CN114362600A - Permanent magnet synchronous motor control system and control method - Google Patents
Permanent magnet synchronous motor control system and control method Download PDFInfo
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Abstract
The invention relates to a permanent magnet synchronous motor control system and a control method, wherein an MTPA module, an internal model current controller, an IPARK conversion module, an inverter and a permanent magnet synchronous motor are connected in sequence, and the actual output voltage of the inverter is input to the internal model current controller through the actual d-axis current and the actual q-axis current obtained by the CLARK conversion module and the PARK conversion module; the rotary transformer is used for acquiring the actual angle of the permanent magnet synchronous motor, obtaining the actual angular speed after differentiation of a differential operator, and inputting the difference between the given angular speed and the actual angular speed into the MTPA module. When the motor running state is greatly influenced by factors such as the environment state, the temperature and the like, the controller regulating quantity is continuously corrected through real-time self-adaptive regulation, and the anti-interference performance and the robustness of the system are enhanced.
Description
Technical Field
The invention relates to the field of control of permanent magnet synchronous motors, in particular to a control system and a control method of a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor has the advantages of high efficiency, high power density, direct drive and the like, and is widely applied to the field of rail transit. For a high-speed electric traction system, the stability of the variable-frequency control performance of a high-power motor is the most important performance index requirement. Under a high-speed state, mutual influence of coupling terms of the permanent magnet motor is gradually increased, and how to realize quick and accurate decoupling control is of great importance. However, the control coupling term is related to the stator parameter of the motor, and the change of the motor parameter is mainly caused by the motorThe magnetic saturation effect of the iron core caused by the change of the working temperature and the stator current, thereby causing the stator inductance L in the motor parameterd、LqAnd permanent magnet flux linkage psifA change in (c). The traditional feedback decoupling control is widely applied to permanent magnet motor control, but the influence of motor parameters along with environmental factors is not considered, and the torque precision and the control performance of the motor are greatly influenced by a coupling term in a high-speed state.
Disclosure of Invention
The invention provides a permanent magnet synchronous motor control system and a control method, aiming at solving the problems that the traditional feedback decoupling control is highly dependent on click parameters, has poor adaptability to the environment, and the coupling item influences the control performance in a high-speed and high-temperature state.
The invention is realized by the following technical scheme: a permanent magnet synchronous motor control system comprises an MTPA module, an internal model current controller, an IPARK conversion module, an inverter, a permanent magnet synchronous motor, a CLARK conversion module, a PARK conversion module and a rotary transformer;
the MTPA module, the internal model current controller, the IPARK conversion module, the inverter and the permanent magnet synchronous motor are sequentially connected, and the actual output voltage of the inverter is input to the internal model current controller through the actual d-axis and q-axis currents obtained by the CLARK conversion module and the PARK conversion module;
the rotary transformer is used for acquiring the actual angle of the permanent magnet synchronous motor, obtaining the actual angular speed after differentiation of a differential operator, and inputting the difference between the given angular speed and the actual angular speed into the MTPA module.
As a further improvement of the technical scheme of the control system, the control system further comprises a parameter change estimator, an output voltage signal of the internal model current controller is input to the parameter change estimator, actual d-axis and q-axis currents obtained by the PARK conversion module are input to the parameter change estimator, actual angular velocities obtained by differentiation of a differential operator are input to the parameter change estimator, and the output of the parameter change estimator is connected with the input of the internal model current controller.
The invention also provides a permanent magnet synchronous motor control method, which comprises the following steps:
given speed of permanent magnet synchronous motor
Obtaining the actual angular velocity omega after differentiation by a differential operatorγThe difference value of (a) is inputted to an MTPA module, and the MTPA module outputs given currents of a d axis and a q axis
As the input of the internal model current controller, the given voltage u of d-axis and q-axis output by the internal model current controllerd *、uq *The given voltage of alpha axis and beta axis output by the IPARK conversion module is used as the input of the IPARK conversion module
The signal is transmitted to a permanent magnet synchronous motor through an SVPWM algorithm and an inverter;
i of actual output voltage of inverter output by CLARK conversion moduleα、iβAs the input of the PARK conversion module, the PARK conversion module outputs the actual current i of d-axis and q-axisd、iqInputting the current into an internal model current controller, and acquiring the actual angle theta of the permanent magnet synchronous motor by a rotary transformereObtaining the actual angular velocity omega through differential processing of a differential operatorγ；
Thereby realizing double closed-loop vector control, wherein the outer ring is used for rotating speed control, and the inner ring is used for current control.
As a further improvement of the technical scheme of the control method, the given voltage u of the d axis and the q axis output by the internal model current controllerd *、uq *The PARK conversion module outputs d-axis and q-axis actual currents id、iqObtaining the actual angular velocity omega after differentiation by a differential operatorγThe disturbance regulating variables of d-axis and q-axis output by the parameter variation estimator
Input to the internal model current controller.
As a further improvement of the technical scheme of the control method of the present invention, the internal model decoupling method of the internal model current controller comprises the following steps:
(1) internal model current controller G for constructing permanent magnet motor voltage equationIMC(s)；
(2) Setting a low-pass filter L(s);
(3) constructing an equivalent feedback controller F(s):
an equivalent feedback controller F(s) outputs given voltages u of d-axis and q-axisd *、uq *And the equivalent feedback controller F(s) is arranged in front of the input end of the permanent magnet synchronous motor to realize the decoupling control of the permanent magnet synchronous motor.
As a further improvement of the technical solution of the control method of the present invention, in step (1), the internal model current controller G for constructing the voltage equation of the permanent magnet motor is describedIMCThe process of(s) comprises the steps of:
(1) converting the permanent magnet motor voltage equation into the following state equation form:
in the formula (1), ud、uqVoltages of d-axis and q-axis, Ld、LqInductances of d-and q-axes, id、iqCurrents of d-and q-axes, RsIs stator resistance, ω is rotor electrical angular velocity, s is Laplace transform, ψfIs a permanent magnet flux linkage;
(1) neglecting the effect of the permanent magnet, equation (1) may become:
(1) u(s) and I(s) correspond to U(s) and Y(s), respectively, and let
I(s) y(s), we can obtain:
I(s)＝G(s)U(s) (3)
in the formula
(1) -4. then G can beIMC(s)＝G-1(s) thus forming an internal model control such that the output current can track a given current signal.
As a further improvement of the technical solution of the control method of the present invention, in the step (2), the method for setting the low pass filter l(s) includes the steps of:
(2) -1. low pass filter set to:
in the formula (4), λ is a filter coefficient;
(2) -2. the internal model current controller converts to:
in the formula (5), the reaction mixture is,
the inductance estimated values of the d axis and the q axis respectively,
is an estimate of the stator resistance.
As a further improvement of the technical solution of the control method of the present invention, in step (3), the method for constructing an equivalent feedback controller includes the steps of:
converting the internal model current controller into an equivalent feedback structure:
as a further improvement of the technical solution of the control method of the present invention, the adaptive law selection method of the parameter variation estimator comprises the following steps:
the equation of the voltage of the motor when the motor parameter changes can be obtained by the formula (1) as follows:
② order
Wherein d isd、dqDisturbance values, Δ R, of d-and q-axes, respectivelysIs the value of variation of stator resistance, Δ Ld、ΔLqInductance change values of d-axis and q-axis, Delta psifIs the variation value of the permanent magnet flux linkage;
and the d-axis and q-axis current state equation of the motor is expressed as follows:
order to
The d-axis and q-axis current state estimation equation of the motor is as follows:
in the formula (9)
The current estimated values of the d axis and the q axis are obtained,
parameter disturbance estimated values of a d axis and a q axis are obtained; set the estimation error of the system state to
Disturbance estimation error is set as
Fourthly, the state error equation is derived according to the formula (9):
in order to design a parameter change adaptive law, a Lyapunov function is selected as follows:
in the formula (11), eTIs a transpose of the natural constant e,
for transposing the number of disturbance estimation values, gamma is the error compensation coefficient, P is the positive definite matrix, and P is PT；
Fifth, the derivation of the formula (11) is obtained:
in the formula (12), ATAs a transpose of the state matrix A, BTFor the transposition of the state matrix B, A is selected so that equation (12) is negativeTP + PA ═ Q, Q > 0, and the parameter change adaptation law was chosen as:
then
Therefore, the parameter change adaptive law can make the estimation error tend to zero;
sixthly, selecting P as unit matrix, then Q is ═ AT+ A) is a positive definite matrix, and the adaptive law of parameter change is:
in the formula (14), the compound represented by the formula (I),
disturbance variables, k, of d-and q-axes, respectivelyi1、ki2Integral regulator coefficients, k, of d-and q-axes, respectivelyp1、kp2Proportional regulator coefficients of d-axis and q-axis, respectively, ed、eqThe error of d-axis and q-axis respectively.
The permanent magnet synchronous motor control system and the control method can efficiently decouple the MTPA, and quickly realize quick decoupling in permanent magnet motor control in a mode of combining the internal model current controller and the self-adaptive regulator. When the motor running state is greatly influenced by factors such as environmental state, temperature and the like, the controller regulating quantity is continuously corrected through real-time self-adaptive regulation, and the anti-interference performance and robustness of the system are enhanced.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a schematic structural diagram of a permanent magnet synchronous motor control system.
Fig. 2 is a schematic structural diagram of the internal model current controller.
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.
As shown in fig. 1, the present invention provides a structural schematic diagram of a permanent magnet synchronous motor control system, which includes an MTPA module, an internal model current controller, an IPARK conversion module, an inverter, a permanent magnet synchronous motor, a CLARK conversion module, a PARK conversion module, and a rotary transformer;
the MTPA module, the internal model current controller, the IPARK conversion module, the inverter and the permanent magnet synchronous motor are sequentially connected, and the actual output voltage of the inverter is input to the internal model current controller through the actual d-axis and q-axis currents obtained by the CLARK conversion module and the PARK conversion module;
the rotary transformer is used for acquiring the actual angle of the permanent magnet synchronous motor, obtaining the actual angular speed after differentiation of a differential operator, and inputting the difference between the given angular speed and the actual angular speed into the MTPA module.
In order to better adapt to the parameter change of the motor control system, preferably, the control system further comprises a parameter change estimator, the output voltage signal of the internal model current controller is input to the parameter change estimator, the actual d-axis and q-axis currents obtained by the PARK transformation module are input to the parameter change estimator, the actual angular velocity obtained by differentiation of a differential operator is input to the parameter change estimator, and the output of the parameter change estimator is connected with the input of the internal model current controller.
The control system of the magnetic synchronous motor comprises the rotating speed control of an outer ring and the current control of an inner ring, and double closed-loop vector control is realized.
The system comprises an MTPA module, an internal model current controller, an IPARK conversion module, an inverter, a permanent magnet synchronous motor, a CLARK conversion module, a PARK conversion module and a parameter change estimator, wherein the MTPA module, the internal model current controller, the IPARK conversion module, the inverter, the permanent magnet synchronous motor, the CLARK conversion module, the PARK conversion module and the parameter change estimator form current control; the MTPA module, the internal model current controller, the IPARK conversion module, the inverter, the permanent magnet synchronous motor, the rotary transformer, the differential operator and the parameter change estimator form rotating speed control.
Wherein,
representing a given speed externally to a Permanent Magnet Synchronous Machine (PMSM),
indicating a specified current, u, output by the MTPA module (maximum torque to current ratio controller)d *、uq *Representing the voltage components of the d-axis and the q-axis after cross decoupling of the internal model current controller,
voltage components i representing the transformation of d-axis and q-axis of two-phase rotating coordinate axis into alpha-axis and beta-axis of two-phase stationary coordinate axisα、iβCurrent components, i, representing the conversion of a three-phase stationary coordinate axis adc into an alpha axis and a beta axis of a two-phase stationary coordinate axisd、iqCurrent components theta representing the conversion of the alpha axis and the beta axis of the two-phase stationary coordinate axis into the d axis and the q axis of the two-phase rotating coordinate axiseRepresenting the actual angle, ω, of the permanent magnet synchronous machine obtained by means of a resolverγThe result of differentiating the actual angle, i.e. the actual angular velocity of the permanent magnet synchronous motor, is represented.
The specific control method of the control system comprises the following steps:
given speed of permanent magnet synchronous motor
Obtaining the actual angular velocity omega after differentiation by a differential operatorγThe difference value of (a) is inputted to an MTPA module, and the MTPA module outputs given currents of a d axis and a q axis
As the input of the internal model current controller, the given voltage u of d-axis and q-axis output by the internal model current controllerd *、uq *As IPARInput of K conversion module, given voltage of alpha axis and beta axis output by IPARK conversion module
The signal is transmitted to a permanent magnet synchronous motor through an SVPWM algorithm and an inverter;
i of actual output voltage of inverter output by CLARK conversion moduleα、iβAs the input of the PARK conversion module, the PARK conversion module outputs the actual current i of d-axis and q-axisd、iqInputting the current into an internal model current controller, and acquiring the actual angle theta of the permanent magnet synchronous motor by a rotary transformereObtaining the actual angular velocity omega through differential processing of a differential operatorγ；
Thereby realizing double closed-loop vector control, wherein the outer ring is used for rotating speed control, and the inner ring is used for current control.
Preferably, the internal model current controller outputs a given voltage u of d-axis and q-axisd *、uq *The PARK conversion module outputs d-axis and q-axis actual currents id、iqObtaining the actual angular velocity omega after differentiation by a differential operatorγThe disturbance regulating variables of d-axis and q-axis output by the parameter variation estimator
Input to the internal model current controller.
Setting the speed of a permanent magnet synchronous machine
Obtaining the actual angular velocity omega after differentiation by a differential operatorγThe difference value of (A) is input into the MTPA module, and is converted into given currents of a d axis and a q axis through effective distribution of the MTPA module
With the actual feedback current id、iqAnd the voltage is output to generate a corresponding PWM driving signal in the internal model current controller, so that the voltage signal output by the inverter is controlled, and the purposes of automatically adjusting the rotating speed and stabilizing the torque are achieved.
The invention further provides an internal model decoupling method of the internal model current controller, which comprises the following steps:
(1) internal model current controller G for constructing permanent magnet motor voltage equationIMC(s)；
(2) Setting a low-pass filter L(s);
(3) constructing an equivalent feedback controller F(s):
an equivalent feedback controller F(s) outputs given voltages u of d-axis and q-axisd *、uq *And the equivalent feedback controller F(s) is arranged in front of the input end of the permanent magnet synchronous motor to realize the decoupling control of the permanent magnet synchronous motor.
In the step (1), the internal model current controller G for constructing the voltage equation of the permanent magnet motorIMCThe process of(s) comprises the steps of:
(1) converting the permanent magnet motor voltage equation into the following state equation form:
in the formula (1), ud、uqVoltages of d-axis and q-axis, Ld、LqInductances of d-and q-axes, id、iqCurrents of d-and q-axes, RsIs stator resistance, ω is rotor electrical angular velocity, s is Laplace transform, ψfIs a permanent magnet flux linkage;
(1) neglecting the effect of the permanent magnet, equation (1) may become:
(1) u(s) and I(s) correspond to U(s) and Y(s), respectively, and let
I(s) y(s), we can obtain:
I(s)＝G(s)U(s) (3)
in the formula
(1) -4. then G can beIMC(s)＝G-1(s) thus forming an internal model control such that the output current can track a given current signal.
Because the transfer function G(s) of the permanent magnet synchronous motor has no pure time delay and a zero current feedback loop of a right half plane can be a first-order system under the condition of high frequency, namely a low-pass filter is added. Therefore, in step (2), the method for setting the low-pass filter l(s) includes the following steps:
(2) -1. low pass filter set to:
in the formula (4), λ is a filter coefficient;
(2) -2. the internal model current controller converts to:
in the formula (5), the reaction mixture is,
the inductance estimated values of the d axis and the q axis respectively,
is an estimate of the stator resistance.
Further, in step (3), the method for constructing the equivalent feedback controller comprises the following steps: converting the internal model current controller into an equivalent feedback structure:
the specific structure of the internal model current controller can be seen in fig. 2, and the combination with the formula (6) shows that the internal model current controller is added with a cross decoupling compensation item in the PI controller, and the main function is to eliminate the cross coupling effect in the voltage and realize complete decoupling.
According to the decoupling control derivation of the internal model current controller, the decoupling system of the internal model control is determined by the motor parameters. In order to better adapt to the parameter change of the motor control system, a parameter change adaptive law is introduced into the internal model decoupling control.
The adaptive law selection method of the parameter change estimator comprises the following steps:
the equation of the voltage of the motor when the motor parameter changes can be obtained by the formula (1) as follows:
② order
Wherein d isd、dqDisturbance values, Δ R, of d-and q-axes, respectivelysIs the value of variation of stator resistance, Δ Ld、ΔLqInductance change values of d-axis and q-axis, Delta psifIs the variation value of the permanent magnet flux linkage;
and the d-axis and q-axis current state equation of the motor is expressed as follows:
order to
The d-axis and q-axis current state estimation equation of the motor is as follows:
in the formula (9)
The current estimated values of the d axis and the q axis are obtained,
parameter disturbance estimated values of a d axis and a q axis are obtained; set the estimation error of the system state to
Disturbance estimation error is set as
Fourthly, the state error equation is derived according to the formula (9):
in order to design a parameter change adaptive law, a Lyapunov function is selected as follows:
in the formula (11), eTIs a transpose of the natural constant e,
for transposing the number of disturbance estimation values, gamma is the error compensation coefficient, P is the positive definite matrix, and P is PT；
Fifth, the derivation of the formula (11) is obtained:
in the formula (12), ATAs a transpose of the state matrix A, BTFor the transposition of the state matrix B, A is selected so that equation (12) is negativeTP + PA ═ Q, Q > 0, and the parameter change adaptation law was chosen as:
then
Therefore, the parameter change adaptive law can make the estimation error tend to zero;
sixthly, selecting P as unit matrix, then Q is ═ AT+ A) is a positive definite matrix, and the adaptive law of parameter change is:
in the formula (14), the compound represented by the formula (I),
disturbance variables, k, of d-and q-axes, respectivelyi1、ki2Integral regulator coefficients, k, of d-and q-axes, respectivelyp1、kp2Proportional regulator coefficients of d-axis and q-axis, respectively, ed、eqThe error of d-axis and q-axis respectively.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A permanent magnet synchronous motor control system is characterized by comprising an MTPA module, an internal model current controller, an IPARK conversion module, an inverter, a permanent magnet synchronous motor, a CLARK conversion module, a PARK conversion module and a rotary transformer;
the MTPA module, the internal model current controller, the IPARK conversion module, the inverter and the permanent magnet synchronous motor are sequentially connected, and the actual output voltage of the inverter is input to the internal model current controller through the actual d-axis and q-axis currents obtained by the CLARK conversion module and the PARK conversion module;
the rotary transformer is used for acquiring the actual angle of the permanent magnet synchronous motor, obtaining the actual angular speed after differentiation of a differential operator, and inputting the difference between the given angular speed and the actual angular speed into the MTPA module.
2. The permanent magnet synchronous motor control system according to claim 1, further comprising a parameter variation estimator, wherein an output voltage signal of the internal model current controller is input to the parameter variation estimator, actual d-axis and q-axis currents obtained by the PARK transformation module are input to the parameter variation estimator, actual angular velocities obtained by differentiation of a differential operator are input to the parameter variation estimator, and an output of the parameter variation estimator is connected with an input of the internal model current controller.
3. A permanent magnet synchronous motor control method is characterized by comprising the following steps:
given speed of permanent magnet synchronous motor
Obtaining the actual angular velocity omega after differentiation by a differential operatorγThe difference value of (a) is inputted to an MTPA module, and the MTPA module outputs given currents of a d axis and a q axis
As input to an internal model current controller, internal model current controlGiven voltage u of d-axis and q-axis output by the controllerd *、uq *The given voltage of alpha axis and beta axis output by the IPARK conversion module is used as the input of the IPARK conversion module
The signal is transmitted to a permanent magnet synchronous motor through an SVPWM algorithm and an inverter;
i of actual output voltage of inverter output by CLARK conversion moduleα、iβAs the input of the PARK conversion module, the PARK conversion module outputs the actual current i of d-axis and q-axisd、iqInputting the current into an internal model current controller, and acquiring the actual angle theta of the permanent magnet synchronous motor by a rotary transformereObtaining the actual angular velocity omega through differential processing of a differential operatorγ；
Thereby realizing double closed-loop vector control, wherein the outer ring is used for rotating speed control, and the inner ring is used for current control.
4. The method as claimed in claim 3, wherein the internal model current controller outputs a given voltage u on d-axis and q-axisd *、uq *The PARK conversion module outputs d-axis and q-axis actual currents id、iqObtaining the actual angular velocity omega after differentiation by a differential operatorγThe disturbance regulating variables of d-axis and q-axis output by the parameter variation estimator
Input to the internal model current controller.
5. The permanent magnet synchronous motor control method according to claim 3 or 4, wherein the internal model decoupling method of the internal model current controller comprises the following steps:
(1) internal model current controller G for constructing permanent magnet motor voltage equationIMC(s)；
(2) Setting a low-pass filter L(s);
(3) constructing an equivalent feedback controller F(s):
an equivalent feedback controller F(s) outputs given voltages u of d-axis and q-axisd *、uq *And the equivalent feedback controller F(s) is arranged in front of the input end of the permanent magnet synchronous motor to realize the decoupling control of the permanent magnet synchronous motor.
6. The PMSM control method according to claim 5, wherein in step (1), the internal model current controller G for constructing the PMSM voltage equationIMCThe process of(s) comprises the steps of:
(1) converting the permanent magnet motor voltage equation into the following state equation form:
in the formula (1), ud、uqVoltages of d-axis and q-axis, Ld、LqInductances of d-and q-axes, id、iqCurrents of d-and q-axes, RsIs stator resistance, ω is rotor electrical angular velocity, s is Laplace transform, ψfIs a permanent magnet flux linkage;
(1) neglecting the effect of the permanent magnet, equation (1) may become:
(1) u(s) and I(s) correspond to U(s) and Y(s), respectively, and let
I(s) y(s), we can obtain:
I(s)＝G(s)U(s) (3)
in the formula
(1) -4. then G can beIMC(s)＝G-1(s) thus forming an internal model control such that the output current can track a given current signal.
7. The permanent magnet synchronous motor control method according to claim 5, wherein in the step (2), the method for setting the low pass filter L(s) comprises the steps of:
(2) -1. low pass filter set to:
in the formula (4), λ is a filter coefficient;
(2) -2. the internal model current controller converts to:
in the formula (5), the reaction mixture is,
the inductance estimated values of the d axis and the q axis respectively,
is an estimate of the stator resistance.
8. The permanent magnet synchronous motor control method according to claim 5, wherein in the step (3), the method for constructing the equivalent feedback controller comprises the following steps:
converting the internal model current controller into an equivalent feedback structure:
9. the permanent magnet synchronous motor control method according to claim 6, wherein the adaptive law selection method of the parameter change estimator comprises the steps of:
the equation of the voltage of the motor when the motor parameter changes can be obtained by the formula (1) as follows:
② order
Wherein d isd、dqDisturbance values, Δ R, of d-and q-axes, respectivelysIs the value of variation of stator resistance, Δ Ld、ΔLqInductance change values of d-axis and q-axis, Delta psifIs the variation value of the permanent magnet flux linkage;
and the d-axis and q-axis current state equation of the motor is expressed as follows:
order to
The d-axis and q-axis current state estimation equation of the motor is as follows:
in the formula (9)
The current estimated values of the d axis and the q axis are obtained,
parameter disturbance estimated values of a d axis and a q axis are obtained;
set the estimation error of the system state to
Disturbance estimation error is set as
Fourthly, the state error equation is derived according to the formula (9):
in order to design a parameter change adaptive law, a Lyapunov function is selected as follows:
in the formula (11), eTIs a transpose of the natural constant e,
for transposing the number of disturbance estimation values, gamma is the error compensation coefficient, P is the positive definite matrix, and P is PT；
Fifth, the derivation of the formula (11) is obtained:
in the formula (12), ATAs a transpose of the state matrix A, BTFor the transposition of the state matrix B, A is selected so that equation (12) is negativeTP+PA＝-Q，Q＞0, and the parameter change adaptive rule is selected as follows:
then
Therefore, the parameter change adaptive law can make the estimation error tend to zero;
sixthly, selecting P as unit matrix, then Q is ═ AT+ A) is a positive definite matrix, and the adaptive law of parameter change is:
in the formula (14), the compound represented by the formula (I),
disturbance variables, k, of d-and q-axes, respectivelyi1、ki2Integral regulator coefficients, k, of d-and q-axes, respectivelyp1、kp2Proportional regulator coefficients of d-axis and q-axis, respectively, ed、eqThe error of d-axis and q-axis respectively.
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| CN115313950A (en) * | 2022-08-19 | 2022-11-08 | 南通帝孚工具科技有限公司 | Driving system of servo motor |
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| CN115313950A (en) * | 2022-08-19 | 2022-11-08 | 南通帝孚工具科技有限公司 | Driving system of servo motor |
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