CN114826057A - Speed-sensorless control method for induction motor with rotor resistance online identification - Google Patents
Speed-sensorless control method for induction motor with rotor resistance online identification Download PDFInfo
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
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Abstract
The invention discloses a speed sensorless control method of an induction motor with rotor resistance online identification, belonging to the technical field of motor driving and control, wherein the control method comprises the following steps: step 1, designing an observer according to a mathematical model of an induction motor; step 2, designing an online rotor resistance identification method; step 3, building a speed sensorless vector control system model of the induction motor; and 4, adjusting observer parameters and controller parameters to enable the performance indexes of the control system to meet actual requirements. The invention solves the problem of observer parameter mismatch caused by the increase of the rotor resistance of the induction motor along with the temperature rise, can effectively reduce the torque pulsation and the rotating speed error when the rotor resistance increases along with the temperature rise, accelerates the response speed of a system, and realizes the high-precision control of the induction motor without a speed sensor.
Description
Technical Field
The invention relates to the field of motor driving and control, in particular to a speed sensorless control method for an induction motor with rotor resistance online identification.
Background
Induction motors are widely used in various industrial applications because of their advantages such as simple structure and low cost. Vector control has the advantage of high voltage utilization, so more and more frequency converters adopt a vector control algorithm. To realize the closed-loop control of the rotating speed, a speed sensor (such as a photoelectric encoder) is required to be installed to detect the rotating speed information under the normal condition, so that not only is the system cost and complexity increased, but also the rotating speed signal is easy to be interfered by electromagnetic waves in the transmission process. Therefore, a speed sensor-less control method becomes a research hotspot, and the method needs to construct an observer according to a mathematical model of the induction motor and calculate the rotating speed of the motor through physical quantities which are easy to measure, such as rotor voltage, rotor current and the like. However, when the induction motor runs for a long time, the rotor resistance increases along with the temperature rise, which causes the mismatch between the observer parameters and the motor parameters, and causes a large rotation speed estimation error, so how to reduce the mismatch between the induction motor and the observer parameters becomes a research hotspot.
At present, the main research for reducing the problem of the mismatch of the control parameters of the non-speed sensor focuses on configuring a feedback matrix for an observer to reduce the rotating speed estimation error caused by the change of the rotor resistance along with the temperature, so that the problems cannot be solved fundamentally, and the problems of low adjusting speed and large system jitter exist when the rotor resistance is mismatched. Based on the above analysis, it is necessary to develop a new online rotor resistance identification method.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a speed sensorless control method of an induction motor with rotor resistance online identification, which identifies the rotor resistance online and feeds the rotor resistance back to an observer, so as to solve the problem of parameter mismatch caused by the increase of the rotor resistance along with the temperature rise in the speed sensorless control of the induction motor and realize the high-precision control of the speed sensorless.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a speed sensorless control method for an induction motor with online rotor resistance identification comprises the following steps:
step 1, designing an observer according to a mathematical model of an induction motor;
step 2, designing an online rotor resistance identification method;
step 3, building a speed sensorless vector control system model of the induction motor;
and 4, adjusting observer parameters and controller parameters to enable the performance indexes of the control system to meet actual requirements.
The technical scheme of the invention is further improved as follows: the specific process of the step 1 is as follows:
step 1.1, providing a dynamic mathematical model of the induction motor under a two-phase static coordinate system, and solving a state equation according to the mathematical model;
the dynamic mathematical model of the induction motor under the two-phase static coordinate system is as follows:
voltage equation:
the flux linkage equation:
in the formula u sα ,u sβ ,u rα ,u rβ α β is the voltage component, V, of the stator and rotor on the corresponding shaft;
i sα ,i sβ ,i rα ,i rβ α β is the stator and rotor on the corresponding axis current component, a;
ψ sα ,ψ sβ ,ψ rα ,ψ rβ α β is the flux linkage component, Wb, of the lower stator and rotor on the corresponding axis;
ω r -rotor electrical angular velocity, rad/s; r s -stator resistance, Ω; r r -rotor resistance, Ω;
L s -a stator inductance, H; l is r -a rotor inductance, H; l is m -motor mutual inductance, H;
the equation of state obtained from the above mathematical model is:
in the formula (I), the compound is shown in the specification,
step 1.2, constructing a self-adaptive full-order observer according to the state equation:
in the formula (I), the compound is shown in the specification,
in the formula (4), the reaction mixture is,
as an estimate of the resistance of the rotor,
is an estimated value of the rotational speed,
and
the component of the stator current estimated value in each coordinate axis of the two-phase static coordinate system,
and
for the rotor to be magneticThe chain estimate is the component of each coordinate axis in the two-phase stationary coordinate system.
The technical scheme of the invention is further improved as follows: the specific process of the step 2 comprises the following steps:
step 2.1, according to the observer model, obtaining an observer observation error model:
in the formula (5), Δ R r Error is identified for rotor resistance, and
estimating the component of each coordinate axis of the stator current estimation error in a two-phase static coordinate system;
step 2.2, because the system output is the stator current, the output convergence is ensured, namely the system convergence can be ensured, and a Lyapunov function is constructed by adopting a system output error term:
and 2.3, obtaining the following by deriving the formula:
due to the fact that
Thus ignoring it
And
to ensure
Only the formula (8) is ensuredImmediately, the method comprises the following steps:
step 2.4, designing a rotor resistance self-adaptive law according to the Lyapunov stability theorem as follows:
in order to ensure the convergence speed of the system, a PI controller is adopted to replace a gain and integral link, and the rotor online identification method obtained by the formula comprises the following steps:
in the formula (10), k p Is the proportionality coefficient, k, of the PI controller i Is the integral coefficient of the PI controller, and s is a differential operator;
and 2.5, introducing the novel rotor resistance online identification method into a full-order adaptive observer.
The technical scheme of the invention is further improved as follows: the specific process of the step 3 comprises the following steps:
step 3.1, sampling stator voltage u A ,u B ,u C And stator current i A ,i B ,i C And transforming the stator voltage and the stator current to a two-phase static coordinate system through Clark transformation, wherein the transformation matrix is C 3/2 ：
Step 3.2, stator voltage u under the two-phase static coordinate system sα ,u sβ And stator current i sα ,i sβ Rotor flux linkage calculated by adaptive full-order observer
And rotational speed
And given rotor flux linkage
And rotational speed
Forming a closed loop, and obtaining the given value of the stator current under a rotating coordinate system through a PI regulator
Step 3.3, the stator current i under the two-phase static coordinate system is processed sα ,i sβ After Park conversion, the reference voltage is converted to a rotating coordinate system and is set with the stator current
Forming a closed loop, and obtaining a stator voltage given value under a two-phase static coordinate system through a PI regulator
Transforming the matrix to C 2s/2r ：
In the formula (12), the reaction mixture is,
is the included angle between the static coordinate system and the rotating coordinate system;
step 3.4, setting the stator voltage under the rotating coordinate system
After Park inverse transformation, converting the voltage into a two-phase static coordinate system, and converting the stator voltage under the two-phase static coordinate system
Through SVPWM modulation, a control signal is output to control the on-off of an inverter power device, so that the input of the stator side of the induction motor is controlled.
The technical scheme of the invention is further improved as follows: the specific process of the step 4 is as follows: and adjusting the parameters according to the selection principle of observer parameters and controller parameters required in the analysis process and the theoretical derivation process until the required performance indexes of the control system are met.
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. the invention provides a novel rotor resistance self-adaptation law by adopting a rotor resistance online identification method, and solves the problem of observer parameter mismatch caused by the change of the rotor resistance of an induction motor along with the temperature.
2. The self-adaptive law of the rotor resistance provided by the invention can effectively reduce the torque pulsation, the rotating speed error and the adjusting time when the rotor resistance is increased along with the temperature rise.
3. The rotor resistance self-adaptive law designed by the invention only contains physical quantities such as stator current, rotor flux linkage and the like, and does not contain internal parameters of the motor, so that the practicability and the transportability of the invention are greatly enhanced.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of the adaptive full-order observer of the present invention;
FIG. 3 is a structural diagram of an adaptive full-order observer based on rotor resistance online identification according to the present invention;
FIG. 4 is a block diagram of an induction motor speed sensorless vector control system of the present invention;
FIG. 5 is a comparison graph I of the rotor resistance identification result of the conventional rotor resistance online identification method and the novel rotor resistance online identification method provided by the invention under no-load working condition;
FIG. 6 is a second comparison graph of the rotor resistance recognition results of the conventional rotor resistance online recognition method and the novel rotor resistance online recognition method of the present invention under no-load conditions;
FIG. 7 is a first comparison graph of the rotation speed, the stator current and the electromagnetic torque under no-load condition of the conventional rotor resistance online identification method and the novel rotor resistance online identification method provided by the invention;
FIG. 8 is a second comparison graph of the rotation speed, the stator current and the electromagnetic torque under no-load condition of the conventional rotor resistance online identification method and the novel rotor resistance online identification method provided by the invention;
FIG. 9 is a first comparison graph of the rotation speed, the stator current and the electromagnetic torque under the load condition of the conventional rotor resistance online identification method and the novel rotor resistance online identification method provided by the invention;
fig. 10 is a second comparison graph of the rotation speed, the stator current and the electromagnetic torque under the loaded condition of the conventional rotor resistance online identification method and the novel rotor resistance online identification method provided by the invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and examples:
in the control without the speed sensor, because the induction motor runs for a long time, the resistance of the rotor is increased along with the temperature rise, so that the parameter mismatch of the observer is caused, and the estimation precision of the rotating speed is further influenced. Aiming at the problem, the invention provides a novel rotor resistance online identification method, which solves the problem of observer parameter mismatch caused by the increase of the rotor resistance of the induction motor along with the temperature rise, can effectively reduce the torque pulsation and the rotating speed error when the rotor resistance increases along with the temperature rise, accelerates the response speed of a system, and realizes the high-precision control of the induction motor without a speed sensor.
With reference to fig. 1, fig. 2, fig. 3, and fig. 4, a method for controlling a non-speed sensor of an induction motor with online rotor resistance identification includes the following steps:
step 1, designing an observer according to a mathematical model of an induction motor;
according to the above, with reference to fig. 2, the specific process of step 1 is:
step 1.1, providing a dynamic mathematical model of the induction motor under a two-phase static coordinate system, and solving a state equation according to the mathematical model;
the dynamic mathematical model of the induction motor under the two-phase static coordinate system is as follows:
voltage equation:
the flux linkage equation:
in the formula u sα ,u sβ ,u rα ,u rβ α β is the voltage component, V, of the stator and rotor on the corresponding shaft;
i sα ,i sβ ,i rα ,i rβ α β is the stator and rotor on the corresponding axis current component, a;
ψ sα ,ψ sβ ,ψ rα ,ψ rβ α β is the flux linkage component, Wb, of the lower stator and rotor on the corresponding axis;
ω r -rotor electrical angular velocity, rad/s; r s -stator resistance, Ω; r r -rotor resistance, Ω;
L s -a stator inductance, H; l is r -a rotor inductance, H; l is m -motor mutual inductance, H;
the equation of state obtained from the above mathematical model is:
in the formula (I), the compound is shown in the specification,
step 1.2, constructing a self-adaptive full-order observer according to the state equation:
in the formula (4), the reaction mixture is,
step 2, designing an online rotor resistance identification method;
obtaining an observer model according to the step 1, wherein the specific process of the step 2 comprises the following steps:
step 2.1, according to the observer model, obtaining an observer observation error model:
in the formula (5), Δ R r Error is identified for rotor resistance, and
estimating the component of each coordinate axis of the stator current estimation error in a two-phase static coordinate system;
step 2.2, because the system output is the stator current, the output convergence is ensured, namely the system convergence is ensured, and a Lyapunov function is constructed by adopting a system output error term:
and 2.3, obtaining the following by deriving the formula:
due to the fact that
Therefore, neglectSlightly less than
And
to ensure
Only by ensuring that equation (8) holds:
step 2.4, designing a rotor resistance self-adaptive law according to the Lyapunov stability theorem as follows:
in order to ensure the convergence speed of the system, a PI controller is adopted to replace a gain and integral link, and the rotor online identification method obtained by the formula comprises the following steps:
in the formula (10), k p Is the proportionality coefficient, k, of the PI controller i Is the integral coefficient of the PI controller, and s is a differential operator;
the derivation process from equation (9) to equation (10) is: in formula (9)
The constant coefficient is adopted, and in order to accelerate the response speed of the system, the PI controller is adopted to replace the constant coefficient and the integral link in the formula (9), so that the novel rotor resistance online identification method shown in the formula (10) does not contain internal parameters of the motor, and the practicability and the portability of the rotor resistance online identification method are greatly enhanced.
And 2.5, introducing the novel rotor resistance online identification method into a full-order adaptive observer.
Step 3, building a speed sensorless vector control system model of the induction motor;
according to the above adaptive state observer model and the rotor resistance online identification method, the specific process of step 3 is as follows:
step 3.1, sampling stator voltage u A ,u B ,u C And stator current i A ,i B ,i C And transforming the stator voltage and the stator current to a two-phase static coordinate system through Clark transformation, wherein the transformation matrix is C 3/2 ：
Step 3.2, stator voltage u under the two-phase static coordinate system sα ,u sβ And stator current i sα ,i sβ Rotor flux linkage calculated by adaptive full-order observer
And rotational speed
And given rotor flux linkage
And rotational speed
Forming a closed loop, and obtaining the given value of the stator current under a rotating coordinate system through a PI regulator
Step 3.3, the stator current i under the two-phase static coordinate system is processed sα ,i sβ After Park conversion, the voltage is converted into a rotating coordinate system and is given with the stator current
Forming a closed loop, and obtaining a stator voltage given value under a two-phase static coordinate system through a PI regulator
Transforming the matrix to C 2s/2r ：
In the formula (12), the reaction mixture is,
is the angle between the stationary coordinate system and the rotating coordinate system.
Step 3.4, setting the stator voltage under the rotating coordinate system
After Park inverse transformation, converting the voltage into a two-phase static coordinate system, and converting the stator voltage under the two-phase static coordinate system
And through SVPWM modulation, a control signal is output to control the on and off of an inverter power device, so that the input of the stator side of the induction motor is controlled.
And 4, adjusting observer parameters and controller parameters to enable the performance indexes of the control system to meet actual requirements.
By adopting the method, the specific process of the step 4 is as follows:
and adjusting the parameters according to the selection principle of observer parameters and controller parameters required in the analysis process and the theoretical derivation process until the required performance indexes of the control system are met.
The following examples were used to demonstrate the beneficial effects of the present invention:
the parameters of the induction motor speed sensorless vector control system model based on rotor resistance online identification shown in fig. 2-4 are as follows:
aiming at the novel rotor resistance online identification method, in order to verify the effectiveness of the invention, the novel rotor resistance online identification method is compared with the traditional rotor resistance online identification method.
Given a rotation speed of 15rad/s and 4s, the rotor resistance is suddenly changed by 1.5 times, and the load torque is zero, as shown in fig. 5 and 6, the rotor resistance identification result is shown, and fig. 7 and 8 are simulation results of the rotation speed, the electromagnetic torque and the stator current.
As can be seen from fig. 5, after the conventional rotor resistance online identification is introduced in 2s, the rotor resistance identification value is stabilized at 2.658 Ω, and after the rotor resistance suddenly changes in 4s, the rotor resistance identification value is once large, but the speed is slow, and the identification result has small fluctuation. As can be seen from fig. 6, after the novel rotor resistance is introduced in 2s for online identification, the identification value of the rotor resistance is stabilized at 2.658 Ω, and after the rotor resistance suddenly changes for 4s, the identification value is stabilized at 3.987 Ω after about 2s adjustment, and the identification result is not jittered. Therefore, the novel rotor resistance online identification method provided by the invention can effectively accelerate the system response speed.
As can be seen from fig. 7, when the rotor resistance is identified by the conventional method and suddenly changed by 1.5 times in 4s, the identification rotating speed fluctuates between 14rad/s and 16rad/s, the real rotating speed drop value is about 0.2rad/s, the electromagnetic torque fluctuates between-10 N.m and 10 N.m, the estimated value of the stator current has obvious 'burr' phenomenon, as the identification result of the rotor resistance gradually approaches to the real value, the identification error of the rotor resistance is smaller and smaller, the fluctuation of the rotating speed and the electromagnetic torque is gradually reduced, and the current 'burr' phenomenon is gradually lightened, however, the traditional method has the problem that the speed of tracking the true value of the rotor resistance identification value is slow, so that the adjustment time of gradually reducing the true value of the rotating speed tracking and the electromagnetic torque is long, an error band is calculated according to 2%, the identification rotating speed is converged into the error band when 8.5s, and the adjustment time is about 4.5 s.
As can be seen from FIG. 8, when the 4s rotor resistance is suddenly changed by 1.5 times, the identification rotation speed fluctuates between 14.1rad/s and 15.9rad/s, the real rotation speed is reduced by about 0.1rad/s, the electromagnetic torque fluctuates between-8 N.m and 8 N.m, the phenomenon of current "glitch" is obviously reduced, as the identification value of the rotor resistance gradually approaches the real value, the fluctuation of the rotation speed and the electromagnetic torque gradually decreases, when the identification rotation speed is 4.7s, the real value is accurately tracked, and the adjustment time is about 0.7 s.
Comparing fig. 7 and fig. 8, the novel rotor resistance online identification method provided by the invention is explained, which can reduce the rotation speed and electromagnetic torque fluctuation in a limited way and shorten the adjustment time when the rotor resistance changes suddenly.
Given rotation speed of 15rad/s, adding 8 load torque suddenly when 4s, and suddenly changing 1.5 times rotor resistance when 6s, as shown in fig. 9 and fig. 10, which are simulation results of the conventional method and the novel rotor resistance identification method provided by the invention, respectively.
As can be seen from fig. 9, when the rotor resistance of 6s suddenly changes by 1.5 times, the real rotation speed drops by about 2rad/s, and as the rotor resistance identification value approaches the real value, the real rotation speed is adjusted back, and the identification rotation speed fluctuation gradually decreases, but because the speed of tracking the real value by the rotor resistance identification result of the conventional method is slower, the adjustment time of the real rotation speed is longer, the electromagnetic torque still has larger fluctuation within a longer time, and the phenomenon of "burr" of the stator current estimation value is more serious.
As can be seen from fig. 10, when the rotor resistance of 6s suddenly changes by 1.5 times, the true rotation speed drop is about 1.5rad/s, and as the identification result of the rotor resistance approaches to the true value, the true rotation speed is adjusted back, the identification rotation speed fluctuation is gradually reduced, the electromagnetic torque fluctuation is small, and the phenomenon of the stator current estimation value "burr" is light.
Compared with the graph in fig. 9 and 10, the novel rotor resistance online identification method provided by the invention can effectively accelerate the system response speed and reduce the torque ripple under the working condition of load.
The present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof, and it is intended that all such changes and modifications be considered within the scope of the appended claims.
Claims (5)
1. A control method of a speed sensorless induction motor with rotor resistance online identification is characterized in that: the method comprises the following steps:
step 1, designing an observer according to a mathematical model of an induction motor;
step 2, designing an online rotor resistance identification method;
step 3, building a speed sensorless vector control system model of the induction motor;
and 4, adjusting observer parameters and controller parameters to enable the performance indexes of the control system to meet actual requirements.
2. The method for controlling the speed sensorless induction motor with the rotor resistance identified online as claimed in claim 1, wherein: the specific process of the step 1 is as follows:
step 1.1, providing a dynamic mathematical model of the induction motor under a two-phase static coordinate system, and solving a state equation according to the mathematical model;
the dynamic mathematical model of the induction motor under the two-phase static coordinate system is as follows:
voltage equation:
the flux linkage equation:
in the formula u sα ,u sβ ,u rα ,u rβ α β is the voltage component, V, of the stator and rotor on the corresponding shaft;
i sα ,i sβ ,i rα ,i rβ α β is the stator and rotor on the corresponding axis current component, a;
ψ sα ,ψ sβ ,ψ rα ,ψ rβ α β is the flux linkage component, Wb, of the lower stator and rotor on the corresponding axis;
ω r -rotor electrical angular velocity, rad/s; r s -stator resistance, Ω; r r -rotor resistance, Ω;
L s -a stator inductance, H; l is r -a rotor inductance, H; l is m -motor mutual inductance, H;
the equation of state obtained from the above mathematical model is:
in the formula (I), the compound is shown in the specification,
u＝[u sα u sβ 0 0] T ，y＝[i sα i sβ ] T ，
step 1.2, constructing a self-adaptive full-order observer according to the state equation:
in the formula (I), the compound is shown in the specification,
in the formula (4), the reaction mixture is,
as an estimate of the resistance of the rotor,
as an estimate of the rotational speed,
and
the component of the stator current estimated value in each coordinate axis of the two-phase static coordinate system,
and
the rotor flux linkage estimation value is the component of each coordinate axis in the two-phase static coordinate system.
3. The method for controlling the speed sensorless induction motor with the rotor resistance identified online as claimed in claim 1, wherein: the specific process of the step 2 comprises the following steps:
step 2.1, according to the observer model, obtaining an observer observation error model:
in the formula (5), Δ R r Error is identified for rotor resistance, and
estimating the component of each coordinate axis of the stator current estimation error in a two-phase static coordinate system;
step 2.2, because the system output is the stator current, the output convergence is ensured, namely the system convergence can be ensured, and a Lyapunov function is constructed by adopting a system output error term:
and 2.3, obtaining the following by deriving the formula:
due to the fact that
Thus ignoring it
And
to ensure
Only by ensuring that equation (8) holds:
step 2.4, designing a rotor resistance self-adaptive law according to the Lyapunov stability theorem as follows:
in order to ensure the convergence speed of the system, a PI controller is adopted to replace a gain and integral link, and the rotor online identification method obtained by the formula comprises the following steps:
in the formula (10), k p Is the scaling factor of the PI-controller,k i is the integral coefficient of the PI controller, and s is a differential operator;
and 2.5, introducing the novel rotor resistance online identification method into a full-order adaptive observer.
4. The method for controlling the speed sensorless induction motor with the rotor resistance identified online as claimed in claim 1, wherein: the specific process of the step 3 comprises the following steps:
step 3.1, sampling stator voltage u A ,u B ,u C And stator current i A ,i B ,i C And transforming the stator voltage and the stator current to a two-phase static coordinate system through Clark transformation, wherein the transformation matrix is C 3/2 ：
Step 3.2, stator voltage u under the two-phase static coordinate system sα ,u sβ And stator current i sα ,i sβ Rotor flux linkage calculated by adaptive full-order observer
And rotational speed
And given rotor flux linkage
And rotational speed
Forming a closed loop, and obtaining the given value of the stator current under a rotating coordinate system through a PI regulator
Step 3.3, under the two-phase static coordinate systemStator current i sα ,i sβ After Park conversion, the voltage is converted into a rotating coordinate system and is given with the stator current
Forming a closed loop, and obtaining a stator voltage given value under a two-phase static coordinate system through a PI regulator
Transforming the matrix to C 2s/2r ：
In the formula (12), the reaction mixture is,
is the included angle between the static coordinate system and the rotating coordinate system;
step 3.4, setting the stator voltage under the rotating coordinate system
After Park inverse transformation, converting the voltage into a two-phase static coordinate system, and converting the stator voltage under the two-phase static coordinate system
And through SVPWM modulation, a control signal is output to control the on and off of an inverter power device, so that the input of the stator side of the induction motor is controlled.
5. The method for controlling the speed sensorless induction motor with the rotor resistance identified online as claimed in claim 1, wherein: the specific process of the step 4 is as follows:
and adjusting the parameters according to the selection principle of observer parameters and controller parameters required in the analysis process and the theoretical derivation process until the required performance indexes of the control system are met.
Priority Applications (1)
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