CN104682805A - Permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on extended state observer - Google Patents

Abstract

The invention provides a permanent magnet synchronous motor full-order sliding mode variable structure position servo control method based on an extended state observer. The permanent magnet synchronous motor full-order sliding mode variable structure position servo control method comprises the following steps of establishing a permanent magnet synchronous motor system, and initializing system state and related control parameters; designing the extended state observer; based on the extended state observer, designing a full-order sliding mode controller, eliminating the chattering problem in sliding mode control, and guaranteeing that the system state can be quickly and stably converged to be zero. According to the full-order sliding mode variable structure position servo control method provided by the invention, the chattering problem of sliding mode control can be improved, the control precision of the system is improved, and the implementation for quick and accurate tracking on desired trajectories of motor output position is guaranteed.

Description

Based on the permagnetic synchronous motor full-order sliding mode structure changes position servo control method of extended state observer

Technical field

The full-order sliding mode that the present invention relates to the equal unknown permagnetic synchronous motor system of a kind of permagnetic synchronous motor full-order sliding mode structure changes position servo control method, particularly components of system as directed state and the Nonlinear uncertainty upper bound controls control method.

Background technology

In permagnetic synchronous motor, due to the existence of the too high of ride gain and sign function in traditional control method, it is caused to there is certain buffeting problem.For in high-performance permanent magnet synchronous electric machine position servo system, how to weaken the chattering phenomenon in sliding formwork control, be a key technology difficult problem urgently to be resolved hurrily, have impact on accurate location and the position tracking performance of electric system, even can cause damage to electric system itself time serious.For solving the buffeting problem in sliding formwork control, alleviating in permagnetic synchronous motor the harmful effect of buffeting and bringing, improving the service behaviour of system, be necessary to adopt suitable control method, realize the quick accurate tracking of motor outgoing position to desired trajectory.

At present, eliminating in the research of buffeting, the sliding-mode control of various improvement is suggested, becomes sliding mode controller and adaptive sliding mode controller when coming CONTROLLER DESIGN, integration as replaced sign function with saturation function.In addition, it is also proposed in recent years and disturbance observer and extended state observer are controlled to combine with sliding formwork, for the speed regulating control of permagnetic synchronous motor with without buffeting sliding-mode control.This controller is a kind of full-order sliding mode controller, and compared with traditional depression of order sliding mode controller, advantage is that control signal is continuous print, can effectively avoid sliding formwork to control chattering phenomenon.The present invention is directed to the permanent magnetism synchronous electric machine position servo system with unknown moment of friction and model indeterminate, design the permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer, realize the quick accurate tracking of motor outgoing position to desired trajectory.

Summary of the invention

The deficiency of chattering phenomenon is controlled to exist in order to overcome sliding formwork in the permanent magnetism synchronous electric machine position servo system with unknown moment of friction and model indeterminate, the invention provides a kind of permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer, avoid sliding formwork to control chattering phenomenon better.Adopt extended state observer estimating system state and indeterminate, and based on estimated value design full-order sliding mode control method, the buffeting problem in suppressing sliding formwork to control, and realize the quick accurate tracking of motor outgoing position to desired trajectory.

In order to the technical scheme solving the problems of the technologies described above proposition is as follows:

Based on a permagnetic synchronous motor full-order sliding mode structure changes position servo control method for extended state observer, comprise the following steps:

Step 1, sets up permagnetic synchronous motor system, initialization system state and controling parameters;

1.1, under d/q rotating coordinate system, permagnetic synchronous motor voltage equation, torque equation and the equation of motion are respectively:

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

T _e＝1.5p _nψ _fi _q(2)

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

Wherein, u _d, u _qbe respectively the component of stator voltage on d, q axle; i _d, i _qbe respectively the component of stator current on d, q axle; R is stator resistance; L _d, L _qbe respectively the component of stator inductance on d, q axle; p _nfor number of pole-pairs; ω is rotor velocity; J is moment of inertia; B is coefficient of friction; T _efor electromagnetic torque; T _lfor load torque; ψ _ffor permanent magnet first-harmonic excitation flux linkage;

1.2, by formula (1)-(3), the second order dynamical equation obtaining permagnetic synchronous motor position ring is

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}=\mathrm{\ω}\\ \stackrel{\·}{\mathrm{\ω}}={\mathrm{bi}}_q+d\end{array}\right.---\left(4\right)$

Wherein, b=1.5p _nψ _f/ J, d are the disturbance of unknown moment of friction and loading moment composition, d=-(T _l+ B ω)/J;

1.3, according to the design philosophy of extended state observer, state variable x _i, i=1,2,3, make x ₁=θ,

X ₂=ω, and define extended mode x ₃=a (t), then formula (4) is written as following equivalents

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

y＝x ₁＝θ (6)

Wherein, for given q shaft current reference input, b ₀for the estimated value of b, u is control inputs, y is the actual outgoing position of permagnetic synchronous motor;

Step 2, extended state observer designs;

Make z _i, i=1,2,3, be respectively state variable x in formula (5) _imeasured value, definition observation error is ε _i=z _i-x _i, then nonlinear extension state observer expression formula is:

$\left\{\begin{array}{c}{\stackrel{\·}{z}}_1=z_2-{\mathrm{\β}}_1{\mathrm{\ϵ}}_1\\ {\stackrel{\·}{z}}_2=z_3-{\mathrm{\β}}_2\mathrm{fal}({\mathrm{\ϵ}}_1,{\mathrm{\α}}_1,\mathrm{\δ})+b_{0}u\\ {\stackrel{\·}{z}}_3=-{\mathrm{\β}}_3\mathrm{fal}({\mathrm{\ϵ}}_1,{\mathrm{\α}}_2,\mathrm{\δ})\end{array}\right.---\left(7\right)$

Wherein, β ₁, β ₂, β ₃be observer gain, β ₁, β ₂, β ₃> 0.fal () is for having the continuous power function of linearity range near initial point, expression formula is:

$\mathrm{fal}({\mathrm{\ϵ}}_1,{\mathrm{\α}}_i,\mathrm{\δ})=\left\{\begin{array}{cc}\frac{{\mathrm{\ϵ}}_1}{{\mathrm{\δ}}^{1-{\mathrm{\α}}_i}},& \left|{\mathrm{\ϵ}}_1\right|\≤\mathrm{\δ}\\ \left|{\mathrm{\ϵ}}_1\right|\mathrm{sign}\left({\mathrm{\ϵ}}_1\right),& \left|{\mathrm{\ϵ}}_1\right|>\mathrm{\δ}\end{array}\right.---\left(8\right)$

Wherein, δ represents the siding-to-siding block length of linearity range, δ > 0,0 < α _i< 1, i=1,2,3, sign (ε ₁) be sign function, expression formula is:

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

Step 3, based on the full-order sliding mode Controller gain variations of extended state observer;

3.1, definition tracking error e is

e＝y-y _d＝x ₁-y _d(9)

Wherein y _dfor desired trajectory;

Then the single order of tracking error e and second dervative are respectively

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

With

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

3.2, according to formula (9)-(11), design following full-order sliding mode face s:

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

Wherein, λ ₁and λ ₂for controling parameters, λ ₁> 0, λ ₂> 0;

Formula (9)-(11) are substituted into formula (12) obtain

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

By formula (13), the full-order sliding mode Controller gain variations based on extended state observer is

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

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

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

u ₂＝-k sgn(s) (17)

Wherein, T>=0, k=k _d+ k _t+ η, η, k _d, k _tbe controller parameter, η > 0, k _d> 0, k _t> 0;

3.3, formula (14)-(17) are substituted in formula (13), has

s ₂＝u ₁+(x ₃-z ₃)+λ ₂(x ₂-z ₂)+λ ₁(x ₁-z ₁) ＝u1+d(x，z) (18)

Wherein, d (x, z)=(x ₃-z ₃)+λ ₂(x ₂-z ₂)+λ ₁(x ₁-z ₁), and meet d (x, z)≤l _d,

l _d＝l ₃+λ ₂l ₂+λ ₁l ₁；

Formula (18) differentiate is obtained

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

3.4, design liapunov function:

V＝0.5s ²(20)

By formula (5), (12), (14)-(17) are updated to formula (20), if decision-making system is stable.

The present invention is in conjunction with extended state observer technology and full-order sliding mode control technology, design a kind of permagnetic synchronous motor full-order sliding mode structure changes Position Servo based on extended state observer, buffeting problem in suppressing sliding formwork to control, and realize the quick accurate tracking of motor outgoing position to desired trajectory.

Technical conceive of the present invention is: traditional sliding formwork unavoidably there will be buffeting problem in controlling.For in the permanent magnetism synchronous electric machine position servo system with unknown moment of friction and model indeterminate, adopt extended state observer estimating system state and indeterminate, and control control method based on estimated value design full-order sliding mode, design a kind of permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer, buffeting problem in suppressing sliding formwork to control, the full-order sliding mode controller of design can ensure tracking error e by stable convergence to zero point.The invention provides a kind of sliding formwork that can improve and control buffeting problem and the full-order sliding mode structure changes position servo control method improving Systematical control precision, guarantee to realize the quick accurate tracking of motor outgoing position to desired trajectory.

Advantage of the present invention is: the quick accurate tracking realizing permagnetic synchronous motor position, effectively eliminates the buffeting problem in sliding formwork control.

Accompanying drawing explanation

Fig. 1 is the flow chart of the permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer;

Fig. 2 is permanent magnetism synchronous electric machine position servo control system block diagram of the present invention;

Fig. 3 is the schematic diagram of permagnetic synchronous motor position of the present invention tracking effect;

Fig. 4 is the schematic diagram of the tracking error of system of the present invention;

Fig. 5 is the schematic diagram of control signal of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

With reference to Fig. 1-Fig. 5, a kind of permagnetic synchronous motor full-order sliding mode structure changes position servo control method based on extended state observer, comprises the following steps:

Step 1, sets up permagnetic synchronous motor system, initialization system state and associated control parameters;

1.1, under d/q rotating coordinate system, permagnetic synchronous motor voltage equation, torque equation and the equation of motion are respectively:

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

T _e＝1.5p _nψ _fi _q(2)

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

Wherein, u _d, u _qbe respectively the component of stator voltage on d, q axle; i _d, i _qbe respectively the component of stator current on d, q axle; R is stator resistance; L _d, L _qbe respectively the component of stator inductance on d, q axle; p _nfor number of pole-pairs; ω is rotor velocity; J is moment of inertia; B is coefficient of friction; T _efor electromagnetic torque; T _lfor load torque; ψ _ffor permanent magnet first-harmonic excitation flux linkage;

1.2, by formula (1)-(3), the second order dynamical equation that can obtain permagnetic synchronous motor position ring is

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

Wherein, b=1.5p _nψ _f/ J, d are the disturbance of unknown moment of friction and loading moment composition, d=-(T _l+ B ω)/J;

1.3, according to the design philosophy of extended state observer, make x ₁=θ, x ₂=ω, and define extended mode x ₃=a (t), then formula (4) can be written as following equivalents

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

y＝x ₁＝θ(6)

Wherein, for given q shaft current reference input, b ₀for the estimated value of b, u is control inputs, y is the actual outgoing position of permagnetic synchronous motor;

Step 2, extended state observer designs;

Make z _i, i=1,2,3, be respectively state variable x in formula (5) _imeasured value, definition observation error is ε _i=z _i-x _i, then the nonlinear extension state observer expression formula designed in the present invention is:

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

Wherein, β ₁, β ₂, β ₃be observer gain, β ₁, β ₂, β ₃> 0.fal () is for having the continuous power function of linearity range near initial point, expression formula is:

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

Wherein, δ represents the siding-to-siding block length of linearity range, δ > 0,0 < α _i< 1, i=1,2,3, sign (ε ₁) be sign function, expression formula is:

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

Step 3, based on the full-order sliding mode Controller gain variations of extended state observer;

3.1, definition tracking error is

e＝y-y _d＝x ₁-y _d(9)

Then the single order of e and second dervative are respectively

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

With

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

3.2, according to formula (9)-(11), design following full-order sliding mode face

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

Wherein, λ ₁and λ ₂for controling parameters, λ ₁> 0, λ ₂> 0;

Formula (9)-(11) are substituted into formula (12) obtain

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

By formula (13), the full-order sliding mode Controller gain variations based on extended state observer is

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

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

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

u ₂＝-ksgn(s) (17)

Wherein, T>=0, k=k _d+ k _t+ η, η, k _d, k _tbe controller parameter, η > 0, k _d> 0, k _t> 0;

3.3, formula (14)-(17) are substituted in formula (13), has

s ₂＝u ₁+(x ₃-z ₃)+λ(x ₂-z ₂)+λ ₁(x ₁-z ₁) ＝u1+d(x，z) (18)

Wherein, d (x, z)=(x ₃-z ₃)+λ ₂(x ₂-z ₂)+λ ₁(x ₁-z ₁), and meet d (x, z)≤l _d,

l _d＝l ₃+λ ₂l ₂+λ ₁l ₁；

Formula (18) differentiate is obtained

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

3.4, design liapunov function:

V＝0.5s ²(20)

By formula (5), (12), (14)-(17) are updated to formula (20), if decision-making system is stable.

For the validity of checking institute extracting method, the present invention is to the full-order sliding mode controller based on extended state observer represented by formula (14)-(17) (full-order sliding mode control based on extended state observer, FSMC+ESO) control effects carries out emulation experiment, and contrast with depression of order sliding mode controller (reduced-order sliding mode control based on extended state observer, the RSMC+ESO) effect based on extended state observer.The partial parameters design of the permagnetic synchronous motor system, extended state observer and the sliding mode controller that adopt in emulation is as follows: permagnetic synchronous motor optimum configurations is: rated power P=0.2kW, rated speed ω=3000r/min, permanent magnet flux linkage ψ _f=0.371Wb, number of pole-pairs p _n=4, d-q axle inductance L _d=L _q=30mH, moment of inertia J=0.17kgcm ², viscous damping coefficient B=0.001Nm/ (r/min); Extended state observer optimum configurations is: β ₁=β ₂=β ₃=100, δ=0.01, b ₀=10; Controller parameter is set to respectively: k=20, λ ₂=2, λ ₁=5, T=0.01.

Fig. 3 gives as load T _l=2Nm, adopts the sine curve tracking effect contrast of RSMC+ESO and FSMC+ESO two kinds of control methods.As can be seen from Figure 3, the FSMC+ESO control method of the present invention's design can realize real system and export effectively following the tracks of fast desired trajectory sinusoidal signal.FSMC+ESO method is adopted to have tracking velocity faster than RSMC+ESO method to tracking sinusoidal signal.FSMC+ESO method tracking error after 2s just tends towards stability scope [-0.01 as can be seen from Figure 4,0.01], the scope [-0.005 and RSMC+ESO tracking error after 3s just tends towards stability, 0.005], the steady-state error of the sine curve tracking of FSMC+ESO method is slightly larger than RSMC+ESO method.The buffeting of the control signal of FSMC+ESO control method is significantly less than RSMC+ESO method as can be seen from Figure 5.On the whole, under the effect of the full-order sliding mode controller device based on extended state observer, not only effectively can eliminate the buffeting problem in sliding formwork control, and the tracking error of system can stable convergence to 0.

What more than set forth is the excellent effect of optimization that an embodiment that the present invention provides shows, obvious the present invention is not just limited to above-described embodiment, do not depart from essence spirit of the present invention and do not exceed scope involved by flesh and blood of the present invention prerequisite under can do all distortion to it and implemented.The control program proposed is effective to the permanent magnetism synchronous electric machine position servo system with unknown moment of friction and model indeterminate, under the effect of proposed controller, buffeting problem in suppressing sliding formwork to control, real electrical machinery outgoing position can quick accurate tracking desired trajectory.

Claims (1)

1., based on a permagnetic synchronous motor full-order sliding mode structure changes position servo control method for extended state observer, it is characterized in that: comprise the following steps:

Step 1, sets up permagnetic synchronous motor system, initialization system state and controling parameters;

1.1, under d/q rotating coordinate system, permagnetic synchronous motor voltage equation, torque equation and the equation of motion are respectively:

T _e＝1.5p _nψ _fi _q(2)

Wherein, u _d, u _qbe respectively the component of stator voltage on d, q axle; i _d, i _qbe respectively the component of stator current on d, q axle; R is stator resistance; L _d, L _qbe respectively the component of stator inductance on d, q axle; p _nfor number of pole-pairs; ω is rotor velocity; J is moment of inertia; B is coefficient of friction; T _efor electromagnetic torque; T _lfor load torque; ψ _ffor permanent magnet first-harmonic excitation flux linkage;

1.2, by formula (1)-(3), the second order dynamical equation obtaining permagnetic synchronous motor position ring is

Wherein, b=1.5p _nψ _f/ J, d are the disturbance of unknown moment of friction and loading moment composition, d=-(T _l+ B ω)/J;

1.3, according to the design philosophy of extended state observer, state variable x _i, i=1,2,3, make x ₁=θ, x ₂=ω, and define extended mode x ₃=a (t), then formula (4) is written as following equivalents

y＝x ₁＝θ (6)

Wherein, for given q shaft current reference input, b ₀for the estimated value of b, u is control inputs, y is the actual outgoing position of permagnetic synchronous motor;

Step 2, extended state observer designs;

Make z _i, i=1,2,3, be respectively state variable x in formula (5) _imeasured value, definition observation error is ε _i=z _i-x _i, then nonlinear extension state observer expression formula is:

Wherein, β ₁, β ₂, β ₃be observer gain, β ₁, β ₂, β ₃> 0.fal () is for having the continuous power function of linearity range near initial point, expression formula is:

Wherein, δ represents the siding-to-siding block length of linearity range, δ > 0,0 < α _i< 1, i=1,2,3, sign (ε ₁) be sign function, expression formula is:

Step 3, based on the full-order sliding mode Controller gain variations of extended state observer;

3.1, definition tracking error e is

e＝y-y _d＝x ₁-y _d(9)

Wherein y _dfor desired trajectory;

Then the single order of tracking error e and second dervative are respectively

With

3.2, according to formula (9)-(11), design following full-order sliding mode face s:

Wherein, λ ₁and λ ₂for controling parameters, λ ₁> 0, λ ₂> 0;

Formula (9)-(11) are substituted into formula (12) obtain

By formula (13), the full-order sliding mode Controller gain variations based on extended state observer is

u ₂＝-ksgn(s) (17)

Wherein, T>=0, k=k _d+ k _t+ η, η, k _d, k _tbe controller parameter, η > 0, k _d> 0, k _t> 0;

3.3, formula (14)-(17) are substituted in formula (13), has

s ₂＝u ₁+(x ₃-z ₃)+λ ₂(x ₂-z ₂)+λ ₁(x ₁-z ₁)

＝u ₁+d(x,z) (18)

Wherein, d (x, z)=(x ₃-z ₃)+λ ₂(x ₂-z ₂)+λ ₁(x ₁-z ₁), and meet d (x, z)≤l _d,

l _d＝l ₃+λ ₂l ₂+λ ₁l ₁；

Formula (18) differentiate is obtained

3.4, design liapunov function:

V＝0.5s ²(20)

By formula (5), (12), (14)-(17) are updated to formula (20), if decision-making system is stable.