CN103414416A - Permanent magnet synchronous motor sensorless vector control system based on EKF - Google Patents

Abstract

The invention discloses a permanent magnet synchronous motor sensorless vector control system based on an EKF. An extended Kalman filter (EKF) is employed as a state estimator to estimate the rotation speed and position of a stator. The input signal of the state estimator is stator phase current Ia, Ib and Ic, and the output signal of the state estimator is estimated position and estimated speed. A system state vector X=(I(alpha) I(beta) omega(e)Theta(e) T(l))<T>, an output vector u=(u(alpha) u(beta) T(e))<T>, an output vector y=( I(alpha) I(beta) Theta(e))<T>, the above three vectors are selected, a state equation and an output equation of EKF state estimation are obtained, a system noise matrix V and a measurement noise matrix W are added, and after the discretization of the state equation and the output equation, x(k+1)=f[x(k)]+Beu(k)+V(k) and y(k)=Cex(k)+W(k). The purpose of the invention is to provide the permanent magnet synchronous motor sensorless vector control system based on the EKF with strong anti-interference ability, low cost, and high reliability.

Description

Permagnetic synchronous motor vector control system without sensor based on EKF

Technical field

The present invention relates to the permagnetic synchronous motor vector control system without sensor based on EKF.

Background technology

Permagnetic synchronous motor (PMSM) because its power density is high, volume is little, do not need excitation, dynamic responding speed and position control accuracy that power factor (PF) is high and superior obtained application more and more widely in the high performance control system.For the control of permagnetic synchronous motor, the measurement of accurate rotor-position and spinner velocity is the most important condition to its control.Referring to Fig. 1, prior art is used photoelectric code disk (i.e. Encoder module in figure) to carry out sample count to the position signalling of permanent-magnetic synchronous motor rotor usually, and then calculating corresponding motor position and speed, concrete control procedure is: according to the motor speed ω detected _refWith the reference rotation velocity ω of input and the relation of rotating speed and torque, Negotiation speed PI controller calculates stator current reference input I _Qref.The phase current I of stator _a, I _b, I _cBy the phase current testing circuit, be extracted, then by the clarke conversion, they be transformed in stator two phase coordinate systems, with the park conversion, they are transformed in the d-q rotating coordinate system, namely the FOC conversion in figure is by I _a, I _b, I _cChange into I _d, I _q.Current signal in the d-q coordinate system again with their reference input I _QrefAnd I _DrefCompare, wherein I _Dref=O, obtain desirable controlled quentity controlled variable by the PI controller.Control signal is carried out the Park inverse transformation again, delivers to the PWM inverter, thus the actual current of controlled stator three-phase symmetric winding.The outer shroud speed ring has produced the reference value of stator current, and interior circular current ring obtains the working control signal, thereby forms a complete speed FOC double loop system.But while using photoelectric code disk, the system rejection to disturbance ability is not good, reduced the reliability of system, and high-precision code-disc is expensive, has increased to a certain extent the cost of system.

Summary of the invention

For solving the problems of the technologies described above, the invention provides the vector control system without sensor of the permagnetic synchronous motor based on EKF that a kind of antijamming capability is strong, cost is relatively low, reliability is high.

The present invention is based on the permagnetic synchronous motor vector control system without sensor of EKF, in described control system, adopt extended Kalman filter EKF as state estimator, stator rotating speed and position are estimated, the input signal of described state estimator is stator phase current I _a, I _bAnd I _c, the output signal of state estimator is estimated position and estimation rotating speed, permagnetic synchronous motor state equation and output equation for the EKF state estimation under the alpha-beta rest frame is:

$\frac{\mathrm{dx}}{\mathrm{dt}}=f\left(x\right)+B_{e}u$

y＝C _ex

x＝(i _α?i _β?ω _e?θ _e?T _l) ^T

u＝(u _α?u _β?T _e) ^T

y＝(i _α?i _β?θ _e) ^T

$f\left(x\right)=\left(\begin{array}{c}-i_{\mathrm{\&alpha;}}{R}_e/L_s+{\mathrm{\&omega;}}_e\sin {\mathrm{\&theta;}}_e{\mathrm{\&psi;}}_f/L_s\\ -i_{\mathrm{\&beta;}}{R}_e/L_s-{\mathrm{\&omega;}}_e{\cos \mathrm{\&theta;}}_e{\mathrm{\&psi;}}_f/L_s\\ -{\mathrm{\&omega;}}_{e}B/J-n_p{T}_l/J\\ {\mathrm{\&omega;}}_e\\ 0\end{array}\right)$

$B_e={\left(\begin{array}{ccccc}1/{\mathrm{<figure-callout\; id="0"\; label="L\; s"\; filenames="HSA0000092355220000031.png"\; state="\{\{state\}\}">L</figure-callout>}}_s& 0& 0& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="0"\; label="L\; s"\; filenames="HSA0000092355220000031.png"\; state="\{\{state\}\}">L</figure-callout>}}_s& 0& 0& 0\\ 0& 0& n_p/\mathrm{<figure-callout\; id="0"\; label="J"\; filenames="HSA0000092355220000031.png"\; state="\{\{state\}\}">J</figure-callout>}& 0& 0\end{array}\right)}^T$

$C_e=\left(\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0\end{array}\right)$

In formula: x is state vector, namely estimates metering; U is input vector; Y is output vector; Function of state f (x) is the coupling terms of state vector and input matrix;

I _α, i _β, u _α, and u _βBe respectively the component of stator current, voltage α, β axle under the Clarke coordinate system; R _sFor the stator phase resistance; L _sFor the equivalent synchronous inductance; ψ _fFor permanent magnet first-harmonic magnetic linkage; ω _eFor rotor electric angle speed; θ _eFor the electric angle displacement;

N _pFor the motor number of pole-pairs; J is the system moment of inertia, converts the moment of inertia on motor shaft comprising rotor and load; B is the viscous friction system; T _eElectromagnetic torque for motor output; T _lFor the equivalent load torque, the torque ripple caused comprising load torque and due to factors such as viscous friction coefficient nonlinear change, given value of current deviations; And assert

Add the system noise matrix V and measure noise matrix W, and will after state equation and output equation discretization, be:

x(k+1)＝f[x(k)]+B _eu(k)+V(k)

y(k)＝C _ex(k)+W(k)

In formula: x (k), u (k), y (k) and f[x (k)] be respectively the discrete form of state vector, input vector, output vector and function of state;

V (k) and W (k) are respectively the system noise vector of discretization and measure noise vector;

The estimation procedure of described state estimator is divided into prediction and proofreaies and correct two stages, and by recursive process approaching to reality state, the recurrence equation formula is:

$\tilde{x}(k+1)=\hat{x}\left(k\right)+T_s\left\{f\right[\hat{x}\left(k\right)]+B_{e}u\left(k\right)\}$

$\tilde{y}(k+1)=C_e\tilde{x}(k+1)$

$\tilde{P}(k+1)=\hat{p}\left(k\right)+T_s[F\left(k\right)\hat{P}\left(k\right)+\hat{P}\left(k\right)F^T\left(k\right)]+Q$

$K(k+1)=\tilde{P}(k+1)C_e^T{[C_e\tilde{P}(k+1)C_e^T+R]}^{-1}$

$\hat{x}(k+1)=\tilde{x}(k+1)+K(k+1)[y(k+1)-\tilde{y}(k+1)]$

$\hat{P}(k+1)=\tilde{P}(k+1)-K(k+1)C_e\tilde{P}(k+1)$

In formula: T _sFor the electric current loop sampling period,

With Be respectively predicted value and the estimated value of state variable;

With

Be respectively prediction covariance matrix and estimate covariance matrix; K (k) is gain matrix; F (k) is gradient matrix, is defined as follows:

$F\left(k\right)=\frac{\&PartialD;f\left(x\right)}{\&PartialD;x}{|}_{x=\hat{x}\left(k\right)}$

Noise covariance matrix Q and R are respectively:

$Q=\left(\begin{array}{ccccc}{Q}_i& & & & \\ & Q_i& & & \\ & & Q_{\mathrm{\&omega;}}& & \\ & & & Q_{\mathrm{\&theta;}}& \\ & & & & Q_T\end{array}\right)$

$R=\left(\begin{array}{ccc}{R}_i& & \\ & R_i& \\ & & R_{\mathrm{\&theta;}}\end{array}\right)$

In formula: Q _iFor stator current system noise covariance value; Q _ω, Q _θAnd Q _TBe respectively the system noise covariance of rotor electric angle speed, electric angle displacement and load torque; R _iFor stator current is measured the noise covariance value; R _θFor rotor electric angle displacement measurement noise covariance value.

The present invention is based on the permagnetic synchronous motor vector control system without sensor of EKF, utilize the observer of EKF as motor speed and rotor-position, EKF has considered system noise and has measured the statistical property of noise, effectively impair system noise and the measurement noise impact on system, the antijamming capability of raising system.With respect to using high-precision photoelectric code disk, adopt extended Kalman filter EKF cost lower in addition.The method on Matlab Simulink platform, the present invention proposed has been carried out simulating, verifying, and motor speed and rotor-position that observation obtains can trace into actual value very soon.Actual speed and observation speed are very approaching as can be seen from Figure 4 and Figure 5, only in the motor speed sudden change, some errors are arranged, but within the short time, error still can revert to O; The rotor-position that can find out the physical location of rotor and EKF observation from Fig. 6 and Fig. 7 is also very approaching.So simulation result shows the permagnetic synchronous motor vector control system without sensor that the present invention is based on EKF and has higher accuracy and reliability.

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.Following examples are used for the present invention is described, but are not used for limiting the scope of the invention.

The accompanying drawing explanation

Fig. 1 is the theory diagram of the control system for permanent-magnet synchronous motor based on photoelectric code disk of prior art;

Fig. 2 is the vector control system without sensor of the permagnetic synchronous motor based on EKF theory diagram of the present invention;

Fig. 3 is the state estimation procedure schematic diagram of EKF;

The comparison diagram of EKF observation speed and motor actual speed in permagnetic synchronous motor based on EKF vector control system without sensor of the present invention when Fig. 4 is system simulation experiments;

EKF observation speed error curve diagram in permagnetic synchronous motor based on EKF vector control system without sensor of the present invention when Fig. 5 is system simulation experiments;

Permagnetic synchronous motor based on EKF vector control system without sensor rotor physical location curve chart of the present invention when Fig. 6 is system simulation experiments;

EKF observation rotor-position curve chart in permagnetic synchronous motor based on EKF vector control system without sensor of the present invention when Fig. 7 is system simulation experiments.

Embodiment

The present invention is based on permagnetic synchronous motor PMSM (the Permanent Magnet Synchronous Motor) vector control system without sensor of EKF, referring to Fig. 2, adopt extended Kalman filter EKF (Extended Kalman Filter) as state estimator, the photoelectric code disk that replaces prior art, stator rotating speed and position are estimated, the input signal of EKF is stator phase current I _a, I _bAnd I _c, output signal is estimated position and estimates rotating speed.

The voltage equation of PMSM (Permanent Magnet Synchronous Motor) is:

$\frac{{\mathrm{di}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}+{\mathrm{\&omega;}}_e\frac{{\mathrm{\&psi;}}_f}{L_s}\sin {\mathrm{\&theta;}}_e+\frac{u_{\mathrm{\&alpha;}}}{L_s}$

$\frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&beta;}}-{\mathrm{\&omega;}}_e\frac{{\mathrm{\&psi;}}_f}{L_s}\sin {\mathrm{\&theta;}}_e+\frac{u_{\mathrm{\&beta;}}}{L_s}$

In formula: i _α, i _β, u _α, and u _βBe respectively the component of stator current, voltage α, β axle under the Clarke coordinate system; R _sFor the stator phase resistance; L _sFor the equivalent synchronous inductance; ψ _fFor permanent magnet first-harmonic magnetic linkage; ω _eFor rotor electric angle speed; θ _eFor the electric angle displacement;

The torque balance equation of PMSM is:

$\frac{{\mathrm{d\&omega;}}_e}{\mathrm{dt}}=\frac{n_p}{J}(T_e-\frac{B}{n_p}{\mathrm{\&omega;}}_e-T_l)$

In formula: n _pFor the motor number of pole-pairs; J is the system moment of inertia, converts the moment of inertia on motor shaft comprising rotor and load; B is the viscous friction system; T _eElectromagnetic torque for motor output; T _lFor the equivalent load torque, the torque ripple caused comprising load torque and due to factors such as viscous friction coefficient nonlinear change, given value of current deviations; And assert $\frac{d{T}_l}{\mathrm{dt}}=0;$

According to voltage equation and torque equation, can draw state equation and the output equation of state estimator:

$\frac{\mathrm{dx}}{\mathrm{dt}}=f\left(x\right)+B_{e}u$

y＝C _ex

x＝(i _α?i _β?Γ _e?θ _e?T _l) ^T

u＝(u _α?u _β?T _e) ^T

y＝(i _α?i _β?θ _e) ^T

$f\left(x\right)=\left(\begin{array}{c}-i_{\mathrm{\&alpha;}}{R}_e/L_s+{\mathrm{\&omega;}}_e\sin {\mathrm{\&theta;}}_e{\mathrm{\&psi;}}_f/L_s\\ -i_{\mathrm{\&beta;}}{R}_e/L_s-{\mathrm{\&omega;}}_e{\cos \mathrm{\&theta;}}_e{\mathrm{\&psi;}}_f/L_s\\ -{\mathrm{\&omega;}}_{e}B/J-n_p{T}_l/J\\ {\mathrm{\&omega;}}_e\\ 0\end{array}\right)$

$B_e={\left(\begin{array}{ccccc}1/{\mathrm{<figure-callout\; id="0"\; label="L\; s"\; filenames="HSA0000092355220000031.png"\; state="\{\{state\}\}">L</figure-callout>}}_s& 0& 0& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="0"\; label="L\; s"\; filenames="HSA0000092355220000031.png"\; state="\{\{state\}\}">L</figure-callout>}}_s& 0& 0& 0\\ 0& 0& n_p/\mathrm{<figure-callout\; id="0"\; label="J"\; filenames="HSA0000092355220000031.png"\; state="\{\{state\}\}">J</figure-callout>}& 0& 0\end{array}\right)}^T$

$C_e=\left(\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0\end{array}\right)$

In formula: x is state vector, namely estimates metering; U is input vector; Y is output vector; Function of state f (x) is the coupling terms of state vector and input matrix.

The consideration model is estimated the impacts such as inaccurate and external interference, in the EKF state equation, adds the system noise matrix V and measures noise matrix W, and by the result after the equation discretization being:

X (k+1)=f[x (k)]+B _eU (k) ten V (k)

y(k)＝C _ex(k)+W(k)

In formula: x (k), u (k), y (k) and f[x (k)] be respectively the discrete form of state vector, input vector, output vector and function of state;

V (k) and W (k) are respectively the system noise vector of discretization and measure noise vector.

Usually, system noise and measurement noise are the zero-mean white Gaussian noise, can obtain thus noise covariance matrix Q and R that EKF needs:

$Q=\left(\begin{array}{ccccc}{Q}_i& & & & \\ & Q_i& & & \\ & & Q_{\mathrm{\&omega;}}& & \\ & & & Q_{\mathrm{\&theta;}}& \\ & & & & Q_T\end{array}\right)$

$R=\left(\begin{array}{ccc}{R}_i& & \\ & R_i& \\ & & R_{\mathrm{\&theta;}}\end{array}\right)$

In formula: Q _iFor stator current system noise covariance value; Q _ω, Q _eAnd Q _TBe respectively the system noise covariance of rotor electric angle speed, electric angle displacement and load torque; R ₁For stator current is measured the noise covariance value; R _θFor rotor electric angle displacement measurement noise covariance value.

Referring to Fig. 3, the total process of the state estimation of EKF is by the k time estimated result

Obtain estimated result the k+1 time Namely by the state of current system state estimation next cycle, thereby solve the problem of M/T speed detection method speed feedback hysteresis one-period.Estimation procedure is divided into prediction and proofreaied and correct for two megastages, by recursive process approaching to reality state.The recurrence equation formula is as follows:

$\tilde{x}(k+1)=\hat{x}\left(k\right)+T_s\left\{f\right[\hat{x}\left(k\right)]+B_{e}u\left(k\right)\}$

$\tilde{y}(k+1)=C_e\tilde{x}(k+1)$

$\tilde{P}(k+1)=\hat{p}\left(k\right)+T_s[F\left(k\right)\hat{P}\left(k\right)+\hat{P}\left(k\right)F^T\left(k\right)]+Q$

$K(k+1)=\tilde{P}(k+1)C_e^T{[C_e\tilde{P}(k+1)C_e^T+R]}^{-1}$

$\hat{x}(k+1)=\tilde{x}(k+1)+K(k+1)[y(k+1)-\tilde{y}(k+1)]$

$\hat{P}(k+1)=\tilde{P}(k+1)-K(k+1)C_e\tilde{P}(k+1)$

In formula: T _sFor the electric current loop sampling period, With

Be respectively predicted value and the estimated value of state variable;

With

Be respectively prediction covariance matrix and estimate covariance matrix; K (k) is gain matrix; F (k) is gradient matrix, is defined as follows:

$F\left(k\right)=\frac{\&PartialD;f\left(x\right)}{\&PartialD;x}{|}_{x=\hat{x}\left(k\right)}$

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the technology of the present invention principle; can also make some improvement and modification, these improve and modification also should be considered as protection scope of the present invention.

Claims (1)

1. based on the permagnetic synchronous motor vector control system without sensor of EKF, it is characterized in that: in described control system, adopt extended Kalman filter EKF as state estimator, stator rotating speed and position are estimated, the input signal of described state estimator is stator phase current I _a, I _bAnd I _c, the output signal of state estimator is estimated position and estimation rotating speed, permagnetic synchronous motor state equation and output equation for the EKF state estimation under the alpha-beta rest frame is:

$\frac{\mathrm{dx}}{\mathrm{dt}}=f\left(x\right)+B_{e}u$

y＝C _ex

x＝(i _α?i _β?ω _e?θ _e?T _l) ^T

u＝(u _α?u _β?T _e) ^T

y＝(i _α?i _β?θ _e) ^T

$f\left(x\right)=\left(\begin{array}{c}-i_{\mathrm{\&alpha;}}{R}_e/L_s+{\mathrm{\&omega;}}_e\sin {\mathrm{\&theta;}}_e{\mathrm{\&psi;}}_f/L_s\\ -i_{\mathrm{\&beta;}}{R}_e/L_s-{\mathrm{\&omega;}}_e{\cos \mathrm{\&theta;}}_c{\mathrm{\&psi;}}_f/L_s\\ -{\mathrm{\&omega;}}_{e}B/J-n_p{T}_l/J\\ {\mathrm{\&omega;}}_e\\ 0\end{array}\right)$

$B_e={\left(\begin{array}{ccccc}1/L_s& 0& 0& 0& 0\\ 0& 1/L_s& 0& 0& 0\\ 0& 0& n_p/J& 0& 0\end{array}\right)}^T$

$C_e=\left(\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0\end{array}\right)$

In formula: x is state vector, namely estimates metering; U is input vector; Y is output vector; Function of state f (x) is the coupling terms of state vector and input matrix;

I _α, i _β, u _α, and u _βBe respectively the component of stator current, voltage α, β axle under the Clarke coordinate system; R _sFor the stator phase resistance; L _sFor the equivalent synchronous inductance; ψ _fFor permanent magnet first-harmonic magnetic linkage; ω _eFor rotor electric angle speed; θ _eFor the electric angle displacement;

N _pFor the motor number of pole-pairs; J is the system moment of inertia, converts the moment of inertia on motor shaft comprising rotor and load; B is the viscous friction system; T _eElectromagnetic torque for motor output; T1 is the equivalent load torque, the torque ripple caused comprising load torque and due to factors such as viscous friction coefficient nonlinear change, given value of current deviations; And assert

Add the system noise matrix V and measure noise matrix W, and will after state equation and output equation discretization, be:

X (k+1)=f[x (k)]+B _eU (k) ten V (k)

y(k)＝C _ex(k)+W(k)

In formula: x (k), u (k), y (k) and f[x (k)] be respectively the discrete form of state vector, input vector, output vector and function of state;

V (k) and W (k) are respectively the system noise vector of discretization and measure noise vector;

The estimation procedure of described state estimator is divided into prediction and proofreaies and correct two stages, and by recursive process approaching to reality state, the recurrence equation formula is:

$\tilde{x}(k+1)=\hat{x}\left(k\right)+T_s\left\{f\right[\hat{x}\left(k\right)]+B_{e}u\left(k\right)\}$

$\tilde{y}(k+1)=C_e\tilde{x}(k+1)$

$\tilde{P}(k+1)=\hat{p}\left(k\right)+T_s[F\left(k\right)\hat{P}\left(k\right)+\hat{P}\left(k\right)F^T\left(k\right)]+Q$

$K(k+1)=\tilde{P}(k+1)C_e^T{[C_e\tilde{P}(k+1)C_e^T+R]}^{-1}$

$\hat{x}(k+1)=\tilde{x}(k+1)+K(k+1)[y(k+1)-\tilde{y}(k+1)]$

$\hat{P}(k+1)=\tilde{P}(k+1)-K(k+1)C_e\tilde{P}(k+1)$

In formula: T _sFor the electric current loop sampling period,

With

Be respectively predicted value and the estimated value of state variable;

With

Be respectively prediction covariance matrix and estimate covariance matrix; K (k) is gain matrix; F (k) is gradient matrix, is defined as follows:

$F\left(k\right)=\frac{\&PartialD;f\left(x\right)}{\&PartialD;x}{|}_{x=\hat{x}\left(k\right)}$

Noise covariance matrix Q and R are respectively:

$Q=\left(\begin{array}{ccccc}{Q}_i& & & & \\ & Q_i& & & \\ & & Q_{\mathrm{\&omega;}}& & \\ & & & Q_{\mathrm{\&theta;}}& \\ & & & & Q_T\end{array}\right)$

$R=\left(\begin{array}{ccc}{R}_i& & \\ & R_i& \\ & & R_{\mathrm{\&theta;}}\end{array}\right)$

In formula: Q _iFor stator current system noise covariance value; Q _ω, Q _θAnd Q _rBe respectively the system noise covariance of rotor electric angle speed, electric angle displacement and load torque; R _iFor stator current is measured the noise covariance value; R _θFor rotor electric angle displacement measurement noise covariance value.

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