CN104682805B - Permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer - Google Patents

Abstract

A kind of permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer, including:Set up permagnetic synchronous motor system, initialization system mode and associated control parameters；Extended state observer is designed；Based on extended state observer, design full-order sliding mode controller, eliminate the buffeting problem in sliding formwork control, and ensure system mode can fast and stable converge to zero point.The present invention proposes a kind of full-order sliding mode structure changes position servo control method, can improve sliding formwork control and buffet problem and improve system control accuracy, it is ensured that realize quick accurate tracking of the motor outgoing position to desired trajectory.

Description

Permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on extended state observer

Technical Field

The invention relates to a full-order sliding mode variable structure position servo control method for a permanent magnet synchronous motor, in particular to a full-order sliding mode control method for a permanent magnet synchronous motor system with unknown system part state and unknown nonlinear uncertainty upper bound.

Background

In a permanent magnet synchronous motor, a conventional control method has a certain buffeting problem due to overhigh control gain and the existence of a sign function. How to weaken buffeting in sliding mode control in a high-performance permanent magnet synchronous motor position servo system is a key technical problem to be solved urgently, accurate positioning and position tracking performance of a motor system are influenced, and even damage can be caused to the motor system in serious cases. In order to solve the problem of buffeting in sliding mode control, reduce adverse effects caused by buffeting in a permanent magnet synchronous motor and improve the working performance of a system, a proper control method is necessary to realize the rapid and accurate tracking of the output position of the motor on an expected track.

Currently, in the research of eliminating buffeting, various improved sliding mode control methods have been proposed, such as designing a controller, an integral time-varying sliding mode controller and an adaptive sliding mode controller by using a saturation function instead of a sign function. In addition, in recent years, a method for speed regulation control and buffeting-free sliding mode control of the permanent magnet synchronous motor by combining a disturbance observer, an extended state observer and sliding mode control is also provided. The controller is a full-order sliding mode controller, and compared with the traditional reduced-order sliding mode controller, the controller has the advantages that control signals are continuous, and the phenomenon of buffeting in sliding mode control can be effectively avoided. Aiming at a permanent magnet synchronous motor position servo system with unknown friction torque and model uncertainty, the invention designs a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer, and realizes the rapid and accurate tracking of the output position of the motor on an expected track.

Disclosure of Invention

In order to overcome the defect of buffeting in sliding mode control in a permanent magnet synchronous motor position servo system with unknown friction torque and model uncertainty, the invention provides a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer, and the buffeting is better avoided in sliding mode control. The extended state observer is adopted to estimate the state and the uncertainty of the system, and a full-order sliding mode control method is designed based on the estimated value, so that the buffeting problem in the sliding mode control is restrained, and the output position of the motor can be quickly and accurately tracked to the expected track.

The technical scheme proposed for solving the technical problems is as follows:

a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer comprises the following steps:

step 1, establishing a permanent magnet synchronous motor system, and initializing a system state and control parameters;

1.1, under a d/q rotating coordinate system, a voltage equation, a torque equation and a motion equation of the permanent magnet synchronous motor are respectively as follows:

T_e＝1.5p_nψ_fi_q(2)

wherein u is_d、u_qThe components of the stator voltage on the d and q axes respectively; i.e. i_d、i_qThe components of the stator current on the d axis and the q axis respectively; r is a stator resistor; l is_d、L_qThe components of the stator inductance on the d axis and the q axis are respectively; p is a radical of_nIs the number of pole pairs; omega is the angular speed of the rotor; j is moment of inertia; b is a friction coefficient; t is_eIs an electromagnetic torque; t is_LIs the load torque; psi_fThe permanent magnet is a permanent magnet fundamental wave excitation flux linkage;

1.2, obtaining a second-order dynamic equation of the position ring of the permanent magnet synchronous motor according to the formulas (1) to (3) as

Wherein, b is 1.5p_nψ_fD is disturbance composed of unknown friction torque and load torque, d ═ T_L+Bω)/J；

1.3, according to the design idea of the extended state observer, the state variable x_iI is 1,2,3, let x₁＝θ，

x₂ω and defines an extended state x₃Where a (t), formula (4) is written as the equivalent

y＝x₁＝θ (6)

Wherein, for a given q-axis current reference input, b₀Is an estimated value of b and is,u is a control input to the controller,y is the actual output position of the permanent magnet synchronous motor;

step 2, expanding the state observer design;

let z_iI is 1,2,3, and is the state variable x in formula (5)_iDefining an observation error of_i＝z_i-x_iThen the nonlinear extended state observer expression is:

wherein, β₁,β₂,β₃Are observer gains, β₁,β₂,β₃Fal (-) is a continuous power function with a linear segment near the origin, expressed as:

wherein, the interval length of the linear segment is more than 0, 0 < α_i＜1,i＝1,2,3，sign(₁) For symbolic functions, the expression is:

step 3, designing a full-order sliding mode controller based on the extended state observer;

3.1, defining the tracking error e as

e＝y-y_d＝x₁-y_d(9)

Wherein y is_dIs a desired trajectory;

the first and second derivatives of the tracking error e are respectively

And

3.2, according to the equations (9) to (11), designing the following full-order slip-form surface s:

wherein λ is₁And λ₂For controlling the parameter, λ₁＞0，λ₂＞0；

By substituting formulae (9) to (11) for formula (12)

The full-order sliding mode controller based on the extended state observer is designed by the formula (13)

u₂＝-k sgn(s) (17)

Wherein T is more than or equal to 0, and k is k_d+k_T+η，η，k_d，k_TAre all controller parameters, η > 0, k_d＞0，k_T＞0；

3.3 substitution of formulae (14) to (17) into formula (13), there are

s₂＝u₁+(x₃-z₃)+λ₂(x₂-z₂)+λ₁(x₁-z₁) ＝u1+d(x，z) (18)

Wherein d (x, z) ═ x₃-z₃)+λ₂(x₂-z₂)+λ₁(x₁-z₁) And d (x, z) is less than or equal to l_d，

l_d＝l₃+λ₂l₂+λ₁l₁；

Derived from formula (18)

3.4, designing a Lyapunov function:

V＝0.5s²(20)

substituting the formulas (5), (12), (14) to (17) into the formula (20) ifThe system is determined to be stable.

The invention designs a permanent magnet synchronous motor full-order sliding mode variable structure position servo controller based on the extended state observer by combining the extended state observer technology and the full-order sliding mode control technology, so that the buffeting problem in sliding mode control is inhibited, and the quick and accurate tracking of the output position of the motor to the expected track is realized.

The technical conception of the invention is as follows: buffeting is inevitably generated in the traditional sliding mode control. Aiming at a permanent magnet synchronous motor position servo system with unknown friction torque and model uncertainty, an extended state observer is adopted to estimate a system state and uncertainty, a full-order sliding mode control method is designed based on the estimated value, a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on the extended state observer is designed, the buffeting problem in sliding mode control is restrained, and a designed full-order sliding mode controller can ensure that a tracking error e can be stably converged to a zero point. The invention provides a full-order sliding mode variable structure position servo control method which can improve the buffeting problem of sliding mode control and improve the system control precision, and the method can ensure that the output position of a motor can quickly and accurately track an expected track.

The invention has the advantages that: the method realizes the rapid and accurate tracking of the position of the permanent magnet synchronous motor, and effectively eliminates the buffeting problem in sliding mode control.

Drawings

FIG. 1 is a flow chart of a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer;

FIG. 2 is a block diagram of a permanent magnet synchronous motor position servo control system of the present invention;

FIG. 3 is a schematic diagram of the position tracking effect of the PMSM according to the present invention;

FIG. 4 is a schematic illustration of the tracking error of the system of the present invention;

FIG. 5 is a diagram of control signals according to the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

Referring to fig. 1 to 5, a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer includes the following steps:

step 1, establishing a permanent magnet synchronous motor system, and initializing a system state and related control parameters;

1.1, under a d/q rotating coordinate system, a voltage equation, a torque equation and a motion equation of the permanent magnet synchronous motor are respectively as follows:

T_e＝1.5p_nψ_fi_q(2)

wherein u is_d、u_qThe components of the stator voltage on the d and q axes respectively; i.e. i_d、i_qThe components of the stator current on the d axis and the q axis respectively; r is a stator resistor; l is_d、L_qThe components of the stator inductance on the d axis and the q axis are respectively; p is a radical of_nIs the number of pole pairs; omega is the angular speed of the rotor; j is moment of inertia; b is a friction coefficient; t is_eIs an electromagnetic torque; t is_LIs the load torque; psi_fThe permanent magnet is a permanent magnet fundamental wave excitation flux linkage;

1.2, the second order dynamic equation of the position ring of the permanent magnet synchronous motor can be obtained by the formulas (1) to (3)

Wherein, b is 1.5p_nψ_fD is disturbance composed of unknown friction torque and load torque, d ═ T_L+Bω)/J；

1.3, according to the design concept of the extended state observer, let x₁＝θ，x₂ω and defines an extended state x₃Where a (t), then equation (4) may be written as the following equivalent

y＝x₁＝θ(6)

Wherein, for a given q-axis current reference input, b₀Is an estimated value of b and is,u is a control input to the controller,y is the actual output position of the permanent magnet synchronous motor;

step 2, expanding the state observer design;

let z_iI is 1,2,3, and is the state variable x in formula (5)_iDefining an observation error of_i＝z_i-x_iThen, the expression of the nonlinear extended state observer designed in the present invention is:

wherein, β₁,β₂,β₃Are observer gains, β₁,β₂,β₃Fal (-) is a continuous power function with a linear segment near the origin, expressed as:

wherein, the interval length of the linear segment is expressed as >)0，0＜α_i＜1,i＝1,2,3，sign(₁) For symbolic functions, the expression is:

step 3, designing a full-order sliding mode controller based on the extended state observer;

3.1, define the tracking error as

e＝y-y_d＝x₁-y_d(9)

The first and second derivatives of e are respectively

And

3.2 designing the following full-step slip-form surface according to equations (9) - (11)

Wherein λ is₁And λ₂For controlling the parameter, λ₁＞0，λ₂＞0；

By substituting formulae (9) to (11) for formula (12)

The full-order sliding mode controller based on the extended state observer is designed by the formula (13)

u₂＝-ksgn(s) (17)

Wherein T is more than or equal to 0, and k is k_d+k_T+η，η，k_d，k_TAre all controller parameters, η > 0, k_d＞0，k_T＞0；

3.3 substitution of formulae (14) to (17) into formula (13), there are

s₂＝u₁+(x₃-z₃)+λ(x₂-z₂)+λ₁(x₁-z₁) ＝u1+d(x，z) (18)

Wherein d (x, z) ═ x₃-z₃)+λ₂(x₂-z₂)+λ₁(x₁-z₁) And d (x, z) is less than or equal to l_d，

l_d＝l₃+λ₂l₂+λ₁l₁；

Derived from formula (18)

3.4, designing a Lyapunov function:

V＝0.5s²(20)

substituting the formulas (5), (12), (14) to (17) into the formula (20) ifThe system is determined to be stable.

In order to verify the effectiveness of the method, the invention carries out simulation experiment on the control effect of the full-order sliding mode controlled on extended state observer (FSMC + ESO) based on the extended state observer represented by the formulas (14) to (17), and compares the control effect with the reduced-order sliding mode controlled on extended state observer (RSMC + ESO) based on the extended state observer. The design of partial parameters of the permanent magnet synchronous motor system, the extended state observer and the sliding mode controller adopted in the simulation is as follows: the parameters of the permanent magnet synchronous motor are set as follows: rated power P is 0.2kW, rated rotation speed omega is 3000r/min, permanent magnet magnetic linkage psi_f0.371Wb, number of pole pairs p_n4, d-q axis inductance L_d＝L_q30mH, and a moment of inertia J of 0.17kg cm²The viscous damping coefficient B is 0.001 N.m/(r/min), and the extended state observer parameter is set to β₁＝β₂＝β₃＝100，＝0.01，b₀10; the controller parameters are set to: k 20, λ₂＝2，λ₁＝5，T＝0.01。

FIG. 3 shows the load T_LThe sinusoidal tracking effect of the two control methods RSMC + ESO and FSMC + ESO were compared at 2 Nm. As can be seen from FIG. 3, the FSMC + ESO control method designed by the invention can realize the fast and effective tracking of the sinusoidal signal of the expected track by the output of the actual system. The FSMC + ESO method has higher tracking speed for tracking the sinusoidal signals than the RSMC + ESO method. It can be seen from FIG. 4 that the tracking error of the FSMC + ESO method after 2s tends to be in the stable range of [ -0.01,0.01 [ ]]And the RSMC + ESO tends to fall within the stable range after 3s with the tracking error of [ -0.005,0.005]The steady-state error of the sinusoidal tracking of the FSMC + ESO method is slightly larger than that of the RSMC + ESO method. It can be seen from fig. 5 that the buffeting of the control signals for the FSMC + ESO control method is significantly less than for the RSMC + ESO method. Viewed as a whole, in the baseUnder the action of a full-order sliding mode controller of the extended state observer, the buffeting problem in sliding mode control can be effectively eliminated, and the tracking error of the system can be stably converged to 0.

While the foregoing has described a preferred embodiment of the invention, it will be appreciated that the invention is not limited to the embodiment described, but is capable of numerous modifications without departing from the basic spirit and scope of the invention as set out in the appended claims. The proposed control scheme is effective for a permanent magnet synchronous motor position servo system with unknown friction torque and model uncertainty, and under the action of the proposed controller, the buffeting problem in sliding mode control is suppressed, and the actual motor output position can quickly and accurately track the expected track.

Claims (1)

1. A permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer is characterized by comprising the following steps: the method comprises the following steps:

step 1, establishing a permanent magnet synchronous motor system, and initializing a system state and control parameters;

1.1, under a d/q rotating coordinate system, a voltage equation, a torque equation and a motion equation of the permanent magnet synchronous motor are respectively as follows:

$\left\{\begin{array}{c}{u}_d={\mathrm{Ri}}_d-{\mathrm{\&omega;p}}_n{L}_q{i}_q+L_d\frac{{\mathrm{di}}_d}{dt}\\ u_q={\mathrm{Ri}}_q+{\mathrm{\&omega;p}}_n{L}_d{i}_d+{\mathrm{\&omega;p}}_n{\mathrm{\&psi;}}_f+L_q\frac{{\mathrm{di}}_q}{dt}\end{array}\right.---\left(1\right)$

T_e＝1.5p_nψ_fi_q(2)

$T_e-T_L=J\frac{d\mathrm{\&omega;}}{dt}+B\mathrm{\&omega;}---\left(3\right)$

wherein u is_d、u_qThe components of the stator voltage on the d and q axes respectively; i.e. i_d、i_qThe components of the stator current on the d axis and the q axis respectively; r is a stator resistor; l is_d、L_qThe components of the stator inductance on the d axis and the q axis are respectively; p is a radical of_nIs the number of pole pairs; omega is the angular speed of the rotor; j is moment of inertia; b is a friction coefficient; t is_eIs an electromagnetic torque; t is_LIs the load torque; psi_fThe permanent magnet is a permanent magnet fundamental wave excitation flux linkage;

1.2, obtaining a second-order dynamic equation of the position ring of the permanent magnet synchronous motor according to the formulas (1) to (3) as

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=\mathrm{\&omega;}\\ \stackrel{\&CenterDot;}{\mathrm{\&omega;}}={\mathrm{bi}}_q+d\end{array}\right.---\left(4\right)$

Wherein, b is 1.5p_nψ_fD is disturbance composed of unknown friction torque and load torque, d ═ T_L+Bω)/J；

1.3, according to the design idea of the extended state observer, the state variable x_iI is 1,2,3, let x₁＝θ，

x₂ω and defines an extended state x₃Where a (t), formula (4) is written as the equivalent

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=x_3+b_{0}u\\ {\stackrel{\&CenterDot;}{x}}_3=h\end{array}\right.---\left(5\right)$

y＝x₁In which (6) in the formula (I), for a given q-axis current reference input, b₀Is an estimated value of b and is,u is a control input to the controller,y is the actual output position of the permanent magnet synchronous motor;

step 2, expanding the state observer design;

let z_iI is 1,2,3, and is the state variable x in formula (5)_iDefining an observation error of_i＝z_i-x_iThen the nonlinear extended state observer expression is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_1{\mathrm{\&epsiv;}}_1\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_{2}fal({\mathrm{\&epsiv;}}_1,{\mathrm{\&alpha;}}_1,\mathrm{\&delta;})+b_{0}u\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_{3}fal({\mathrm{\&epsiv;}}_1,{\mathrm{\&alpha;}}_2,\mathrm{\&delta;})\end{array}\right.---\left(7\right)$

wherein, β₁,β₂,β₃Are observer gains, β₁,β₂,β₃> 0, fal (·) is a continuous power function with a linear segment near the origin, and the expression is:

$fal({\mathrm{\&epsiv;}}_1,{\mathrm{\&alpha;}}_i,\mathrm{\&delta;})=\left\{\begin{array}{cc}\frac{\mathrm{\&epsiv;}}{{\mathrm{\&delta;}}^{1-{\mathrm{\&alpha;}}_i}},& \left|{\mathrm{\&epsiv;}}_1\right|\&le;\mathrm{\&delta;}\\ \left|{\mathrm{\&epsiv;}}_1\right|sign\left({\mathrm{\&epsiv;}}_1\right),& \left|{\mathrm{\&epsiv;}}_1\right|>\mathrm{\&delta;}\end{array}\right.---\left(8\right)$

wherein, the interval length of the linear segment is more than 0, 0 < α_i＜1,i＝1,2,3，sign(₁) For symbolic functions, the expression is:

$sign\left({\mathrm{\&epsiv;}}_1\right)=\left\{\begin{array}{cc}1,& {\mathrm{\&epsiv;}}_1\&GreaterEqual;0\\ -1,& {\mathrm{\&epsiv;}}_1<0\end{array}\right.;$

step 3, designing a full-order sliding mode controller based on the extended state observer;

3.1, defining the tracking error e as

e＝y-y_d＝x₁-y_d(9)

Wherein y is_dIs a desired trajectory;

the first and second derivatives of the tracking error e are respectively

$\stackrel{\&CenterDot;}{e}=x_2-{\stackrel{\&CenterDot;}{y}}_d---\left(10\right)$

And

$\stackrel{\&CenterDot;\&CenterDot;}{e}={\stackrel{\&CenterDot;\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d=x_3+b_{0}u-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d---\left(11\right)$

3.2, according to the equations (9) to (11), designing the following full-order slip-form surface s:

$s=\stackrel{\&CenterDot;\&CenterDot;}{e}+{\mathrm{\&lambda;}}_2\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}_{1}e---\left(12\right)$

wherein λ is₁And λ₂For controlling the parameter, λ₁＞0，λ₂＞0；

By substituting formulae (9) to (11) for formula (12)

$\begin{array}{c}s=\stackrel{\&CenterDot;\&CenterDot;}{e}+{\mathrm{\&lambda;}}_2\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}_{1}e\\ ={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d+{\mathrm{\&lambda;}}_2(x_2-{\stackrel{\&CenterDot;}{y}}_d)+{\mathrm{\&lambda;}}_1(x_1-y_d)\\ =x_3+b_{0}u-{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d+{\mathrm{\&lambda;}}_2(x_2-{\stackrel{\&CenterDot;}{y}}_d)+{\mathrm{\&lambda;}}_1(x_1-y_d)\end{array}---\left(13\right)$

The full-order sliding mode controller based on the extended state observer is designed by the formula (13)

$u=\frac{1}{b_0}(u_0+u_1)---\left(14\right)$

$u_0=-z_3+{\stackrel{\&CenterDot;\&CenterDot;}{y}}_d-{\mathrm{\&lambda;}}_2(z_2-{\stackrel{\&CenterDot;}{y}}_d)-{\mathrm{\&lambda;}}_1(z_1-y_d)---\left(15\right)$

${\stackrel{\&CenterDot;}{u}}_1+{\mathrm{Tu}}_1=u_2---\left(16\right)$

u₂＝-ksign(s) (17)

Wherein T is more than or equal to 0, and k is k_d+k_T+η，η，k_d，k_TAre all controller parameters, η > 0, k_d＞0，k_T＞0；

3.3 substitution of formulae (14) to (17) into formula (13), there are

$\begin{array}{c}s=u_1+(x_3-z_3)+{\mathrm{\&lambda;}}_2(x_2-z_2)+{\mathrm{\&lambda;}}_1(x_1-z_1)\\ =u_1+d(x,z)\end{array}---\left(18\right)$

Wherein,d(x,z)＝(x₃-z₃)+λ₂(x₂-z₂)+λ₁(x₁-z₁) And d (x, z) is less than or equal to l_d，

l_d＝l₃+λ₂l₂+λ₁l₁；

Derived from formula (18)

$\stackrel{\&CenterDot;}{s}={\stackrel{\&CenterDot;}{u}}_1+\stackrel{\&CenterDot;}{d}(x,z)=\stackrel{\&CenterDot;}{d}(x,z)+u_2-{\mathrm{Tu}}_1---\left(19\right)$

3.4, designing a Lyapunov function:

V＝0.5s²(20)

substituting the formulas (5), (12), (14) to (17) into the formula (20) ifThe system is determined to be stable.