T α=100s, and transmission is disturbed used for single order in K α=1 outside Property link, inertia constant 10s, during inertia gain 1, with PV (t) expression the output of process signal obtain contrast and experiment.
In the present embodiment, the present count parameter of inertial object is acquired by various identification Methods；By wave filter according to Secondary combination forms junction filter；Inertial object is in parallel with junction filter progress, pseudo- three ranks inertial element is obtained, will be described Inertial object is converted to the pseudo- three ranks inertial element, when solving automatic disturbance rejection controller for across rank control, there is anti-interference The technical problem of hydraulic performance decline, show the present invention anti-outer immunity can on good advantage.
It is apparent to those skilled in the art that, for convenience and simplicity of description, the system of foregoing description, The specific work process of device and unit, may be referred to the corresponding process in preceding method embodiment, will not be repeated here.
Described above, the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to before Embodiment is stated the present invention is described in detail, it will be understood by those within the art that：It still can be to preceding State the technical scheme described in each embodiment to modify, or equivalent substitution is carried out to which part technical characteristic；And these Modification is replaced, and the essence of appropriate technical solution is departed from the spirit and scope of various embodiments of the present invention technical scheme.

Claims (2)

1. a kind of method for obtaining pseudo- three ranks inertial element, it is characterised in that including：
S1：It is described used by the present count inertia constant of Model Distinguish acquisition inertial object, present count gain, present count exponent number Sex object is expressed as formula：
<mrow> <munder> <mrow> <mi>I</mi> <mi>O</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>n</mi> <mo>&gt;</mo> <mn>3</mn> </mrow> </munder> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mi>&amp;alpha;</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>&amp;alpha;</mi> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mfrac> </mrow>
Wherein, IO (s) is the transmission function of the inertial object；TαFor the present count inertia constant of the inertial object；KαFor institute State the present count gain of inertial object；N is the present count exponent number of the inertial object；
S2：Uniform filtering time constant, the first filter gain of first wave filter are set, and first wave filter is expressed as public affairs Formula：
<mrow> <mi>F</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> </mrow>
Wherein, F1 (s) is the transmission function of first wave filter；TFFor the uniform filtering time constant；KF1For described One filter gain；
S3：Second wave filter is set to the uniform filtering time constant of present count filter order, second wave filter is arrived The present count filter order is expressed as formula：
<mrow> <mi>F</mi> <mi>m</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> </mrow>
Wherein, Fm (s) is the described second transmission function for arriving the present count filter order；M is described second described in The numbering of present count filter order, 2≤m≤n；N is the present count exponent number；TFFor the uniform filtering time constant；
S4：First wave filter is connected to the present count filter order, and the 4th wave filter is pre- to described If the output result of number filter order is sequentially overlapped output, junction filter is formed, the junction filter is expressed as formula：
<mrow> <munder> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>n</mi> <mo>&gt;</mo> <mn>3</mn> </mrow> </munder> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mi>n</mi> <mo>-</mo> <mn>4</mn> </mrow> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>i</mi> </msup> </mfrac> </mrow>
Wherein, F (s) is the transmission function of the junction filter；KF1For first filter gain；TFFor the unified filter Ripple time constant；N is the present count exponent number；
S5：Set first filter gain to be equal to the present count gain, set the uniform filtering time constant to be equal to The present count inertia constant, the inertial object is in parallel with junction filter progress, pseudo- three ranks inertial element is obtained, The pseudo- three ranks inertial element is expressed as formula：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mi>O</mi> <mi>I</mi> <mi>O</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>I</mi> <mi>O</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mi>&amp;alpha;</mi> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>&amp;alpha;</mi> </msub> <mi>s</mi> </mrow> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mi>n</mi> <mo>-</mo> <mn>4</mn> </mrow> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>i</mi> </msup> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mi>&amp;alpha;</mi> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>&amp;alpha;</mi> </msub> <mi>s</mi> </mrow> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, FOIO (s) is the transmission function of the pseudo- three ranks inertial element；IO (s) is the transmission function of the inertial object； F (s) is the transmission function of the junction filter；TαFor the present count inertia constant；KαFor the present count gain；N is institute State present count exponent number；KF1For first filter gain；TFFor the uniform filtering time constant.
2. a kind of device for obtaining pseudo- three ranks inertial element, it is characterised in that including predetermined inertial object, Model Distinguish list Member, the first digital filter device, the second wave filter to present count filter order, three rank linear active disturbance rejection controllers, described One wave filter is first differential device, and second wave filter to present count filter order is one order inertia wave filter；
First wave filter is connected to the present count filter order and the 4th wave filter is to the present count The output result of filter order is sequentially overlapped output and forms junction filter, and the junction filter and the inertial object are simultaneously Connection forms pseudo- three ranks inertial element, and the output end of the pseudo- three ranks inertial element is inputted with the three ranks linear active disturbance rejection controller End is connected；
First wave filter is expressed as formula：
<mrow> <mi>F</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> </mrow>
Wherein, F1 (s) is the transmission function of first wave filter；TFFor the uniform filtering time constant；KF1For described One filter gain；
Second wave filter is expressed as formula to the present count filter order：
<mrow> <mi>F</mi> <mi>m</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> </mrow>
Wherein, Fm (s) is the described second transmission function for arriving the present count filter order；M is described second described in The numbering of present count filter order, 2≤m≤n；N is the present count exponent number；TFFor the uniform filtering time constant；
The junction filter is expressed as formula：
<mrow> <munder> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>n</mi> <mo>&gt;</mo> <mn>3</mn> </mrow> </munder> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mi>n</mi> <mo>-</mo> <mn>4</mn> </mrow> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>i</mi> </msup> </mfrac> </mrow>
Wherein, F (s) is the transmission function of the junction filter；KF1For first filter gain；TFFor the unified filter Ripple time constant；N is the present count exponent number；
The pseudo- three ranks inertial element is expressed as formula：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mi>O</mi> <mi>I</mi> <mi>O</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>I</mi> <mi>O</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mi>&amp;alpha;</mi> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>&amp;alpha;</mi> </msub> <mi>s</mi> </mrow> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mi>n</mi> <mo>-</mo> <mn>4</mn> </mrow> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>i</mi> </msup> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mi>&amp;alpha;</mi> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mi>&amp;alpha;</mi> </msub> <mi>s</mi> </mrow> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, FOIO (s) is the transmission function of the pseudo- three ranks inertial element；IO (s) is the transmission function of the inertial object； F (s) is the transmission function of the junction filter；TαFor the present count inertia constant；KαFor the present count gain；N is institute State present count exponent number；KF1For first filter gain；TFFor the uniform filtering time constant.
CN201710494581.2A 2017-06-26 2017-06-26 A kind of method and apparatus for obtaining pseudo- three ranks inertial element Pending CN107102556A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112099358A (en) * 2020-09-23 2020-12-18 广东电网有限责任公司云浮供电局 Optimal parameter obtaining method of three-stage controller
CN113162567A (en) * 2021-05-26 2021-07-23 广东电网有限责任公司 Design method and device of inertia combined filter and terminal equipment

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112099358A (en) * 2020-09-23 2020-12-18 广东电网有限责任公司云浮供电局 Optimal parameter obtaining method of three-stage controller
CN113162567A (en) * 2021-05-26 2021-07-23 广东电网有限责任公司 Design method and device of inertia combined filter and terminal equipment
CN113162567B (en) * 2021-05-26 2022-04-12 广东电网有限责任公司 Design method and device of inertia combined filter and terminal equipment

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