CN114598206B - Design method of permanent magnet synchronous motor wide-speed-domain rotor position observer - Google Patents
Design method of permanent magnet synchronous motor wide-speed-domain rotor position observer Download PDFInfo
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- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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Abstract
The invention relates to the field of sensorless control of a permanent magnet synchronous motor, in particular to a design method of a permanent magnet synchronous motor wide-speed-range rotor position observer, which comprises the steps of taking voltage and estimated back electromotive force of a three-phase permanent magnet synchronous motor under a Park-transformed two-phase static coordinate system as input variables of a control system, and establishing a permanent magnet synchronous motor current model; using a Gaussian error function to replace a sign function to establish a permanent magnet synchronous motor sliding mode observer, filtering specific subharmonics of back electromotive force observed by the permanent magnet synchronous motor sliding mode observer through a multi-proportion resonator, and calculating an estimated rotor rotating speed and an estimated rotor position through a normalized phase-locked loop; the counter electromotive force harmonic wave is effectively restrained through the multi-proportion resonance controller; the buffeting problem of the system is effectively restrained through the continuous Gaussian error function, and the rotating speed of the motor in the full rotating speed range and the rotor position estimation accuracy are improved.
Description
Technical Field
The invention relates to the field of sensorless control of permanent magnet synchronous motors, in particular to a design method of a permanent magnet synchronous motor wide-speed-range rotor position observer.
Background
In the control system of the permanent magnet synchronous motor, the position and speed detection of the rotor is indispensable, and the position and speed are generally measured by installing a mechanical sensor, but the installation of the mechanical sensor causes great disadvantages, and even the installation of the mechanical sensor is not supported in some special environments. Therefore, the position, speed and other information of the rotor can be estimated by detecting some electric signals (such as current and voltage) of the permanent magnet synchronous motor through proper signal processing, and the closed-loop control system technology formed by adopting the method is called a permanent magnet synchronous motor sensorless technology.
Sensorless control techniques can be divided into two categories: (1) The back emf based or flux linkage method (2) is based on the saliency method. The first is a PMSM-based model approach, such as: sliding Mode Observer (SMO), model Reference Adaptation (MRAS), kalman filtering (EKF), etc. The second method is to inject a high frequency signal into the stator winding and obtain rotor position information (rotor electrical angle and rotor electrical angular velocity) from the output current, and the method is suitable for starting and low-speed operation of the motor when the motor is stationary. Such as spin-high frequency injection, pulse-high frequency voltage injection, and high frequency square wave injection.
The SMO method has the advantages of simple algorithm, robustness to interference, good dynamic performance and the like, and is widely applied to the sensorless driver of the PMSM. The sliding mode observer is a special nonlinear control system, is an observer for estimating rotor position information based on the back electromotive force of a reconstruction motor, has strong robustness and is insensitive to parameter change and external interference, but because of discontinuous control, the sliding mode observer has large high-frequency jitter, particularly the sliding mode observer is represented on the estimated back electromotive force, so that the suppression of sliding mode buffeting is a main problem, and along with the development of an electric automobile, a permanent magnet synchronous motor position sensor-free control strategy has a wide development prospect.
Disclosure of Invention
The invention aims to solve the problems, so as to provide a design method of a permanent magnet synchronous motor wide-speed-range rotor position observer, which can improve the control precision of a system and reduce the calculation errors of the electrical angle and the electrical angular velocity of a rotor.
The invention solves the problems, and adopts the following technical scheme:
a design method of a permanent magnet synchronous motor wide-speed-domain rotor position observer comprises the following steps:
s1: the three-phase permanent magnet synchronous motor is used as a control object, the mathematical model of the permanent magnet synchronous motor under a two-phase static coordinate system is that,
wherein u is α And u β Is the stator voltage component in a two-phase stationary coordinate system, e α And e β Counter electromotive forces i in two-phase stationary coordinate systems, i α And i β Is the stator current component in a two-phase stationary coordinate system, R is the equivalent resistance on the stator winding, L is the equivalent inductance on the stator winding, ω e Is the rotor electric angular velocity, theta e Is the rotor electrical angle, ψ is the rotor permanent magnet flux linkage;
the current and voltage components of the three-phase stationary coordinate system a-b-c and the two-phase stationary coordinate system α - β satisfy the following relation:
the current components of the two-phase stationary coordinate system alpha-beta and the two-phase rotating coordinate system d-q may be interconverted by Park variation and anti-Park transformation,
the inverse Park transform is used to determine the inverse of the Park transform,
wherein i is a 、i b i c U a 、u b 、u c Representing three-phase current and three-phase voltage values, i, respectively d And i q Representing the current components in the two-phase rotating coordinate system, respectively.
S2: the definition of using a gaussian error function in the sliding mode control function is,
the sliding mode observer is a special nonlinear control system, is an observer for estimating rotor position information based on the back electromotive force of a reconstruction motor, has strong robustness, and is realized by selecting a sliding mode surface function and selecting a sliding mode gain, wherein the sliding mode surface model s is formed by the method n The design is as follows,
the sliding mode control function is
Wherein,and->Is an estimated stator current component in a two-phase stationary coordinate system;
s3: taking the voltage of the three-phase permanent magnet synchronous motor under a Park converted two-phase static coordinate system and the estimated back electromotive force as input variables of a control system, establishing a permanent magnet synchronous motor Sliding Mode Observer (SMO) model,
where k is the switching gain of the observer, k>{|e α |,|e β |; when the sliding mode reaches the sliding mode surface, z α 、z β Estimated back emf equivalent to the alpha and beta axes;
s4: the characteristics of the inverter show nonlinear change, and in addition, the back electromotive force harmonic wave is increased due to the influence of the permanent magnet material and the topological structure of the permanent magnet synchronous motor; the 6k±1 harmonic exists in the back electromotive force estimation result, which causes the stator current to be distorted, and the non-sinusoidal back electromotive force causes the estimated rotor electrical angle and the estimated rotor electrical angular velocity to generate fluctuation errors.
The proportional resonance controller can realize no static difference tracking on alternating current signals, and because the gain of the proportional resonance controller at a resonance point is infinite and the gain of the proportional resonance controller outside the resonance point is very small, the effect of inhibiting harmonic waves can be achieved, therefore, a counter electromotive force multi-proportional resonance filter of the permanent magnet synchronous motor is established on the basis of a formula (9), and specific harmonic wave filtering is carried out on the estimated counter electromotive force;
the ideal proportional resonant controller (PR) transfer function is,
wherein: k (K) P Is proportional gain, K R For resonance gain omega f For the resonant angular frequency, the ideal proportional resonant controller has an infinite gain at the resonant frequency;
because the bandwidth of an ideal PR controller is narrow and the frequency response gain is infinite, the system is very sensitive to the change of parameters, so that the ideal proportional resonance controller is difficult to realize in actual control;
therefore, the invention adopts the quasi-proportional resonance controller to filter the estimated back electromotive force so as to widen the filtering bandwidth, and the transfer function of the multi-proportional resonance filter is that,
wherein omega c Is the system cut-off angle frequency;
because 6K plus or minus 1 harmonic exists in the counter electromotive force, the invention uses a plurality of quasi-proportional resonance controllers to carry out specific harmonic filtering on the estimated counter electromotive force in parallel, and a multi-proportional resonance filter model adopted by the invention is as follows:
wherein K is P Is proportional gain omega c Is the cut-off angle frequency of the system, h is the specific frequency harmonic wave, K rh The resonance gain of the h-order harmonic wave, s represents complex number, namely represents complex frequency domain;
estimated back electromotive force z obtained through permanent magnet synchronous motor sliding mode observer α 、z β Simultaneously extracting the estimated back electromotive force z through a multi-proportion resonant filter α 、z β Five times and seven times harmonics of (a) to obtain a filtered back electromotive forceAnd feeding back to the input end of the sliding mode observer of the permanent magnet synchronous motor to form closed-loop control;
s5: when the motor runs at a low speed, the signal-to-noise ratio of the back electromotive force is low, so that the rotating speed estimation error can be increased, and the high-precision control is not facilitated. Thus, the amplification factor H is introduced in equation (9), H being the back emf filtered by the multi-scale resonant controller. Because the filtered back electromotive force is closer to the fundamental wave, the accuracy of the estimated value is improved, the estimated back electromotive force is expanded due to the introduction of H, when the motor runs at a low speed, the system can still accurately extract the rotor position information, and the novel Sliding Mode Observer (SMO) model of the permanent magnet synchronous motor is that,
wherein,for estimating back electromotive force after being filtered by the multi-proportion resonant filter, H is an amplification factor;
s6: the filtered estimated back EMFAs input variables of the normalization phase-locked loop, calculating the rotor electric angle and the rotor electric angular velocity through the normalization phase-locked loop, and simultaneously taking the estimated rotor electric angular velocity as the resonant frequency of the multi-proportion resonant filter, thereby realizing frequency self-adaptive control; the calculation model of the estimated rotor electric angular velocity and the estimated rotor electric angle is as follows:
wherein k is i To integrate gain, k p In order to achieve a proportional gain,is to estimate the rotor electrical angular velocity,/, for>Is to estimate the rotor electrical angle.
Compared with the prior art, the invention adopting the technical scheme has the outstanding characteristics that:
the invention provides a permanent magnet synchronous motor wide-speed-domain rotor position observation method, which belongs to the technical field of sensorless control of permanent magnet synchronous motors; according to the invention, a Gaussian error function (erf) is used for replacing a sign function (sign) in a sliding mode control function to operate, so that the buffeting problem of the sliding mode control function is restrained; meanwhile, a multi-proportion resonance filter (MPR) is used for filtering specific subharmonics in back electromotive force observed by a novel permanent magnet synchronous motor Sliding Mode Observer (SMO), and a low-pass filter in a traditional permanent magnet synchronous motor sliding mode observer is removed; the amplification factor is introduced to expand the back electromotive force after filtering, so that a sliding mode observer can accurately calculate the rotor position when the motor runs at a low speed, and the estimation accuracy of the rotor position (rotor electric angle) and the rotor speed (rotor electric angular velocity) under the condition of the motor running at the low speed is improved; the method improves the rotor rotating speed and rotor position estimation data precision of the permanent magnet synchronous motor in the full rotating speed range, comprehensively improves the motor control precision, and provides a method for sensorless control of the permanent magnet synchronous motor.
Drawings
FIG. 1 is a Gaussian error function and sign function image;
FIG. 2 is an overall control block diagram of a permanent magnet synchronous motor control system of the present invention;
FIG. 3 is a block diagram of a permanent magnet synchronous motor sliding mode observer and a multi-scale resonant filter in an embodiment of the invention;
FIG. 4 is a block diagram of a normalized phase-locked loop embodying the present invention;
FIG. 5 is a block diagram of a proportional resonant structure;
FIG. 6 is a block diagram of a multi-scale resonator filter in accordance with an embodiment of the invention;
FIG. 7- (a) is an error waveform of the estimated rotor electrical angular velocity and the actual rotor electrical angular velocity under steady state of the sliding mode observer of the permanent magnet synchronous motor according to the embodiment of the invention;
fig. 7- (b) is an error waveform of the estimated rotor electric angle and the actual rotor electric angle in the steady state of the sliding mode observer of the permanent magnet synchronous motor according to the embodiment of the invention.
Detailed Description
The invention is further described below in connection with the following examples which are provided for the purpose of better understanding of the present invention and are, therefore, not to be construed as limiting the scope of the invention.
As shown in fig. 1 to 7, the parameters of the three-phase permanent magnet synchronous motor in the present embodiment are as follows:
in the embodiment, the permanent magnet synchronous motor control strategy adopts the initial value of the d-axis reference current componentAs shown in fig. 2, the permanent magnet synchronous motor control system adopted in the embodiment mainly includes: the device comprises a d-axis current PI regulator, a q-axis current PI regulator, a rotating speed PI regulator, a sliding mode controller based on multi-proportion resonance (a permanent magnet synchronous motor sliding mode observer and a multi-proportion resonance filter), a normalized phase-locked loop, a Clark conversion module, a Park conversion module, an inverse Park conversion module, a space vector pulse width modulation module, a three-phase inverter and a three-phase permanent magnet synchronous motor.
First, a reference electrical angular velocity omega is given ref The difference value between the reference electric angular velocity and the estimated rotor electric angular velocity value is input into a rotating speed PI regulator to output the q-axis reference current of the motor
Reference current of q-axisWith q-axis actual current i q Is input to the q-axis current PI regulator to supply the d-axis reference currentWith d-axis actual current i d The difference value of the two phases is input into a d-axis current PI regulator to obtain a stator voltage component u under a two-phase rotating coordinate system q ，u d ；
Will u q ，u d Input into a reverse Park conversion module, and output a stator voltage component u under a two-phase stationary coordinate system α 、u β ；
Will u α 、u β Inputting the PWM signals to a space vector pulse width modulation module, and outputting six paths of PWM signals with dead zones;
six paths of PWM with dead zones are input into a three-phase inverter, and three-phase voltages are output;
inputting three-phase voltage into a three-phase permanent magnet synchronous motor, and simultaneously collecting three-phase current i of the three-phase permanent magnet synchronous motor a 、i b 、i c ；
Will i a 、i b 、i c Input into Clark conversion module, output stator current component i under two-phase static coordinate system α ，i β ；
Will i α ，i β Inputting the current into a Park conversion module to obtain q-axis actual current i q And d-axis actual current i d At this time, a current closed loop is formed;
as in FIG. 3, u α 、u β 、i α 、i β In an input-based proportional-resonant sliding-mode observer, the output estimates the back electromotive force
Will beInput to a normalized phase-locked loop, output an estimated rotor electrical angular velocity +.>And estimating rotor electrical angle +.>
Will beThen inputting the current component conversion parameters of the two-phase static coordinate system and the two-phase rotating coordinate system into a Park change module and an anti-Park change module in the system;
will beThe input quantity is input into a rotating speed PI regulator to form a rotor rotating speed closed loop.
Further, as shown in fig. 3, the calculation process of the estimated rotor electric angular velocity and the estimated rotor electric angle based on the multi-proportion resonance sliding mode controller includes:
inputting stator voltage component u in two-phase stationary coordinate system α 、u β Estimated back emf z before filtering α 、z β And estimated back EMF after filteringObtaining a stator current estimated value under a two-phase stationary coordinate system by a current error model
Will beAnd i obtained by collecting actual current of three-phase permanent magnet synchronous motor α 、i β The Gaussian processing is carried out by inputting the sliding mode control function to obtain the estimated back electromotive force z before filtering α 、z β ；
Estimated back EMF z before filtering α 、z β And estimating rotor electrical angular velocitySubstituted into the multi-scale resonator filter of fig. 6, the output filtered estimate is back-electromotiveVigor->Is carried into a normalized phase locked loop as in fig. 4 to obtain an estimated rotor electrical angular velocity and an estimated rotor position.
The design process of the permanent magnet synchronous motor sliding mode observer model is as follows:
first, a slip-form surface model s is defined n ，
Wherein i is α And i β Is the stator current component in the alpha-beta coordinate system,and->The stator current component is estimated.
Then, the permanent magnet synchronous motor model is:
wherein u is α And u β Is the stator voltage component in a two-phase stationary coordinate system, e α And e β Counter electromotive forces i in two-phase stationary coordinate systems, i α And i β Is the stator current component in a two-phase stationary coordinate system, R is the equivalent resistance on the stator winding, L is the equivalent inductance on the stator winding, ω e Is the rotor electric angular velocity, theta e Is the rotor electrical angle, ψ is the rotor permanent magnet flux linkage.
The novel permanent magnet synchronous motor sliding mode observer model can be expressed as:
wherein "∈A" represents the estimated value, E(s) α ) And E(s) β ) Is a sliding mode control function, k is the switching gain of the observer, and H is the amplification factor.
When the sliding mode motion occurs, E (s α ) And E(s) β ) Including useful rotor position information (rotor electrical angle, rotor electrical angular velocity), the sliding mode control function is expressed as a gaussian error function:
wherein the gaussian error function is defined as:
equation (12) minus equation (1) yields the actual current and estimated current error model as in fig. 3:
as can be seen from the above equation, the switching function contains back emf information, so that the rotor electrical angular velocity and the rotor electrical angle can be calculated, but the control system error is large due to the harmonic wave contained in the back emf.
As shown in fig. 5, the present embodiment filters the estimated back electromotive force by using a quasi-proportional resonance controller, and the quasi-proportional resonance controller model is as follows:
in this embodiment, a plurality of quasi-proportional resonant controllers are connected in parallel to form a multi-proportional resonant controller, and the estimated back electromotive force of the alpha axis and the beta axis is z α 、z β Filtering by a multi-proportion resonance controller, filtering out fifth and seventh harmonic waves to obtain a filtered estimated counter electromotive forceThe multi-proportion resonant filter model is as follows:
wherein, the value of h can be adjusted according to the actual control requirement;
meanwhile, when the system reaches the sliding mode, there are:
meanwhile, the formula (18) is written as:
at this time, the value of H is twice of the counter electromotive force, so that H is used for replacing the traditional counter electromotive force to estimate the rotor electric angle and the rotor electric angular speed, and the problem of calculation error caused by small counter electromotive force and small signal-to-noise ratio when the motor runs at a low speed is solved.
If the slip mode exists and stabilizes, the error tends to zero as the time tends to infinity. According to the lyapunov stability principle, select:
the SMO stabilization condition is:
by bringing formula (18) into formula (20)The sliding mode controller based on the wide speed domain in the present embodiment is stable.
At the normalized phase-locked loop module, the normalized back EMF error can be expressed as:
when the electrical angle estimation error of the rotor is smaller thanWhen this is the case, the above equation can be rewritten as:
the normalized phase-locked loop may track the input signal such that the output signal has the same frequency or phase as the input signal. Therefore, the phase-locked loop with back electromotive force normalization is not affected by the rotor speed, and the robustness of the system can be improved.
The electrical angular velocity of the motor and the rotor electrical angle can be expressed as:
according to the control block diagram shown in fig. 2, experimental simulation is performed on the control system of the invention based on the dspace semi-physical simulation experiment platform, fig. 7- (a) is a waveform diagram of the motor rotation speed and a rotation speed error when the motor is under a rated load and the rotation speed is 1500/min, and fig. 7- (b) is a waveform diagram of the motor rotor position and a position error when the motor is under a rated load and the rotation speed is 1500/min.
The system uses a multi-proportion resonance sliding mode observer and a normalization phase-locked loop to replace a traditional mechanical sensor to calculate the rotor and the rotating speed, so as to form a speed and current double closed-loop system. The counter electromotive force harmonic wave can be effectively restrained through the multi-proportion resonance controller; the continuous Gaussian error function is used for replacing a sign function, so that system buffeting is effectively restrained; by introducing the amplification factor, the low-speed precision of the sliding mode observer is improved; furthermore, the method improves the rotating speed of the motor in the full rotating speed range and the rotor position estimation precision.
The foregoing description of the preferred embodiments of the invention is not intended to limit the scope of the claims, but rather to cover all equivalent modifications within the scope of the present invention as defined by the appended claims.
Claims (1)
1. A design method of a permanent magnet synchronous motor wide-speed-domain rotor position observer comprises the following steps:
s1: the three-phase permanent magnet synchronous motor is used as a control object, the mathematical model of the permanent magnet synchronous motor under the alpha-beta of the two-phase static coordinate system is as follows,
wherein u is α And u β Is the stator voltage component in a two-phase stationary coordinate system, e α And e β Counter electromotive forces i in two-phase stationary coordinate systems, i α And i β Is the stator current component in a two-phase stationary coordinate system, R is the equivalent resistance on the stator winding, L is the equivalent inductance on the stator winding, ω e Is the rotor electric angular velocity, theta e Is the rotor electrical angle, ψ is the rotor permanent magnet flux linkage;
the current and voltage components of the three-phase stationary coordinate system a-b-c and the two-phase stationary coordinate system α - β satisfy the following relation:
the current component in the two-phase stationary coordinate system alpha-beta and the current component in the two-phase rotating coordinate system d-q can be converted into each other by Park transformation and anti-Park transformation,
the inverse Park transform is used to determine the inverse of the Park transform,
wherein i is a 、i b i c U a 、u b 、u c Three-phase current and three-phase voltage values, i d And i q Respectively representing current components under a two-phase rotation coordinate system;
the method is characterized in that:
s2: the sliding mode control function is processed by a gaussian error function,
construction of a slip-form surface model s n In order to achieve this, the first and second,
the gaussian error function is defined as,
the sliding mode control function is
Wherein,and->Is the stator current component estimated value under a two-phase stationary coordinate system; erf (x) is a gaussian error function;
s3: a model equation under a two-phase static coordinate system of the three-phase permanent magnet synchronous motor is adopted, wherein voltage and estimated back electromotive force are used as input variables of a control system, a Sliding Mode Observer (SMO) model of the permanent magnet synchronous motor is established,
where k is the switching gain of the observer, k>{|e α |,|e β |; when the sliding mode reaches the sliding mode surface, z α 、z β Estimated back emf equivalent to the alpha and beta axes;
s4: a plurality of quasi-proportional resonance controllers are connected in parallel to carry out specific harmonic filtering on the estimated back electromotive force, the model of the multi-proportional resonance filter is that,
wherein K is P Is proportional gain omega c Is the cut-off angle frequency of the system, h is the specific frequency harmonic wave, K rh Is the resonance gain of the h order harmonic, omega f S represents complex number, which is the complex frequency domain;
estimated back electromotive force z obtained through permanent magnet synchronous motor sliding mode observer α 、z β Simultaneously extracting the estimated back electromotive force z through a multi-proportion resonant filter α 、z β Five times and seven times harmonics of (a) to obtain a filtered back electromotive forceAnd feeding back to the input end of the sliding mode observer of the permanent magnet synchronous motor to form closed-loop control;
s5: introducing an amplification factor H into a permanent magnet synchronous motor Sliding Mode Observer (SMO) model, wherein the novel permanent magnet synchronous motor sliding mode observer model after introducing the amplification factor is that,
wherein,for estimating back electromotive force after being filtered by the multi-proportion resonant filter, H is an amplification factor;
s6: the filtered estimated back EMFAs input variables of the normalized phase-locked loop, the rotor electric angle and the rotor electric angular velocity are calculated through the normalized phase-locked loop, and the rotor is estimated at the same timeThe electric angular velocity is used as the resonant frequency of the multi-proportion resonant filter, so that the frequency self-adaptive control is realized; the calculation model of the estimated rotor electric angular velocity and the estimated rotor electric angle is as follows:
wherein k is i To integrate gain, k p In order to achieve a proportional gain,is to estimate the rotor electrical angular velocity,/, for>Is to estimate the rotor electrical angle.
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