CN117200621A - Permanent magnet synchronous motor parameter identification method based on improved model reference adaptive system - Google Patents
Permanent magnet synchronous motor parameter identification method based on improved model reference adaptive system Download PDFInfo
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Abstract
The invention discloses a permanent magnet synchronous motor parameter identification method based on an improved model reference self-adaptive system, which comprises the following steps: establishing a state space equation model of the surface-mounted permanent magnet synchronous motor as a reference model of the MRAS; establishing an MRAS adjustable model; establishing an MRAS error state space equation; a first order ADRC adaptation law is designed. Aiming at the problem that MRAS is easily affected by high-frequency noise, the invention improves the traditional PI adaptive law into ADRC adaptive law. Firstly, selecting a proper reference model, secondly, designing an adjustable model according to the reference model, and finally, sending the difference value between the reference model and the adjustable model into a first-order ADRC self-adaptive law and feeding back output to the adjustable model to form the whole MRAS system. Compared with the traditional PI adaptive law, the ADRC adaptive law can effectively filter noise, and the jitter amplitude of an on-line parameter identification result is obviously reduced.
Description
Technical Field
The invention belongs to the technical field of motor control, and particularly relates to a permanent magnet synchronous motor parameter identification method based on an improved model reference self-adaptive system.
Background
The electromagnetic parameters of the permanent magnet synchronous motor are changed along with the running of the equipment under the influence of various factors such as the self structure, the limitation of the power density, various complex motor running environments and the like, so that the vector control performance of the motor is most likely to be reduced. Therefore, the on-line parameter identification of the permanent magnet synchronous motor has important scientific research and practical application value in the aspects of high-performance motor control, fault early warning and the like.
In a plurality of online parameter identification algorithms, the model reference adaptive Method (MRAS) has the advantages of simple design process, small calculated amount, high precision, easy practical realization and the like, and is widely applied to motor parameter identification and sensorless control. The MRAS utilizes the difference between the reference model and the adjustable model to input errors into a proper self-adaptive mechanism, and feeds back the output of the self-adaptive mechanism to parameters to be identified in the adjustable model, so that the parameters are identified on line. However, in the application process of the MRAS, the amplitude of the bird chart of the classical PI adaptive law is zero in the high frequency band, so that the MRAS cannot filter out high-frequency noise possibly brought by the sensor, and further the parameter identification result of the MRAS is easily disturbed by noise.
Disclosure of Invention
Aiming at the problem of poor MRAS noise immunity performance based on the conventional PI adaptive law, the invention provides a permanent magnet synchronous motor parameter identification method based on an improved model reference adaptive system, which utilizes an Active Disturbance Rejection Controller (ADRC) as the adaptive law of a MARS to inhibit high-frequency noise, has reasonable design, overcomes the defects of the prior art and has good effect.
A permanent magnet synchronous motor parameter identification method based on an improved model reference adaptive system comprises the following steps:
step one, a state space equation model of the surface-mounted permanent magnet synchronous motor is established and used as a reference model of the MRAS;
step two, establishing an MRAS adjustable model;
step three, establishing an MRAS error state space equation;
and step four, designing a first-order ADRC self-adaptive law.
Further, in the first step, a mathematical model of a state space equation of the surface-mounted permanent magnet synchronous motor using current as a state variable is:
wherein,u＝[u d u q ] T ；i＝[i d i q ] T ；u d 、u q d and q axis components of the stator voltage, respectively; i.e d 、i q D and q axis components of the stator current, respectively; r is R s Is a stator resistor; l is stator inductance; w (w) e For rotor electrical angular velocity; psi phi type f Is a rotor permanent magnet flux linkage; let equation (1) be the reference model of the MRAS.
Further, in the second step, based on the formula (1), an adjustable model of the MRAS is established:
wherein, to identify the inductance; />To identify flux linkage.
Further, in the third step, the reference model type (2) is subtracted from the adjustable model type (3) to obtain an error state space equation, which is expressed as:
wherein,
from the theory of wave-front superstability, to stabilize the system of formula (3), the wave-front integration inequality needs to be satisfied, which is expressed as:
wherein e T W is the output and feedback loop of the error state equation; t is t 1 For any time r 0 Is any finite constant independent of time t; substituting formula (3) into formula (4):
wherein,r 1 、r 2 is any finite constant independent of time t.
Further, in the fourth step, the first-order ADRC is introduced into the formula (5), where the first-order ADRC is expressed as:
wherein beta is 1 、β 2 Gain, beta, of ESO 1 、β 2 Respectively take the bandwidths w 0 Is twice and squares; b 0 To control gain; a is a given amount; b is feedback quantity; c is output quantity; the fal function in equation (6) is a nonlinear function, and its equation is:
wherein delta is a linear interval value; a is a power coefficient; e, e a Is an observation error; z 1 Tracking the feedback signal for ESO;
let a given amount a equal to 0, the feedback amount B be:
wherein B is 1 Is an inductance self-adaptive law component; b (B) 2 Is a component of flux linkage self-adaption rate;
by combining the formula (5), the formula (6), the formula (7) and the formula (8), a new Bofft inequality can be obtained:
wherein,the inferred values of b and c, respectively;
the equation (9) is the wave-f integral inequality of inductance and flux linkage on-line identification under the ADRC self-adaptive law, and when the parameter value satisfies the equation (9), the MRAS system is stable.
The invention has the beneficial technical effects that:
the invention provides a permanent magnet synchronous motor parameter identification method based on an improved model reference self-adaptive system. Aiming at the problem that MRAS is susceptible to high-frequency noise, the traditional PI adaptive law is improved to ADRC adaptive law. Firstly, selecting a proper reference model, secondly, designing an adjustable model according to the reference model, and finally, sending the difference value between the reference model and the adjustable model into a first-order ADRC self-adaptive law and feeding back output to the adjustable model to form the whole MRAS system. Compared with the traditional PI adaptive law, the ADRC adaptive law can effectively filter noise, and the jitter amplitude of an on-line parameter identification result is obviously reduced.
Drawings
FIG. 1 is a block diagram of a model reference adaptive system of the present invention;
FIG. 2 is a block diagram of a system of error state space equations in accordance with the present invention;
FIG. 3 is a first order ADRC block diagram of the present invention;
FIG. 4 is a diagram of flux linkage identification first order ADRC versus PI;
FIG. 5 is a diagram of PI adaptive law flux linkage recognition simulation results;
FIG. 6 is a graph of ADRC adaptive law flux linkage recognition simulation results;
FIG. 7 is a diagram of PI adaptive law inductance identification simulation results;
FIG. 8 is a diagram of ADRC adaptive law inductance identification simulation results;
Detailed Description
The following is a further description of embodiments of the invention, in conjunction with the specific examples:
a permanent magnet synchronous motor parameter identification method based on an improved model reference adaptive system comprises the following steps:
step one, a state space equation model of the surface-mounted permanent magnet synchronous motor is established and used as a reference model of the MRAS;
the stator voltage equation of the surface-mounted permanent magnet synchronous motor under the d-q axis is as follows:
wherein u is d 、u q D and q axis components of the stator voltage, respectively; i.e d 、i q Respectively are provided withIs the d, q-axis component of the stator current; r is R s Is a stator resistor; l is stator inductance; w (w) e For rotor electrical angular velocity; psi phi type f Is a rotor permanent magnet flux linkage;
the equation (1) is rewritten into a state space equation form using current as a state variable:
wherein,u＝[u d u q ] T ；i＝[i d i q ] T the method comprises the steps of carrying out a first treatment on the surface of the The equation (2) is a state space equation set with voltage as input quantity and current as output quantity, and the equation (2) is regarded as a reference model of MRAS;
step two, establishing an MRAS adjustable model;
the MRAS overall structure is shown in FIG. 1, and an adjustable model of the MRAS is established by taking the on-line identification of inductance and flux linkage as an example based on the formula (2) by the MRAS overall structure:
wherein, to identify the inductance; />To identify flux linkage;
step three, establishing an MRAS error state space equation;
subtracting the reference model type (2) from the adjustable model type (3) to obtain an error state space equation, wherein the error state space equation is expressed as:
wherein,
since the values of the parameters to be identified in Δa, Δb and Δc are functions of the stator voltage and the stator current, and the stator voltage and the stator current are functions of the time, the w has the characteristics of nonlinearity and time-varying. The overall structure of formula (4) is shown in FIG. 2. In order for the system of class 2 to be stable and for e to converge to zero, a suitable parameter adaptation law must be designed. From the theory of wave-front superstability, to stabilize the system of fig. 2, the wave-front integration inequality needs to be satisfied, and the wave-front integration inequality is expressed as:
wherein e T W is the output and feedback loop of the error state equation; t is t 1 For any time r 0 Is any finite constant independent of time t; substituting formula (4) into formula (5):
wherein,r 1 、r 2 equation (5) can be used to identify inductance and flux linkage on-line, for any finite constant independent of time t.
Step four, designing a first-order ADRC self-adaptive law;
the adaptive law using first order ADRC as MRAS, whose structure is shown in fig. 3, introduces first order ADRC into equation (6), expressed as:
wherein beta is 1 、β 2 Gain, beta, of ESO 1 、β 2 Respectively take the bandwidths w 0 Is twice and squares; b 0 To control gain; a is a given amount; b is feedback quantity; c is output quantity; bandwidth w 0 The larger the first-order ADRC, the faster the response speed, but the weaker the resistance to high-frequency noise;
the fal function in equation (7) is a nonlinear function, and its equation is:
wherein delta is a linear interval value; a is a power coefficient; e, e a Is an observation error; z 1 Tracking the feedback signal for ESO; fal the function adopts the form of a piecewise function to divide the working range of the controller into two parts, namely a large error range and a small error range, wherein the large error range is responsible for regulating the speed, and the small error range is responsible for steady-state immunity, so that the contradiction between the regulating speed and the immunity performance is effectively solved.
Let a given amount a equal to 0, the feedback amount B be:
wherein B is 1 Is an inductance self-adaptive law component; b (B) 2 Is a flux linkage self-adaptive law component part;
by combining the formula (6), the formula (7), the formula (8) and the formula (9), a new Bofft inequality can be obtained:
wherein,push b, c respectivelyMeasuring a value;
the equation (10) is the wave-f integral inequality of inductance and flux linkage on-line identification under ADRC self-adaptive law.
Taking inductance on-line parameter identification as an example, stability analysis is carried out on the ADRC self-adaptive law. When e a >And (3) at delta, deriving and simplifying C in the step (7) to finally obtain:
since the feedback quantity B may take a negative value to cause inequality, a larger beta can be selected 1 、β 2 Make the following stepsGreater than b 0 Can make e a >Delta time->Monotonically increasing. Similarly, at e a <-interval of δ, deriving and simplifying C to obtain finally:
order theFar greater than b 0 Can make e a <-delta time->Monotonically decreasing. Thereby making ADRC consist of |e a |>Delta interval direction |e a The interval of the I is less than or equal to delta is converged.
In interval |e a When the I is less than or equal to delta, the ADRC formula is as follows:
wherein b 1 Is thatb 2 Is->Calculating the transfer function between the feedback quantity B and the controller output C according to the step (13):
and (4) carrying out the pull type inverse transformation on the (14) to obtain the following components:
substituting (15) back into (10) and splitting into two equations yields:
wherein r is 11 、r 12 Is any finite constant independent of time. It can be seen that the method consists ofGreater than 0 and less than 1, so when +.16>Above zero, the inequality holds. It can be demonstrated that when the first order ADRC converges to the linear interval |e a When the I is less than or equal to delta, the designed self-adaptive law is stable. The adaptive law derivation of flux linkage identification and its stability prove similar to inductance and are omitted here as well.
The first order ADRC adaptive law frequency domain performance was analyzed and its linear region bode plot is shown in fig. 4. Wherein the solid line is a first order ADRC frequency domain response; the dashed line is the PI frequency domain response. In the figure, the amplitude and the phase of PI are zero in the high frequency range, which means that PI can not filter high frequency noise, while ADRC is smaller and smaller in the high frequency range, and the ADRC self-adaptive law has low-pass characteristic in the linear interval, so that the PI can filter high frequency noise, namely has stronger anti-interference performance than PI.
Fig. 5 and fig. 6 are respectively simulation graphs of magnetic linkage on-line identification and comparison effects of a classical PI adaptive law and a first-order ADRC adaptive law in a noise environment, and fig. 7 and fig. 8 are respectively simulation graphs of inductance on-line identification and comparison effects of the classical PI adaptive law and the first-order ADRC adaptive law in the noise environment. It can be seen that under the condition that the sensor has high-frequency noise, the classical PI adaptive law is influenced by disturbance to identify that the jitter amplitude is larger, and the first-order ADRC adaptive law identifies that the jitter amplitude is significantly smaller. In conclusion, the first-order ADRC adaptive law designed by the invention has better anti-noise and anti-interference performance than the traditional PI adaptive law.
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (5)
1. The permanent magnet synchronous motor parameter identification method based on the improved model reference adaptive system is characterized by comprising the following steps of:
step one, a state space equation model of the surface-mounted permanent magnet synchronous motor is established and used as a reference model of the MRAS;
step two, establishing an MRAS adjustable model;
step three, establishing an MRAS error state space equation;
and step four, designing a first-order ADRC self-adaptive law.
2. The method for identifying parameters of a permanent magnet synchronous motor based on an improved model reference adaptive system according to claim 1, wherein in the first step, a mathematical model of a state space equation of the surface-mounted permanent magnet synchronous motor using current as a state variable is as follows:
wherein,u＝[u d u q ] T ；i＝[i d i q ] T ；u d 、u q d and q axis components of the stator voltage, respectively; i.e d 、i q D and q axis components of the stator current, respectively; r is R s Is a stator resistor; l is stator inductance; w (w) e For rotor electrical angular velocity; psi phi type f Is a rotor permanent magnet flux linkage; let equation (1) be the reference model of the MRAS.
3. The method for identifying parameters of a permanent magnet synchronous motor based on an improved model reference adaptive system according to claim 2, wherein in the second step, an adjustable model of the MRAS is established based on the formula (1):
wherein, to identify the inductance; />To identify flux linkage.
4. The method for identifying parameters of a permanent magnet synchronous motor based on an improved model reference adaptive system according to claim 3, wherein in the third step, the reference model (2) is subtracted from the adjustable model (3) to obtain an error state space equation, which is expressed as:
wherein,
from the theory of wave-front superstability, to stabilize the system of formula (3), the wave-front integration inequality needs to be satisfied, which is expressed as:
wherein e T W is the output and feedback loop of the error state equation; t is t 1 For any time r 0 Is any finite constant independent of time t; substituting formula (3) into formula (4):
wherein,r 1 、r 2 is any finite constant independent of time t.
5. The method for identifying parameters of a permanent magnet synchronous motor based on an improved model reference adaptive system according to claim 4, wherein in the fourth step, a first order ADRC is introduced into formula (5), and the first order ADRC is expressed as:
wherein beta is 1 、β 2 Gain, beta, of ESO 1 、β 2 Respectively take the bandwidths w 0 Is twice and squares; b 0 To control gain; a is a given amount; b is feedback quantity; c is output quantity; the fal function in equation (6) is a nonlinear function, and its equation is:
wherein delta is a linear interval value; a is a power coefficient; e, e a Is an observation error; z 1 Tracking the feedback signal for ESO;
let a given amount a equal to 0, the feedback amount B be:
wherein B is 1 Is an inductance self-adaptive law component; b (B) 2 Is a flux linkage self-adaptive law component part;
by combining the formula (5), the formula (6), the formula (7) and the formula (8), a new Bofft inequality can be obtained:
wherein,the inferred values of b and c, respectively;
the equation (9) is the wave-f integral inequality of inductance and flux linkage on-line identification under the ADRC self-adaptive law, and when the parameter value satisfies the equation (9), the MRAS system is stable.
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| CN111711396A (en) * | 2020-04-13 | 2020-09-25 | 山东科技大学 | Method for setting control parameters of speed ring of permanent magnet synchronous motor based on fractional order sliding mode controller |
| CN116094390A (en) * | 2023-01-13 | 2023-05-09 | 无锡信捷电气股份有限公司 | Two-degree-of-freedom speed regulation method of asynchronous motor based on novel active disturbance rejection algorithm |
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| CN111711396A (en) * | 2020-04-13 | 2020-09-25 | 山东科技大学 | Method for setting control parameters of speed ring of permanent magnet synchronous motor based on fractional order sliding mode controller |
| CN116094390A (en) * | 2023-01-13 | 2023-05-09 | 无锡信捷电气股份有限公司 | Two-degree-of-freedom speed regulation method of asynchronous motor based on novel active disturbance rejection algorithm |
Non-Patent Citations (1)
| Title |
|---|
| LIPENG WANG 等: "Robust sensorless of ADRC controlled PMSM based on MRAS with stator resistance identification", 《PROCEEDINGS OF THE 30TH CHINESE CONTROL CONFERENCE》, 25 August 2011 (2011-08-25), pages 3575 - 3579 * |
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