CN102570956A - Direct-current motor control method based on resonance suppression - Google Patents

Abstract

The invention discloses a direct-current motor control method based on resonance suppression. The method comprises five steps of: 1, drawing a baud diagram according to a transmission function of a dynamics simplified model of a direct-current motor with resonance; 2, calculating a resonance point on the baud diagram, which corresponds to the frequency of a resonance point according to a formula; 3, respectively designing a trap filter and a peak filter according to a design method for a resonance suppression filter; 4, connecting the trap filter as well as the peak filter with the simplified model of the direct-current motor to correct the simplified model of the direct-current motor, obtaining a nominal model corrected by the filters by fitting the baud diagram, and obtaining a dynamics equation of an actual object by considering a modeling uncertainty; and 5, designing a proportional-integral-derivative (PID) controller according to the model of the direct-current motor, which is corrected by the filters, so that high-precision control over the direct-current motor is realized. According to the direct-current motor control method, the problem about resonance produced by a loaded direct-current motor during running is solved; and on the premise of guaranteeing the dynamic performance of the system, high-precision control over the direct-current motor is realized.

Description

A kind of DC motor control method that suppresses based on resonance

(1) technical field

The present invention relates to a kind of DC motor control method that suppresses based on resonance; It is to the direct current machine dynamics simplified model that has resonance; And a kind of proportional-integral-differential (Proportional-Integral-Derivative that suppresses resonance through filter of design; PID) control method belongs to the electric machines control technology field.

(2) background technology

At present, in the DC MOTOR CONTROL field, resonance problems more and more comes into one's own.How to suppress resonance and realize that the High Accuracy Control to direct current machine is the focus of DC MOTOR CONTROL area research.

In servo system, the output shaft of direct current machine directly links to each other with bearing axle, and rotatable parts are fixed on the bearing axle, is common single axle rotation.If consider that then be called simple substance amount servo system, this system and actual characteristic have very big difference to motor and load as a rigid body.For real system, although motor and load are direct-coupled, power transmission shaft has certain elastic deformation in transmission process, and transmission is flexible in essence, and bearing and framework also all not exclusively are rigidity.Under the effect of motor-driven moment, mechanical axis can receive crooked and distortion to a certain degree.Require high system of big, rapidity and required precision or the system that moment of inertia is big, performance requirement is high for acceleration, elastic deformation can not be ignored the influence of systematic function.Because the crooked and distortion of power transmission shaft contains energy-storage travelling wave tube when transmitting motion.Under the little situation of speed damping, higher mechanical resonant can appear in its transmission characteristic, and this resonance possibly cause the deterioration of dynamic performance in some cases, even makes system unstable.This resonance is bigger to the dynamic property influence of system.

(3) summary of the invention

1, purpose: in view of this; The purpose of this invention is to provide a kind of DC motor control method that suppresses based on resonance; To solve the problem of the resonance that direct current machine produces in having the running of load; Thereby under the prerequisite that guarantees dynamic performance, realize High Accuracy Control to direct current machine.

2, technical scheme: for achieving the above object:

A kind of DC motor control method that suppresses based on resonance of the present invention, this method may further comprise the steps:

Step 1: according to the transfer function of the direct current machine dynamics simplified model that has resonance, its baud (Bode) that draws figure;

Step 2: calculate the frequency of resonance point, the resonance point on the corresponding Bode figure according to formula;

Step 3:, design notch filter and peak filter respectively according to the method for designing of resonance rejects trap;

Step 4: notch filter and peak filter are connected with the direct current machine simplified model; Realization, obtains through the nominal model after the filter correction through Bode figure match the correction of direct current machine simplified model; Consider that modeling is uncertain, obtain the kinetics equation of practical object;

Step 5: according to the model through the direct current machine after the filter correction, design PID controller is realized the High Accuracy Control to direct current machine.

Wherein, the described transfer function that has the direct current machine dynamics simplified model of resonance of step 1 is:

$G\left(s\right)=\frac{\frac{1}{{110}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.02}{110}s+1}{(\frac{1}{{68}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.07}{68}s+1)(\frac{1}{{130}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.1}{130}s+1)}.$

S=σ+j ω is a complex variable in the formula.

Wherein, the frequency computation part formula of the described resonance point of step 2 does

The transfer function of oscillation element ζ is the damping ratio (0＜ζ＜1) of oscillation element in the formula, ω _nThe natural frequency of oscillation of oscillation element.Calculate G successively ₁, G ₂, G ₃Three corresponding resonance point frequencies of link.

Wherein, the method for designing of the said resonance rejects trap of step 3 is following:

To the model that has resonance

$G_p\left(s\right)=\underset{m=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Pi;}}}\frac{s^{}}{}\frac{{}^2+2{\mathrm{\&zeta;}}_1{\mathrm{\&omega;}}_{1}s+{{\mathrm{\&omega;}}_1}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_2{\mathrm{\&omega;}}_{2}s+{{\mathrm{\&omega;}}_2}^2}$

In order to suppress resonance, notch filter has been proposed and the peak filter method for designing is following

$C_{\mathrm{notch}\_\mathrm{filters}}=\underset{m=1}{\overset{n_1}{\mathrm{\&Pi;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}{\mathrm{\&omega;}}_{n_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\mathrm{\&omega;}}_{n_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}}^2}$

$C_{peak\_\mathrm{filters}}=\underset{m=1}{\overset{n_2}{\mathrm{\&Pi;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}{\mathrm{\&omega;}}_{p_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}{\mathrm{\&omega;}}_{p_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}}^2}$

N in the formula ₁, n ₂Be respectively the number of trap and peak value resonance, With

Be respectively the damping ratio of notch filter and peak filter,

With Be respectively the resonance point frequency.Usually, get

Wherein, step 4 described through the nominal model after the filter correction be

practical object kinetics equation is

Wherein, the described PID design of Controller of step 5 is following:

The PID controller is a kind of linear controller, and it is according to set-point y _d(t) constitute control deviation with real output value y (t)

e(t)＝y _d(t)-y(t)

The control law of PID does

$u\left(t\right)=k_P[e\left(t\right)+\frac{1}{T_I}{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}+\frac{T_D\mathrm{de}\left(t\right)}{\mathrm{dt}}]=k_{P}e\left(t\right)+k_I{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}+\frac{k_D\mathrm{de}\left(t\right)}{\mathrm{dt}}$

In the formula, k _PBe proportionality coefficient; T _IBe integration time constant; T _DBe derivative time constant.

Model with through the direct current machine after the filter correction is a controlled device, gets k _P, k _I, k _D,, input instruction y _dSimulation time is set.Finally obtain emulation output and can be good at following the tracks of input signal, i.e. set-point y _d(t) constitute control deviation e (t)=y with real output value y (t) _d(t)-and y (t)=0, realized having the direct current machine High Accuracy Control of resonance.

3, advantage and effect: a kind of DC motor control method that suppresses based on resonance of the present invention, its advantage is:

(1) combines the frequency domain analysis method of having used; The method for designing of the method for designing of resonance rejects trap and PID control law; Calculate the frequency of a plurality of resonance points; Provided the design process and the result of resonance filter, utilization PID control law method for designing has realized having the direct current machine High Accuracy Control of resonance.

(2) can effectively suppress through designing filter to the situation of the one or more resonance that produce in the motor operation course.

(3) solved the control of DC problem that has resonance, had characteristics simple, that be easy to realize, universality is good, and can improve the dynamic property of the direct current machine that has resonance.

(4) description of drawings

Fig. 1: closed-loop control system structural representation of the present invention;

Fig. 2: the FB(flow block) of the DC motor control method that suppresses based on resonance of the present invention;

Fig. 3: the present invention has the direct current machine-power transmission shaft-load module sketch map of resonance;

Fig. 4: the present invention has the direct current machine dynamics simplified model Bode figure of resonance;

Fig. 5: the Bode figure of three resonance filter series connection of the present invention;

Fig. 6: the model after the present invention proofreaies and correct through resonance filter and the Bode figure of match thereof;

Fig. 7: the step response sketch map that the present invention proofreaies and correct without resonance filter;

Fig. 8: the step response sketch map after the present invention proofreaies and correct through resonance filter.

Label among the figure, symbol and lines etc. are explained as follows:

Among Fig. 3, u _aBe motor input voltage, ω _mBe rotating speed of motor, T _mBe the torque of motor, J _aBe the moment of inertia of power transmission shaft, θ _mAnd θ _LBe respectively the corner of motor and load, J _LBe the moment of inertia of load, b _mAnd b _LBe respectively the viscous damping coefficient of motor and load, K _LBe the coupling stiffness coefficient between motor and the framework, T _MLBe load end output torque square.

Among Fig. 4, last figure is the log magnitude-frequency characteristics curve, and figure below is corresponding with it log phase-frequency characteristics curve.

Among Fig. 5, last figure is the log magnitude-frequency characteristics curve, and figure below is corresponding with it log phase-frequency characteristics curve.

Among Fig. 6, last figure is the log magnitude-frequency characteristics curve, and figure below is corresponding with it log phase-frequency characteristics curve.

(5) embodiment

For making the object of the invention, technical scheme and advantage express clearlyer, the present invention is remake further detailed explanation below in conjunction with accompanying drawing and specific embodiment.

Basic ideas of the present invention are according to the transfer function that has the direct current machine dynamics simplified model of resonance, and its Bode figure draws; Calculate the frequency of resonance point, the resonance point on the corresponding Bode figure according to formula; According to the method for designing of resonance rejects trap, design notch filter and peak filter respectively; Notch filter and peak filter are connected with the direct current machine simplified model; Realization, obtains through the nominal model after the filter correction through Bode figure match the correction of direct current machine simplified model; Consider that modeling is uncertain, obtain the kinetics equation of practical object; According to the model through the direct current machine after the filter correction, design PID controller is realized the High Accuracy Control to direct current machine.

The hardware system aspect has the general-purpose machine of load.The software systems aspect, system emulation is a foundational development with software MATLABR2008b.Fig. 1 is a closed-loop control system structural representation of the present invention.

Describe with an instance below, the dc motor model that has resonance is set as follows: its structure is as shown in Figure 3.See Fig. 2, a kind of DC motor control method that suppresses based on resonance of the present invention, it may further comprise the steps:

Step 1: according to the transfer function of the direct current machine dynamics simplified model that has resonance, its baud (Bode) that draws figure;

The transfer function that has the direct current machine dynamics simplified model of resonance is:

$G\left(s\right)=\frac{\frac{1}{{110}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.02}{110}s+1}{(\frac{1}{{68}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.07}{68}s+1)(\frac{1}{{130}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.1}{130}s+1)}$

Controlled device G (s) can decompose as follows:

G＝G ₁G ₂G ₃

Wherein ${\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">G</figure-callout>}}_1=\frac{{68}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+68\&times;0.07s+{68}^2},$ ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">G</figure-callout>}}_2=\frac{1}{{110}^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.02}{110}s+1,$ ${\mathrm{<figure-callout\; id="3"\; label="G"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">G</figure-callout>}}_3=\frac{{130}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+130\&times;0.1s+{130}^2}.$

S=σ+j ω is a complex variable in the formula.Bode figure is Fig. 4.

Step 2: calculate the frequency of resonance point, the resonance point on the corresponding Bode figure according to formula;

The frequency computation part formula of resonance point does

The transfer function of oscillation element

ζ is the damping ratio (0＜ζ＜1) of oscillation element in the formula, ω _nThe natural frequency of oscillation of oscillation element.Calculate G successively ₁, G ₂, G ₃Three corresponding resonance point frequencies of link are 68rad/s, 110rad/s and 130rad/s.

Step 3:, design notch filter and peak filter respectively according to the method for designing of resonance rejects trap;

The method for designing of resonance rejects trap is following:

To the model that has resonance

$G_p\left(s\right)=\underset{m=1}{\overset{n}{\mathrm{\&Pi;}}}\frac{s^2+2{\mathrm{\&zeta;}}_1{\mathrm{\&omega;}}_{1}s+{{\mathrm{\&omega;}}_1}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_2{\mathrm{\&omega;}}_{2}s+{{\mathrm{\&omega;}}_2}^2}$

In order to suppress resonance, notch filter has been proposed and the peak filter method for designing is following

$C_{\mathrm{notch}\_\mathrm{filters}}=\underset{m=1}{\overset{n_1}{\mathrm{\&Pi;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}{\mathrm{\&omega;}}_{n_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\mathrm{\&omega;}}_{n_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}}^2}$

$C_{\mathrm{peak}\_\mathrm{filters}}=\underset{m=1}{\overset{n_2}{\mathrm{\&Pi;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}{\mathrm{\&omega;}}_{p_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}{\mathrm{\&omega;}}_{p_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}}^2}$

N in the formula ₁, n ₂Be respectively the number of trap and peak value resonance, With Be respectively the damping ratio of notch filter and peak filter,

With

Be respectively the resonance point frequency.Usually, get

Design notch filter and peak filter: Bode figure respectively like Fig. 5.

(1) the peak value resonance that produces by

to the 68rad/s place; The design notch filter offset peak value resonance, then should get then notch filter do

$C_{\mathrm{notch}\_\mathrm{<figure-callout\; id="1"\; label="filter"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">filter</figure-callout>}1}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}{\mathrm{\&omega;}}_{n_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\mathrm{\&omega;}}_{n_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}}^2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.07\&times;68s+{68}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\&times;68s+{68}^2}$

Then ${\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">G</figure-callout>}}_1\&times;C_{\mathrm{Notch}\_\mathrm{<figure-callout\; id="1"\; label="Filter"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">Filter</figure-callout>}1}=\frac{{68}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+68\&times;0.07s+{68}^2}\&times;\frac{s^2+0.07\&times;68s+{68}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\&times;68s+{68}^2}=\frac{{68}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\&times;68s+{68}^2}$

The following formula amplitude-frequency does $L\left(\mathrm{\&omega;}\right)=201g\left|H\left(\mathrm{J\&omega;}\right)\right|=201\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">g</figure-callout>}\frac{1}{2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\sqrt{1-{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}^2}}.$

Because 68rad/s is in low-frequency range; In order to make Bode scheme that amplitude-frequency is unattenuated herein, get

and then can get

(2) the peak value resonance that produces by

to the 130rad/s place; The design notch filter offset peak value resonance, then should get then notch filter do

$C_{\mathrm{notch}\_\mathrm{<figure-callout\; id="2"\; label="filter"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">filter</figure-callout>}2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}{\mathrm{\&omega;}}_{n_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\mathrm{\&omega;}}_{n_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}}^2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.10\&times;130s+{130}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\&times;130s+{130}^2}$

Then ${\mathrm{<figure-callout\; id="3"\; label="G"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">G</figure-callout>}}_3\&times;C_{\mathrm{Notch}\_\mathrm{<figure-callout\; id="2"\; label="Filter"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">Filter</figure-callout>}2}=\frac{{130}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+130\&times;0.10s+130^2}\&times;\frac{s^2+0.10\&times;130s+{130}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\&times;130s+{130}^2}=\frac{{130}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\&times;130s+{130}^2}$

The following formula amplitude does $L\left(\mathrm{\&omega;}\right)=201g\left|H\left(\mathrm{J\&omega;}\right)\right|=201\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">g</figure-callout>}\frac{1}{2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\sqrt{1-{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}^2}}$

Because 130rad/s is in Mid Frequency, amplitude-frequency is that monotonic decay does not have peak value in order to make Bode scheme herein, should get

Get

Then can get $C_{\mathrm{Notch}\_\mathrm{<figure-callout\; id="2"\; label="Filter"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">Filter</figure-callout>}2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.10\&times;130s+{130}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+1.5\&times;130s+{130}^2}.$

(3) to the trap value at 110rad/s place be by ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">G</figure-callout>}}_2=\frac{1}{110^2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+\frac{0.02}{110}s+1=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.02\&times;110s+{110}^2}{{110}^2}$ Produce, the design peak filter is got

Then peak filter does

$C_{\mathrm{peak}\_\mathrm{filter}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}{\mathrm{\&omega;}}_{p_1}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}{\mathrm{\&omega;}}_{p_2}s+{{\mathrm{\&omega;}}_{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}}^2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}\&times;110s+{110}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.02\&times;110s+{110}^{\text{2}}}$

Then ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\&times;C_{\mathrm{Peak}\_\mathrm{Filter}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.02\&times;110s+{110}^2}{{110}^2}\&times;\frac{s^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}\&times;110s+{110}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.02\&times;110s+{110}^2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}\&times;110s+{110}^2}{{110}^2}$

The following formula amplitude-frequency does $L\left(\mathrm{\&omega;}\right)=201g\left|H\left(\mathrm{J\&omega;}\right)\right|=201g\left(2{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}\sqrt{1-{\mathrm{\&zeta;}}_{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000136314100000021.png,HDA0000136314100000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}^2}\right).$

Because 110rad/s is in Mid Frequency, amplitude-frequency is that monotonic decay does not have peak value in order to make Bode scheme herein, should get

Get

Then can get $C_{\mathrm{Peak}\_\mathrm{Filter}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+1.5\&times;110s+{110}^2}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000136314100000022.png,HDA0000136314100000032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+0.02\&times;110s+{110}^2}.$

Step 4: notch filter and peak filter are connected with the direct current machine simplified model; Realization, obtains through the nominal model after the filter correction through Bode figure match the correction of direct current machine simplified model; Consider that modeling is uncertain, obtain the kinetics equation of practical object;

Nominal model through after the filter correction does

The kinetics equation of practical object does

A wherein ₁=90.26, a ₂=6346, b=6392.As shown in Figure 6.

Step 5: according to the model through the direct current machine after the filter correction, design PID controller is realized the High Accuracy Control to direct current machine.

The PID design of Controller is following:

The PID controller is a kind of linear controller, and it is according to set-point y _d(t) constitute control deviation with real output value y (t)

e(t)＝y _d(t)-y(t)

The control law of PID does

$u\left(t\right)=k_P[e\left(t\right)+\frac{1}{T_I}{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}+\frac{T_D\mathrm{de}\left(t\right)}{\mathrm{dt}}]=k_{P}e\left(t\right)+k_I{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}+\frac{k_D\mathrm{de}\left(t\right)}{\mathrm{dt}}$

In the formula, k _PBe proportionality coefficient; T _IBe integration time constant; T _DBe derivative time constant.

Model with through the direct current machine after the filter correction is a controlled device, as input, gets k with unit step signal _P=5, k _I=5, k _D=0.1,, input instruction y _d=1 (t), wherein t>=0.Simulation time is 10s.Finally obtain emulation output and can be good at following the tracks of input signal, i.e. set-point y _d(t) constitute control deviation e (t)=y with real output value y (t) _d(t)-and y (t)=0, realized having the direct current machine High Accuracy Control of resonance.Unit step response such as Fig. 7, shown in Figure 8 before and after the filtering.

Claims (6)

1. DC motor control method that suppresses based on resonance, it is characterized in that: this method may further comprise the steps:

Step 1: according to the transfer function of the direct current machine dynamics simplified model that has resonance, its baud that draws is Bode figure;

Step 2: calculate the frequency of resonance point, the resonance point on the corresponding Bode figure according to formula;

Step 3:, design notch filter and peak filter respectively according to the method for designing of resonance rejects trap;

Step 4: notch filter and peak filter are connected with the direct current machine simplified model; Realization, obtains through the nominal model after the filter correction through Bode figure match the correction of direct current machine simplified model; Consider that modeling is uncertain, obtain the kinetics equation of practical object;

Step 5: according to the model through the direct current machine after the filter correction, design PID controller is realized the High Accuracy Control to direct current machine.

2. a kind of DC motor control method that suppresses based on resonance according to claim 1, it is characterized in that: the described transfer function that has the direct current machine dynamics simplified model of resonance of step 1 is:

$G\left(s\right)=\frac{\frac{1}{{110}^2}{s}^2+\frac{0.02}{110}s+1}{(\frac{1}{{68}^2}{s}^2+\frac{0.07}{68}s+1)(\frac{1}{{130}^2}{s}^2+\frac{0.1}{130}s+1)}.$

S=σ+j ω is a complex variable in the formula.

3. a kind of DC motor control method that suppresses based on resonance according to claim 1, it is characterized in that: the frequency computation part formula of the described resonance point of step 2 does

The transfer function of oscillation element

In the formula, ζ is the damping ratio (0＜ζ＜1) of oscillation element, ω _nThe natural frequency of oscillation of oscillation element calculates G successively ₁, G ₂, G ₃Three corresponding resonance point frequencies of link.

4. a kind of DC motor control method that suppresses based on resonance according to claim 1, it is characterized in that: the method for designing of the said resonance rejects trap of step 3 is following:

To the model that has resonance

$G_p\left(s\right)=\underset{m=1}{\overset{n}{\mathrm{\&Pi;}}}\frac{s^2+2{\mathrm{\&zeta;}}_1{\mathrm{\&omega;}}_{1}s+{{\mathrm{\&omega;}}_1}^2}{s^2+2{\mathrm{\&zeta;}}_2{\mathrm{\&omega;}}_{2}s+{{\mathrm{\&omega;}}_2}^2}$

In order to suppress resonance, notch filter has been proposed and the peak filter method for designing is following

$C_{\mathrm{notch}\_\mathrm{filters}}=\underset{m=1}{\overset{n_1}{\mathrm{\&Pi;}}}\frac{s^2+2{\mathrm{\&zeta;}}_{n_1}{\mathrm{\&omega;}}_{n_1}s+{{\mathrm{\&omega;}}_{n_1}}^2}{s^2+2{\mathrm{\&zeta;}}_{n_2}{\mathrm{\&omega;}}_{n_2}s+{{\mathrm{\&omega;}}_{n_2}}^2}$

$C_{peak\_\mathrm{filters}}=\underset{m=1}{\overset{n_2}{\mathrm{\&Pi;}}}\frac{s^2+2{\mathrm{\&zeta;}}_{p_1}{\mathrm{\&omega;}}_{p_1}s+{{\mathrm{\&omega;}}_{p_1}}^2}{s^2+2{\mathrm{\&zeta;}}_{p_2}{\mathrm{\&omega;}}_{p_2}s+{{\mathrm{\&omega;}}_{p_2}}^2}$

N in the formula ₁, n ₂Be respectively the number of trap and peak value resonance,

With

Be respectively the damping ratio of notch filter and peak filter,

With

Be respectively the resonance point frequency; Usually, get

5. a kind of DC motor control method that suppresses based on resonance according to claim 1 is characterized in that: step 4 described through the nominal model after the filter correction for

practical object kinetics equation is

6. a kind of DC motor control method that suppresses based on resonance according to claim 1, it is characterized in that: the described PID design of Controller of step 5 is following:

The PID controller is a kind of linear controller, and it is according to set-point y _d(t) constitute control deviation with real output value y (t)

e(t)＝y _d(t)-y(t)

The control law of PID does

$u\left(t\right)=k_P[e\left(t\right)+\frac{1}{T_I}{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}+\frac{T_D\mathrm{de}\left(t\right)}{\mathrm{dt}}]=k_{P}e\left(t\right)+k_I{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}+\frac{k_D\mathrm{de}\left(t\right)}{\mathrm{dt}}$

In the formula, k _PBe proportionality coefficient; T _IBe integration time constant; T _DBe derivative time constant;

Model with through the direct current machine after the filter correction is a controlled device, gets k _P, k _I, k _D,, input instruction y _d, simulation time is set; Finally obtain emulation output and can be good at following the tracks of input signal, i.e. set-point y _d(t) constitute control deviation e (t)=y with real output value y (t) _d(t)-and y (t)=0, realized having the direct current machine High Accuracy Control of resonance.

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