Disclosure of Invention
In view of this, the present invention provides an improved method for predicting dead beat of a single current sensor of a permanent magnet synchronous motor, which specifically includes the following steps:
step one, collecting three-phase current i of permanent magnet synchronous motor at current k moment in real time on linea、ib、icA rotor speed w and a rotor position angle theta;
establishing mathematical models of the permanent magnet synchronous motor in an alpha-beta coordinate system and a d-q coordinate system, and establishing a traditional dead-beat current prediction control model; improving the traditional deadbeat current prediction control model based on the difference between the current measured value and the predicted value at the current k moment caused by parameter disturbance to obtain an improved deadbeat current prediction control model corresponding to the k +1 moment; calculating reference voltage within the SVPWM output voltage range at the k +1 moment in real time by combining the data acquired in the step one;
step three, the improved permanent magnet synchronous motor dead-beat prediction control and the single current sensor bus current sampling are combined, namely, the three-phase current i is reconstructed by utilizing the real-time switching state of the inverter and the acquired inverter bus current ia、ib、icReplacing the three-phase current i of the permanent magnet synchronous motor acquired in real time in the step onea、ib、icAnd calculating actual predicted values of d-axis current and q-axis current at the k moment based on a volt-second balance principle by using the actual values of the d-axis current and the q-axis current at the first rising edge moment in the switching period at the k-1 moment, and replacing corresponding current values in the improved deadbeat current prediction control model.
Further, in the second step, a mathematical model of the permanent magnet synchronous motor in the α - β coordinate system is as follows:
uα=Rsiα+Lspiα-weψrsinθ
uβ=Rsiβ+Lspiβ+weψrcosθ
ψα=Lsiα+ψrcosθ
ψβ=Lsiβ+ψrsinθ
Te=1.5pmψr(iβcosθ-iαsinθ)
in the formula uα、uβIs the stator voltage under an alpha-beta coordinate system; i.e. iα、iβIs in an alpha-beta coordinate systemA stator current; ΨrIs a rotor flux linkage; rsIs a stator resistor; l issIs a stator inductance; w is ae、wmThe electrical angular velocity of the rotor and the mechanical angular velocity of the rotor, respectively; theta is a rotor position angle; p is a differential operator; t iseIs an electromagnetic torque; t isLIs the load torque; b is a viscosity coefficient; p is a radical ofmThe number of pole pairs of the motor is shown; Ψα、ΨβIs a stator flux linkage under an alpha-beta coordinate system; t is a time variable; j is load moment of inertia;
the mathematical model of the permanent magnet synchronous motor under a d-q coordinate system is as follows:
ud=Rsid+pψd-weψq
uq=Rsiq+pψq+weψd
ψd=Ldid+ψr
ψq=Lqiq
Te=1.5pm(ψriq+(Ld-Lq)idiq)
in the formula ud、uqIs the stator voltage under a d-q coordinate system; i.e. id、iqIs the stator current under a d-q coordinate system; Ψd、ΨqIs a stator flux linkage under a d-q coordinate system; l isd、LqArmature inductances of d and q axes, respectively;
the traditional deadbeat current prediction control model is established as follows:
id-p(k+1)=id(k)×(1-Ts×Rs/Ls)+iq(k)×Ts×we+Ts/Ls×ud(k)
iq-p(k+1)=iq(k)×(1-Ts×Rs/Ls)-id(k)×Ts×we+Ts/Ls×uq(k)-Ts×we×ψr/Ls
ud-p(k+1)=Ls/Ts×(id-ref-(1-Ts×Rs/Ls)×id-p(k+1)-Ts×iq-p(k+1)×we)
uq-p(k+1)=Ls/Ts×(iq-ref-(1-Ts×Rs/Ls)×iq-p(k+1)+Ts×id-p(k+1)×we+Ts×we/Ls×ψr)
in the formula id-p(k +1) d-axis predicted current, i, at time k +1q-p(k +1) is the predicted current of the q-axis at the time k +1, id-refFor d-axis reference current, iq-refFor q-axis reference current, ud-p(k +1) d-axis predicted voltage at time k +1, uq-p(k +1) is the predicted voltage of the q-axis at time k +1, TsIs a switching cycle;
the improved deadbeat current prediction control model is as follows:
id-error(k)=id-p(k)-id(k)
iq-error(k)=iq-p(k)-iq(k)
Kd2=(ud(k-1)-ud(k-2))
Kq2=(uq(k-1)-uq(k-2))
Xd=(id-err(k)-id-error(k-1))/Kd2/TsXq
=(iq-error(k)-iq-err(k-1))/Kq2/Ts
Kd=1/Ls-Xd
Kq=1/Ls-Xq
id-p(k+1)
=ud(k)×Kd×Ts+id(k)×(1-Ts×Rs/Ls)+iq(k)×Ts×we-(id-error(k)-Xd×Ts×ud(k))
iq-p(k+1)
=uq(k)×Kq×Ts+iq(k)×(1-Ts×Rs/Ls)-id(k)×Ts×we-Ts×we×Ψf/Ls-(iq-error(k)-Xq×Ts×uq(k))
ud-p(k+1)
=(id-ref-id-p(k+1)×(1-Ts×Rs/Ls)-iq-p(k+1)×Ts×we+id-err(k))/(Kd+Xd)/Ts
uq-p(k+1)
=(iq-ref-iq-p(k+1)×(1-Ts×Rs/Ls)+id-p(k+1)×Ts×we+Ts×we×Ψf/Ls+iq-error(k))/(Kq+Xq)/Ts
in the formula id-err(k)、iq-error(k) D and q axis current prediction errors i at time kd-p(k)、iq-p(k) D and q axis current predicted values i at the k timed(k)、iq(k) Actual measured values of d-and q-axis currents at time k, ud(k-1) and ud(k-2) d-axis voltages respectively acting at the k-1 moment and the k-2 moment, and u can be obtained by the same principleq(k-1) and uq(k-2),id-p(k +1) is the improved d-axis predicted current at time k +1, iq-pAnd (k +1) is the improved q-axis predicted current at the k +1 moment.
Further, the third step is specifically:
calculating the current at the k moment according to the reconstructed current at the k-1 switching cycle current updating momentPredicted value i of actual valued′(k)、iq' (k) replacing the actual value of the current at the time k, the current update time pair u of the k-1 cycle is calculatedd(k-1) and uq(k-1) performing compensation;
id′(k)=id(k-1,t1)×(1-(Ts-t1)×Rs/Ls)+iq(k-1,t1)×(Ts-t1)×we+(Ts-t1)/Ls×ud(k-1)×Ts/(Ts-t1)
iq′(k)=iq(k-1,t1)×(1-(Ts-t1)×Rs/Ls)-id(k-1,t1)×(Ts-t1)×we+(Ts-t1)/Ls×uq(k-1)×Ts/(Ts-t1)-(Ts-t1)×we×Ψf/Ls
wherein id' (k) is a predicted value of the actual value of the d-axis current at time k, iq' (k) is a predicted value of the actual value of the q-axis current at time k, t1For the first rising edge instant i in a switching cycled(k-1,t1) Is the d-axis current actual value, i, at the time of the k-1 period t1q(k-1,t1) Is k-1 period t1An actual value of q-axis current at a time;
then using id' (k) and iq' (k) replacement of i in the improved deadbeat current predictive control model in step twod(k) And iq(k)。
The improved single-current-sensor dead-beat prediction control method for the permanent magnet synchronous motor has the characteristic of good parameter disturbance suppression, and can completely replace the three-phase current of the motor to carry out prediction control by combining the improved dead-beat prediction control with the phase current reconstruction based on the bus current sensor, and simultaneously still maintain certain parameter disturbance suppression capability. It can be seen that the method of the present invention has at least the following beneficial effects compared to the prior art:
(1) the method effectively inhibits the influence caused by the change of the motor parameters by utilizing the improved dead-beat predictive control, so that the system has good control characteristics.
(2) The method combines improved dead-beat predictive control with phase current reconstruction based on the bus current sensor, reduces the cost of a control system, reduces the volume of the control system, and avoids the limitation of the difference between different sensors on the performance improvement of the whole system.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The improved single-current sensor dead-beat prediction control method for the permanent magnet synchronous motor, as shown in fig. 1, specifically comprises the following steps:
step one, collecting three-phase current i of permanent magnet synchronous motor at current k moment in real time through online dataa、ib、icA rotor speed w and a rotor position angle theta;
establishing mathematical models of the permanent magnet synchronous motor in an alpha-beta coordinate system and a d-q coordinate system, establishing a traditional deadbeat current prediction control model, and improving the traditional deadbeat current prediction control model based on the difference between a current measured value and a predicted value at the current moment caused by parameter disturbance to obtain an improved deadbeat current prediction control model corresponding to the k +1 moment; calculating reference voltage within the SVPWM output voltage range at the next moment in real time by combining the data collected in the first step;
thirdly, reconstructing a three-phase current i by utilizing the real-time switching state of the inverter and the acquired bus current i of the invertera、ib、icReplacing the three-phase current i of the permanent magnet synchronous motor acquired in real time in the step onea、ib、icAnd calculating actual predicted values of d-axis current and q-axis current at the k moment by using the actual values of the d-axis current and the q-axis current at the first rising edge moment in the switching period at the k-1 moment and a volt-second balance principle, and replacing corresponding current values in the improved deadbeat current prediction control model. .
Conventional deadbeat current predictive control is based on a current reference irefAnd the voltage vector u (k) applied to the motor at the current moment and the motor parameters, and outputting the motor reference voltage u (k +1) at the next moment. At the k-th instant u (k +1) is calculated and applied at the next instant, so that the motor current reaches the current reference value at the instant k + 2. Thus, u (k +1) can be calculated at the kth time according to the following relation:
ud(k+1)=(2TsRs-2Ls)wiq(k)-(Ls/Ts+TsRsRs/Ls-2Rs)id(k)+TsLswwid(k)-Tswuq(k)-(1-TsRs/Ls)ud(k)+wwTsψf
uq(k+1)=Ls/Ts×iq-ref-(Ls/Ts+TsRsRs/Ls-2Rs)iq(k)-(2TsRs-2Ls)id(k)iq(k)+TsLswwiq(k)+Tswud(k)-(1-TsRs/Ls)uq(k)+w(2ψf-TsRsψf/Ls)
in the formula TsIs a control period; i.e. iq-refIs a q-axis reference current.
When the calculated reference voltage exceeds the maximum output voltage limit of the SVPWM, the output reference voltage needs to be adjusted to obtain the reference voltage within the SVPWM output range:
in the formula ud-j、uq-jThe calculated stator reference voltage under the d-q coordinate system; u. ofd-x、uq-xThe reference voltage within the corrected SVPWM output voltage range under the d-q coordinate system is obtained; u. ofdcIs the dc bus voltage.
It can be seen that the traditional dead-beat predictive control has high dependence on the motor model and parameter accuracy, and once the motor has parameter mismatch in the running process, the control effect is rapidly reduced. The invention changes the traditional dead-beat prediction control, and can be seen from the traditional dead-beat model that the current predicted value at the k +1 moment is different from the measured value due to parameter disturbance, and the error magnitude of the current predicted value is related to the variable quantity of the parameter:
for the d-axis, there are:
id-p(k)=id(k-1)×(1-Ts×Rs′/Ls′)+iq(k-1)×Ts×we+Ts×ud(k-1)/Ls′
id(k)=id(k-1)×(1-Ts×Rs/Ls)+iq(k-1)×Ts×we+Ts×ud(k-1)/Ls
in the formula, Rs′、Ls' is the theoretical value of the resistance and inductance of the stator of the motor, Rs、LsIs its actual value.
Δid(k)=id-p(k)-id(k)
=ud(k-1)×(Ts/Ls′-Ts/Ls)+id(k-1)×(Ts×Rs/Ls-Ts′×Rs′/Ls′)
In the same way, the method for preparing the composite material,
Δid(k-1)=ud(k-2)×(Ts/Ls′-Ts/Ls)+id(k-2)×(Ts×Rs/Ls-Ts′×Rs′/Ls′)
in the above two equations, the second term is very small compared with the first term and can be ignored, so that:
Δσd=Δid(k)-Δid(k-1)=(Ts/Ls′-Ts/Ls)×(ud(k-1)-ud(k-2))
then order:
Kd1=Δσd/(ud(k-1)-ud(k-2))=Ts/Ls′-Ts/Ls
the predicted value of the current at the k +1 moment is optimized for the first time:
id-p′(k+1)=(Ts/Ls′-Kd1)×ud(k)+id(k)×(1-Ts×Rs/Ls)+iq(k)×Ts×ωe
and then ordering:
Kd2=Δid(k)-Kd1×ud(k-1)
and (3) carrying out second optimization on the predicted value of the current at the k +1 moment:
id-p(k+1)=id-p′(k+1)-Kd2
thus, the predicted current value at the time k +1 is optimized by using the error between the predicted current value and the actual current value at the time k, and the obtained optimized value can contain the information of the parameter disturbance, namely, the predicted current value at the time k +1 of the parameter disturbance is considered. The q-axis current can also be obtained based on the same principle.
Since the dead beat prediction control is a two beat prediction, i after optimization is usedd-pWhen calculating the reference voltage at the time k +1 from the reference currents at the times (k +1) and k +2, the parameter disturbance is also considered:
id-p′(k+2)=(Ts/Ls′-Kd1)×ud(k+1)+id-p(k+1)×(1-Ts×Rs/Ls)+iq-p(k+1)×Ts×we
id-ref=id-p(k+2)=id-p′(k+2)-Kd2
=(Ts/Ls′-Kd1)×ud(k+1)+id-p(k+1)×(1-Ts×Rs/Ls)+iq-p(k+1)×Ts×we-Kd2
solving the value of ud (k +1) according to the two formulas;
ud(k+1)=(id-ref+Kd2-id-p(k+1)×(1-Ts×Rs/Ls)-iq-p(k+1)×Ts×we)/(Ts/Ls′-Kd1)
the q-axis voltage can also be obtained based on the same principle as described above.
The above derivation process is simplified, so that an improved deadbeat current prediction control model can be obtained:
id-error(k)=id-p(k)-id(k)
iq-e(k)=iq-p(k)-iq(k)
Kd2=(ud(k-1)-ud(k-2))
Kq2=(uq(k-1)-uq(k-2))
Xd=(id-error(k)-id-err(k-1))/Kd2/Ts
Xq=(iq-err(k)-iq-err(k-1))/Kq2/Ts
Kd=1/Ls-Xd
Kq=1/Ls-Xq
id-p(k+1)
=ud(k)×Kd×Ts+id(k)×(1-Ts×Rs/Ls)+iq(k)×Ts×we-(id-error(k)-Xd×Ts×ud(k))
iq-p(k+1)
=uq(k)×Kq×Ts+iq(k)×(1-Ts×Rs/Ls)-id(k)×Ts×we-Ts×we×Ψf/Ls-(iq-error(k)-Xq×Ts×uq(k))
ud-p(k+1)
=(id-ref-id-p(k+1)×(1-Ts×Rs/Ls)-iq-p(k+1)×Ts×we+id-error(k))/(Kd+Xd)/Ts
uq-p(k+1)
=(iq-r-iq-p(k+1)×(1-Ts×Rs/Ls)+id-p(k+1)×Ts×we+Ts×we×Ψf/Ls+iq-err(k))/(Kq+Xq)/Ts
the improved dead-beat current prediction control model provided by the invention is applied to the bus current sensor, and the bus current sensor collects bus current twice at different voltage vector action moments in the first half period of a switching period according to the SVPWM seven-segment modulation mode. The specific acquisition method comprises the following steps: the current value at the moment when the switch state changes from 0 to 1 (i.e., the first two rising edges) is collected. Is provided with the firstA rising edge at time t1The second rising edge at time t2Since this time is not the initial time of each switching cycle, this means that only the current value reconstructed at the rising edge time of the previous cycle is available for the dead-beat prediction control of each cycle, and therefore, it is necessary to calculate the predicted value of the current actual value at the time k in place of the actual value of the current at the time k, based on the reconstructed current at the current update time of the previous switching cycle. And because the voltage vector in the dead-beat prediction model is an average value in a whole switching period, and when the predicted value of the current actual value at the k moment is calculated according to the reconstructed current at the current updating moment of the previous switching period, the time span is not the whole period, but Ts-t1Therefore, the current updating time of k-1 period is needed to be calculated according to the volt-second balance principled(k-1) and uq(k-1) compensate, i.e. multiply both of the equations by a factor: t iss/(Ts-t1). The method specifically comprises the following steps:
id′(k)=id(k-1,t1)×(1-(Ts-t1)×Rs/Ls)+iq(k-1,t1)×(Ts-t1)×we+(Ts-t1)/Ls×ud(k-1)×Ts/(Ts-t1)
iq′(k)=iq(k-1,t1)×(1-(Ts-t1)×Rs/Ls)-id(k-1,t1)×(Ts-t1)×we+(Ts-t1)/Ls×uq(k-1)×Ts/(Ts-t1)-(Ts-t1)×we×Ψf/Ls
fig. 2 and 3 show that in a preferred embodiment of the invention, the resistance mismatch (Rs ═ 10 Rs') and flux linkage mismatch (ψ) are presentf=2ψf') in different cases, the d and q axis currents obtained on the basis of the invention are compared with a reference current.
It should be understood that, the sequence numbers of the steps in the embodiments of the present invention do not mean the execution sequence, and the execution sequence of each process should be determined by the function and the inherent logic of the process, and should not constitute any limitation on the implementation process of the embodiments of the present invention.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.