CN105652661B - A kind of method for controlling permanent magnet synchronous motor towards injection moulding process - Google Patents
A kind of method for controlling permanent magnet synchronous motor towards injection moulding process Download PDFInfo
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Abstract
The invention discloses a kind of method for controlling permanent magnet synchronous motor towards injection moulding process, including:Build speed ring transmission function of the permanent magnet synchronous motor in injection moulding process, after the PD control device model for building control system for permanent-magnet synchronous motor, according to the performance indicator of given control system, in conjunction with speed ring transmission function, after parameter tuning being carried out to PD control device, the control output for obtaining PD control device, finally exports according to the control of PD control device and carries out motion control to permanent magnet synchronous motor.The present invention can calculate the control parameter for obtaining permanent magnet synchronous motor automatically, manual adjustment is not needed, and the response signal of permanent magnet synchronous motor may make quickly to follow input signal, system tracking error Fast Convergent, real-time is higher, it can be achieved to accurately control, to greatly improve the injecting products quality that injection molding generates, can be widely applied in injection molding control industry.
Description
Technical field
The present invention relates to the industrial control fields of injection molding production, more particularly to a kind of permanent-magnet synchronous towards injection moulding process
Motor control method.
Background technology
One injection molding production process can be divided into:Guan Mo (mold-close) is injected (filling), pressurize (packing-
Holding), (cooling)/plasticizing (plasticizing) is condensed, (mold-open) five stages are molded.Wherein inject rank
Section, the key variables of required control are injection speeds, and it is permanent-magnet synchronous that screw rod, which pushes the power source of high molecular material injection,
Motor (or asynchronous machine).Therefore, the injection speed for controlling nozzle is really the rotating speed for controlling magneto.
When controlling the permanent magnet synchronous motor of injection moulding process, need to establish relevant model, the method modeled at present
Substantially it is confined to integer rank calculus theoretical category, such as injection stage in above-mentioned injection molding process, usually with one
Rank or second order differential equation describe injection speed model.It theoretically analyzes, less than the differential equation of single order, whether there is or not several forms
(such as 1/2,1/3 ... 1/n ...);Similarly, higher than single order and less than second order the differential equation also whether there is or not several forms (such as 3/2,
4/3 ... (n+1)/n ... etc.).But the rate pattern of injection stage will not such coincidence, in exactly countless differential equation
Single order or second-order model, only integer rank calculus theoretical developments comparative maturity, people get used to using integer rank calculus side
Journey approaches the realistic model of controlled device.In addition, for processing of high molecular material the study found that objective in injection moulding process deposit
In the behavior of fractional order, such as the unwinding of injection moulding process high molecular material and the Viscous Elastic Mechanics of molten material and non-newtonian fluid
The behavior that mechanics etc. shows dimension is true.Specific manifestation is as follows:
According to mechanics hook laws, the elastic force σ and flexible deformation ε of ideal high molecular material meet following equation:
σ (t)=E ε (t) (1)
And ideal Newton stresss of fluidity σ meets following equation with strain stress:
Wherein, E, γ are material property coefficient.
But the high molecular material of injection moulding process is neither ideal solid material, nor ideal fluent material, but be situated between
Between ideal solid and fluid.As it can be seen that tradition cannot obtain accurately mathematical modulo to the integer model description of injection moulding process
Type, and then cannot objectively reflect the essence of things, the mismatch of model is eventually caused, thus can not be accurately to injection moulding process
Permanent magnet synchronous motor is controlled, and causes finally to be molded the injecting products produced second-rate.
Invention content
In order to solve the above technical problems, the object of the present invention is to provide a kind of permanent magnet synchronous electrics towards injection moulding process
Machine control method.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of method for controlling permanent magnet synchronous motor towards injection moulding process, including:
The speed ring transmission function of S1, structure permanent magnet synchronous motor in injection moulding process;
S2, the PD control device model for building control system for permanent-magnet synchronous motor;
The performance indicator of S3, the given control system of basis carry out parameter in conjunction with speed ring transmission function to PD control device
After adjusting, the control output of PD control device is obtained;
S4, motion control is carried out to permanent magnet synchronous motor according to the control of PD control device output.
Further, the step S1, including:
The mathematical model of S11, structure permanent magnet synchronous motor in injection moulding process, the expression formula of the mathematical model is as follows
Fractional Differential Equation:
In above formula, ωrIndicate the rotating speed of permanent magnet synchronous motor,Indicate the fractional order of the rotating speed of permanent magnet synchronous motor
Differential value, iqIndicate the stator current of permanent magnet synchronous motor,BmIt is friction coefficient, J is rotary inertia, kpp
Indicate the proportionality coefficient of the controller of permanent magnet synchronous motor;
S12, after the Fractional Differential Equation of structure is carried out Laplace transform, the speed ring of permanent magnet synchronous motor is obtained
Transmission function is as follows:
In above formula, P (S) is indicatedLaplace transform, Wr(s) ω is indicatedrLaplace transform, Iq(s)
Indicate iqLaplace transform, k=a/b, T=1/a, s indicate Laplace operator, r indicate fractional order differential coefficient.
Further, the step S2 is specially:
The PD control device model of control system for permanent-magnet synchronous motor is built according to the following formula:
C (s)=kp(1+kds)
In above formula, C (S) indicates the control output of PD control device, kpIndicate proportional gain, kdIndicate the differential gain.
Further, the step S3, including:
S31, according to the speed ring transmission function of permanent magnet synchronous motor and the PD control device model of control system, controlled
The open-loop transfer function of system is as follows:
G (s)=C (s) P (s)
In above formula, G (S) indicates the open-loop transfer function of control system;
S32, corresponding frequency spy is obtained after carrying out frequency-domain transform to speed ring transmission function and PD control device model respectively
Property, the expression formula of the frequency characteristic obtained is as follows:
In above formula, Arg [C (j ω)] indicates the phase angle characteristics of C (S), | C (j ω) | indicate the amplitude characteristic of C (S), Arg [P
(j ω)] indicate P (S) phase angle characteristics, | P (j ω) | indicate P (S) amplitude characteristic;
S33, the frequency characteristic for calculating the open-loop transfer function G (S) for obtaining control system according to the following formula::
Wherein, Arg [G (j ω)] indicates the phase angle characteristics of G (S), | G (j ω) | indicate the amplitude characteristic of G (S);
S34, G (S) is obtained according to the open-loop gain robustness index of given cross-over frequency, Phase margin and control system
The following condition that need to meet of frequency characteristic after, calculate and obtain the control of PD control device and export kp and kd:
In above formula, ωcIndicate given cross-over frequency,Indicate given Phase margin, given control system
Open-loop gain robustness index is 0.
Further, the control of the PD control device exports kpAnd kdIt is calculated by the following formula out:
Wherein,
The beneficial effects of the invention are as follows:A kind of method for controlling permanent magnet synchronous motor towards injection moulding process of the present invention, it is first
First speed ring transmission function of the structure permanent magnet synchronous motor in injection moulding process, and build the PD of control system for permanent-magnet synchronous motor
After controller model, PD control device is joined in conjunction with speed ring transmission function according to the performance indicator of given control system
After number is adjusted, the control output of PD control device is obtained, is finally exported according to the control of PD control device and permanent magnet synchronous motor is carried out
Motion control.This control method can calculate the control parameter for obtaining permanent magnet synchronous motor automatically, not need manual adjustment, Er Qieke
So that the response signal of permanent magnet synchronous motor quickly follows input signal, system tracking error Fast Convergent, real-time is higher, can
Realization accurately controls, to greatly improve the injecting products quality that injection molding generates.
Description of the drawings
The invention will be further described with reference to the accompanying drawings and examples.
Fig. 1 is a kind of flow chart of method for controlling permanent magnet synchronous motor towards injection moulding process of the present invention;
Fig. 2 is the structure diagram of the control system speed ring of permanent magnet synchronous motor in specific embodiments of the present invention;
Fig. 3 is the main program flow chart of the control system speed ring of permanent magnet synchronous motor in specific embodiments of the present invention;
Fig. 4 is the interrupt routine flow of the control system speed ring of permanent magnet synchronous motor in specific embodiments of the present invention
Figure;
Fig. 5 is the control system speed ring control using the present invention of permanent magnet synchronous motor in specific embodiments of the present invention
Step response curve figure after method.
Specific implementation mode
Referring to Fig.1, the present invention provides a kind of method for controlling permanent magnet synchronous motor towards injection moulding process, including:
The speed ring transmission function of S1, structure permanent magnet synchronous motor in injection moulding process;
S2, the PD control device model for building control system for permanent-magnet synchronous motor;
The performance indicator of S3, the given control system of basis carry out parameter in conjunction with speed ring transmission function to PD control device
After adjusting, the control output of PD control device is obtained;
S4, motion control is carried out to permanent magnet synchronous motor according to the control of PD control device output.
It is further used as preferred embodiment, the step S1, including:
The mathematical model of S11, structure permanent magnet synchronous motor in injection moulding process, the expression formula of the mathematical model is as follows
Fractional Differential Equation:
In above formula, ωrIndicate the rotating speed of permanent magnet synchronous motor,Indicate the fractional order of the rotating speed of permanent magnet synchronous motor
Differential value, iqIndicate the stator current of permanent magnet synchronous motor,BmIt is friction coefficient, J is rotary inertia, kpp
Indicate the proportionality coefficient of the controller of permanent magnet synchronous motor;
S12, after the Fractional Differential Equation of structure is carried out Laplace transform, the speed ring of permanent magnet synchronous motor is obtained
Transmission function is as follows:
In above formula, P (S) is indicatedLaplace transform, Wr(s) ω is indicatedrLaplace transform, Iq(s)
Indicate iqLaplace transform, k=a/b, T=1/a, s indicate Laplace operator, r indicate fractional order differential coefficient.
It is further used as preferred embodiment, the step S2 is specially:
The PD control device model of control system for permanent-magnet synchronous motor is built according to the following formula:
C (s)=kp(1+kds)
In above formula, C (S) indicates the control output of PD control device, kpIndicate proportional gain, kdIndicate the differential gain.
It is further used as preferred embodiment, the step S3, including:
S31, according to the speed ring transmission function of permanent magnet synchronous motor and the PD control device model of control system, controlled
The open-loop transfer function of system is as follows:
G (s)=C (s) P (s)
In above formula, G (S) indicates the open-loop transfer function of control system;
S32, corresponding frequency spy is obtained after carrying out frequency-domain transform to speed ring transmission function and PD control device model respectively
Property, the expression formula of the frequency characteristic obtained is as follows:
In above formula, Arg [C (j ω)] indicates the phase angle characteristics of C (S), | C (j ω) | indicate the amplitude characteristic of C (S), Arg [P
(j ω)] indicate P (S) phase angle characteristics, | P (j ω) | indicate P (S) amplitude characteristic;
S33, the frequency characteristic for calculating the open-loop transfer function G (S) for obtaining control system according to the following formula::
Wherein, Arg [G (j ω)] indicates the phase angle characteristics of G (S), | G (j ω) | indicate the amplitude characteristic of G (S);
S34, G (S) is obtained according to the open-loop gain robustness index of given cross-over frequency, Phase margin and control system
The following condition that need to meet of frequency characteristic after, calculate and obtain the control of PD control device and export kp and kd:
In above formula, ωcIndicate given cross-over frequency,Indicate given Phase margin, given control system
Open-loop gain robustness index is 0.
It is further used as preferred embodiment, the control of the PD control device exports kpAnd kdIt is by following formula meter
It calculates:
Wherein,
It elaborates to the present invention below in conjunction with specific embodiment.
Embodiment one
(1) mathematical model of permanent magnet synchronous motor model is as follows:
Wherein, subscript d, q indicates d, q coordinates, u* d,u* qIt is d, the stator voltage under q coordinates, i*d,i*qIt is stator current,
λd,λqIt is stator magnetic linkage, Ld,LqFor inductive component, ωf、ω* rIt is motor electrical angle and given rotating speed, L respectivelymdIt is stator mutually electricity
Sense, IdfIt is equivalent current, npIt is magnetic pole of the stator logarithm, Rs is stator resistance.
Electromagnetic torque equation corresponding with formula (3) is:
Kinetic equation corresponding with formula (3) is:
Wherein, TlFor mechanical resistive torque, BmIt is friction coefficient, J is rotary inertia.
By applying vector controlled, kinetic equation that can be simplified as:
kppIndicate the proportionality coefficient of the controller of permanent magnet synchronous motor;
Kinetic equation (6) is substituted into electromagnetic torque equation (4), can be obtained:
In practical application, mechanical load hinders square very little (Tl≈ 0), it can ignore, above formula can convert following first differential
Equation:
As can be seen from the above equation, it is differential equation of first order mould according to speed ring model obtained by permanent magnet synchronous motor modelling by mechanism
Type, ωrIndicate the rotating speed of permanent magnet synchronous motor,Indicate rotational speed omegarDerivative.
(2) foundation of mathematical model of the permanent magnet synchronous motor in injection moulding process
The speed ring modeling method of above-mentioned traditional general permanent magnet synchronous motor, individually abstracts motor, does not examine
The practical application object and load changing condition for considering motor, cause built mathematical model and realistic model mismatch.For being molded
Cheng Zhong, high molecular material are between ideal solid material and fluent material, i.e., math equation is in 0 rank and the 1 rank differential equation
Between.Therefore, the present invention is defined as follows fractional order (r ∈ [0, the 1]) differential equation to describe the pass of injection moulding process stress and strain
System:
In above formula, ρ is material property coefficient,For fractional order differential operator, using Ceaputo fractional calculus
It is defined as follows:
The strain stress of material is defined as:
Stress σ suffered by high molecular material shown in formula (9) is generated by the power of motor, macromolecule material shown in formula (11)
The suffered strain stress of material is related with the modification speed of material, and modification (extruding) speed of material is related with the rotating speed of motor.Cause
This, kinetic equation of the motor when squeezing or shearing high molecular material can be converted by formula (5) and (not considered mechanical resistive torque):
Wushu (6) substitutes into above formula (12), and according to formula (4), can obtain mathematical modulo of the permanent magnet synchronous motor in injection moulding process
Type is:
According to above-mentioned reasoning, it can learn that injection moulding process permanent magnet synchronous motor speed ring model is above-mentioned fractional order differential side
Journey (13).
Formula (13) progress Laplace transform, which is obtained the speed ring transmission function of permanent magnet synchronous motor, is:
In above formula, P (S) is indicatedLaplace transform, Wr(s) ω is indicatedrLaplace transform, Iq(s)
Indicate iqLaplace transform, k=a/b, T=1/a, s indicate Laplace operator, r indicate fractional order differential coefficient.
(3) identification of Model Parameters and optimal control method
From above formula (14) as can be seen that parameter k, T in permanent magnet synchronous motor speed ring model can consult motor handbook
Relevant parameter simultaneously carries out simple computation acquisition.In addition, motor speed ring moulds can be obtained as long as picking out fractional order differential coefficient r
Type.The present embodiment propose by given system performance indicator include cross-over frequency, Phase margin and control system open-loop gain
Robustness index, in conjunction with common PD control device, the method for integrated identification control system model and controller parameters setting.
Using PD control device below:
C (s)=kp(1+kds) (15)
Wherein, kp, kdDevice parameter in order to control, kpIndicate proportional gain, kdIndicate the differential gain;
Frequency-domain transform is carried out to above formula to obtain:
C (j ω)=kp(1+jkdω) (16)
Then there is following frequency domain characteristic:
Frequency-domain transform is carried out to formula (14) to obtain:
The frequency characteristic that above formula can then be obtained is as follows:
Therefore, the open-loop transfer function of control system is:
G (s)=C (s) P (s) (22)
According to formula (17) and formula (20), the phase angle characteristics that can obtain the open-loop transfer function G (S) of formula (22) are:
The amplitude characteristic of G (S) is:
Wherein in order to which convenience of calculation enables kp+1=kkp, k=a/b is known.
PD is calculated below in conjunction with the open-loop gain robustness index of given cross-over frequency, Phase margin and control system
The control of controller exports kp、kdWith the fractional order differential coefficient r of motor model:
A) according to given cross-over frequency ωc:
It can get following parametric equation:
Solution above formula can obtain:
B) according to given Phase marginIt can get:
According to above formula, show that parametric equation is as follows:
C) according to the open-loop gain robustness index of control system:
Obtain parametric equation:
It enablesThen above formula can be converted into:
Solution above formula can obtain:
Therefore, r and kd can be solved according to formula (33) and (29), then substitutes into formula (27), you can solve kp+1, into
And obtain kp。
Finally, the control of control system PD control device exports kpAnd kdMotion control is carried out to permanent magnet synchronous motor:Control system
PD control device of uniting executes PD control, that is, proportional-plus-derivative control, and proportional-plus-derivative control is carried out by the tracking error to motor, real
Existing error is equal to 0.After the proportional gain for obtaining PD control device is calculated in above-mentioned steps with the differential gain, you can realize automatic control
System, without obtaining the two parameters by manual debugging as the prior art.
Embodiment two
Control strategy proposed by the present invention control system for permanent-magnet synchronous motor speed ring on injection molding machine is succeeded application.
The structure of control system for permanent-magnet synchronous motor speed ring is by speed control, coordinate transformation module, pulse wide modulation module, inversion
The modules such as device, permanent magnet synchronous motor (PMSM) and encoder form, as shown in Figure 2.In Fig. 2, Sref(k) given speed, S are indicatedb
(k) feedback speed, U are indicatedαIndicate the phase voltage of α phases, UβIndicate the phase voltage of β phases.
Speed ring controller is realized on the dsp chip stm320f2812 of TI companies, servo motor be SANYO GS forever
Magnetic-synchro motor, power 1kw, rated speed 1000r/min.Parameter tuning performance indicator is cross-over frequency ωc=30, phase angle is abundant
π/3 δ=2 are spent, according to equation (29), (33) and (27) solve parameter kp=1.365, kd=0.132 and r=0.586.
The specific algorithm and control flow of control system for permanent-magnet synchronous motor speed ring are as shown in Figures 3 and 4.This implementation
In example, according to kpAnd kdMotion control, the step response of control system for permanent-magnet synchronous motor speed ring are carried out to permanent magnet synchronous motor
The results are shown in Figure 5, although can see that system open loop gain coefficient constantly changes from figure, speed is held essentially constant, and rings
Induction signal quickly follows input signal, system tracking error to rapidly converge to zero.Therefore, this method can reach higher comprehensive control
Performance processed.
It is to be illustrated to the preferable implementation of the present invention, but the invention is not limited to the implementation above
Example, those skilled in the art can also make various equivalent variations or be replaced under the premise of without prejudice to spirit of that invention
It changes, these equivalent modifications or replacement are all contained in the application claim limited range.
Claims (4)
1. a kind of method for controlling permanent magnet synchronous motor towards injection moulding process, which is characterized in that including:
The speed ring transmission function of S1, structure permanent magnet synchronous motor in injection moulding process;
S2, the PD control device model for building control system for permanent-magnet synchronous motor;
The performance indicator of S3, the given control system of basis carry out parameter tuning in conjunction with speed ring transmission function to PD control device
Afterwards, the control output of PD control device is obtained;
S4, motion control is carried out to permanent magnet synchronous motor according to the control of PD control device output;
The step S1, including:
The expression formula of the mathematical model of S11, structure permanent magnet synchronous motor in injection moulding process, the mathematical model is following divides
The number rank differential equation:
In above formula, ωrIndicate the rotating speed of permanent magnet synchronous motor,Indicate the fractional order differential of the rotating speed of permanent magnet synchronous motor
Value, iqIndicate the stator current of permanent magnet synchronous motor,BmIt is friction coefficient, J is rotary inertia, kppIt indicates
The proportionality coefficient of the controller of permanent magnet synchronous motor;
S12, after the Fractional Differential Equation of structure is carried out Laplace transform, the speed ring transmission of permanent magnet synchronous motor is obtained
Function is as follows:
In above formula, P (S) is indicatedLaplace transform, Wr(s) ω is indicatedrLaplace transform, Iq(s) i is indicatedq
Laplace transform, k=a/b, T=1/a, s indicate Laplace operator, r indicate fractional order differential coefficient.
2. a kind of method for controlling permanent magnet synchronous motor towards injection moulding process according to claim 1, which is characterized in that institute
Step S2 is stated, is specially:
The PD control device model of control system for permanent-magnet synchronous motor is built according to the following formula:
C (s)=kp(1+kds)
In above formula, C (S) indicates the control output of PD control device, kpIndicate proportional gain, kdIndicate the differential gain.
3. a kind of method for controlling permanent magnet synchronous motor towards injection moulding process according to claim 2, which is characterized in that institute
Step S3 is stated, including:
S31, according to the speed ring transmission function of permanent magnet synchronous motor and the PD control device model of control system, obtain control system
Open-loop transfer function it is as follows:
G (s)=C (s) P (s)
In above formula, G (S) indicates the open-loop transfer function of control system;
S32, corresponding frequency characteristic, institute are obtained after carrying out frequency-domain transform to speed ring transmission function and PD control device model respectively
The expression formula of the frequency characteristic of acquisition is as follows:
In above formula, Arg [C (j ω)] indicates the phase angle characteristics of C (S), | C (j ω) | indicate the amplitude characteristic of C (S), Arg [P (j
ω)] indicate the phase angle characteristics of P (S), | P (j ω) | indicate the amplitude characteristic of P (S);
S33, the frequency characteristic for calculating the open-loop transfer function G (S) for obtaining control system according to the following formula:
Wherein, Arg [G (j ω)] indicates the phase angle characteristics of G (S), | G (j ω) | indicate the amplitude characteristic of G (S);
S34, the frequency that G (S) is obtained according to the open-loop gain robustness index of given cross-over frequency, Phase margin and control system
After the following condition that rate characteristic need to meet, the control output kp and kd for obtaining PD control device is calculated:
In above formula, ωcIndicate given cross-over frequency,Indicate given Phase margin, the open loop of given control system
Gain robustness index is 0.
4. a kind of method for controlling permanent magnet synchronous motor towards injection moulding process according to claim 3, which is characterized in that institute
State the control output k of PD control devicepAnd kdIt is calculated by the following formula out:
Wherein,
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