CN108964545A - A kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering - Google Patents

Abstract

The synchronous motor neural network contragradience Discrete Control Method based on command filtering that the invention discloses a kind of, it is more for permasyn morot variable, coupling is strong, and the problem of being highly susceptible to external loading and the variation influence of motor relevant parameter, a kind of neural network adaptive controller is devised based on command filtering technology and Backstepping principle, nerual network technique is for approaching unknown nonlinear terms, adaptive Backstepping is used for the design of controller, and command filtering technology is for solving the problems, such as " calculating explosion ".Part of the present invention supplemented with the complete controller design lacked in conventional method increases Liapunov stability analysis；After being controlled to adjust by controller, motor running can be rapidly achieved stable state, it is more suitable for needing the control object of fast dynamic response, simulation result shows that this new controller overcomes the influence of parameter inaccuracy and ensure that ideal control effect, realizes the quickly and stably tracking to position.

Description

A kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering

Technical field

The invention belongs to permasyn morot Position Tracking Control technical fields, more particularly to one kind to be based on command filtering Synchronous motor neural network contragradience Discrete Control Method.

Background technique

In recent years, with power electronic technique, microelectric technique, novel motor control theory and rare earth permanent-magnetic material Fast development, permasyn morot are rapidly promoted and applied.Compared with traditional electrically excited synchronous motor, permanent magnetism is same Walk motor, especially rare-earth permanent-magnet synchronous motor have loss less, high-efficient, power savings clear advantage.

Permasyn morot provides excitation with permanent magnet, keeps electric motor structure relatively simple, reduces processing and assembly Expense, and the collector ring and brush to easily go wrong is eliminated, improve the reliability of motor running；Again because without excitation electricity Stream improves the efficiency and power density of motor without excitation loss, thus it be studied in recent years it is more and in each neck A kind of more and more extensive motor is applied in domain, therefore it is studied and is just very necessary.

However since synchronous motor mathematical model has the characteristics that non-linear, close coupling, multivariable, while vulnerable to electronic Therefore the influence of the uncertain factors such as machine Parameters variation and external loading disturbance will realize the high performance control of synchronous motor It is a challenging project.Since the eighties, control technology especially control theory strategy development is very swift and violent, Some advanced control strategy methods (such as sliding formwork control, variable-structure control, fuzzy control, Backstepping, Multimode Control) just quilt It attempts to be introduced into permasyn morot controller, this sends out for promotion high-performance to intelligence, flexibility, totally digitilized direction Exhibition opens new road.However, these above-mentioned control technologies and method have mostly been frequently used in permasyn morot Continuous model controller design process in, and the research of its discrete model is seldom related to.

It is compared due to the extensive use of computer control system, and with continuous control method, discrete control method In the stabilization that ensures system and can realize that aspect is more superior so that the modeling of discrete system, analysis, design theoretical research in In more and more important position.Backstepping biggest advantage is can to simplify original high order system with virtual controlling variable, To which final output result can be automatically derived by suitable Lyapunov Equation.

Complicated nonlinear system is resolved into the subsystem of multiple simple low orders by adaptive backstepping control method, by drawing Enter virtual controlling variable gradually to carry out controller design, finally determine control law and adaptive law, to realize to system Effective control.However, carrying out continuous derivation to virtual master function in traditional Reverse Step Control, easily causes and " calculate quick-fried It is fried " problem.Command filtering technology is introduced during controller design can be with effective solution " calculating explosion " problem.

In addition, ability of the nerual network technique in terms of handling unknown nonlinear function causes the wide of the circle of control both at home and abroad General concern, and for having in nonlinearity and probabilistic Complex control system design.

Summary of the invention

It is an object of the invention to propose a kind of discrete controlling party of synchronous motor neural network contragradience based on command filtering Method, by nerual network technique come the unknown nonlinear terms of approximation system, command filtering technology is used to solve " calculating explosion " The problem of, controller is constructed using Backstepping, to realize the tracing control to synchronous motor position.

The present invention to achieve the goals above, adopts the following technical scheme that

A kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering, includes the following steps:

A. the dynamic model of permasyn morot is established

Under synchronous rotary d-q coordinate, the dynamic model expression of permasyn morot are as follows:

Wherein, Θ is permanent-magnet synchronous motor rotor angle position, ω is permanent-magnet synchronous motor rotor angular speed, J is Rotary inertia, T_LIt is magnetic linkage, the n that permanent magnet generates for load torque, Φ_pFor number of magnetic pole pairs, i_qFor q axis stator current, i_dFor d Axis stator current, u_qFor permasyn morot q axis stator voltage, u_dFor permasyn morot d axis stator voltage, L_dAnd L_q For stator inductance, the R under d-q coordinate system_sIt is coefficient of friction for permasyn morot stator equivalent resistance, B；

For the dynamic model for simplifying permasyn morot, it is defined as follows variable:

Then the discrete dynam ic m odeX of permasyn morot indicates are as follows:

Wherein, x₁(k+1) rotor angular position of kth+1 time sampling is indicated；

x₂(k+1) rotor velocity of kth+1 time sampling is indicated；

x₃(k+1) the q axis stator current of kth+1 time sampling is indicated；

x₄(k+1) it is expressed as the d axis stator current of kth+1 time sampling；Δ_tIndicate the sampling period；

B. according to Backstepping principle, a kind of discrete controlling party of synchronous motor neural network contragradience based on command filtering is designed Method, above-mentioned discrete dynam ic m odeX is simplified to two independent subsystems, i.e., by state variable x₁(k),x₂(k) and control inputs u_q (k) form subsystem and by state variable x₄(k) and control inputs u_d(k) subsystem formed；Wherein:

First subsystem are as follows:

Second subsystem are as follows: x₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Use RBF neural Approximation of Continuous Functions f (Z (k)) below: Rⁿ→R；F (Z (k))=W^TS(Z(k))；

Wherein,It is input vector, q is neural network input dimension, R^qFor real vector collection；

W=[W₁,...,W_l]^T∈R^lIt is weight vectors, neural network node number l is positive integer, and l > 1, R^lFor real number to Quantity set；

RⁿRefer to that n Wei Shishuoxiangliangji, R refer to set of real numbers；Wherein, W₁,...,W_lIt is the weight of weight vectors；

S (Z (k))=[s₁(Z(k)),...,s_l(Z(k))]^T∈R^lFor basis function vector, wherein s_i(Z (k)) is used as height This function, form are as follows:

Wherein, μ_i=[μ_i1,...,μ_iq]^TIt is the center of acceptance region, and η_iIt is then the width of Gaussian function；

And when neural network node number l is sufficiently large, RBF neural, which is approached, compactsOn arbitrary continuation function f (Z (k)) arrives arbitrary accuracy ε > 0；

Definition command filter are as follows:

Wherein, ζ, ω_nFor command filtering device parameter；

x_jc(k) and x_jc(k+1) kth time of j-th of command filtering device and the output signal of kth+1 time sampling are indicated；

z_j,1(k),z_j,2It (k) is the output signal of the kth of command filtering device time sampling；

z_j,1(k+1),z_j,2It (k+1) is the output signal of kth+1 time sampling of command filtering device；

α_jIt (k) is the input signal of the kth of j-th of command filtering device time sampling；

If input signal α_j(k) for all constant k >=0, so that | α_j(k+1)-α_j(k)|≤ρ₁And | α_j(k+ 2)-2α_j(k+1)+α_j(k)|≤ρ₂It sets up, then can obtain, to arbitrary constant, τ_j> 0, there are ω_n> 0 and ζ ∈ (0,1] so that |z_j,1(k)-α_j(k)|≤τ_j, Δ z_j,1(k)=| z_j,1(k+1)-z_j,1(k) | it is bounded；

Wherein, ρ₁And ρ₂It is normal number, α_j(k+1) the input letter of kth+1 time sampling of j-th of command filtering device is indicated Number, α_j(k+2) input signal of kth+2 times samplings of j-th of command filtering device is indicated；Z simultaneously_j,1(0)=α_j(0), z_j,2(0) =0 is the initial value of command filtering device, α_j(0) original input signal of command filtering device is indicated；

It is as follows to define systematic error variable:

Wherein, x_dIt (k) is desired position signal, x_1c(k)、x_2cIt (k) is the output signal of command filtering device；

It c.1. is to ensure x₁(k) desired position signal x can effectively be tracked_d(k), Liapunov control function is chosen such as Under:

According to the 1st EQUATION x in discrete dynam ic m odeX formula (3)₁(k+1)=x₁(k)+Δ_tx₂(k) error can be acquired Variable are as follows:

e₁(k+1)=x₁(k+1)-x_d(k+1)=x₁(k)+Δ_tx₂(k)-x_d(k+1)；

Ask difference that can obtain formula (5):

By x₂(k) it is considered as the control input of first subsystem, x_dIt (k+1) is the desired locations signal of kth+1 time sampling, If error variance e₂(k)=x₂(k)-x_1c(k), virtual master function is constructedThen obtain:

C.2. according to the 2nd equation in discrete dynam ic m odeX formula (3):

x₂(k+1)=a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L, error variance can be acquired:

e₂(k+1)=a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L-x_1c(k+1)；

Select liapunov function:Then to V₂(k) ask difference that can obtain:

The load torque T in permasyn morot real work_LThere are upper limit d, therefore | T_L|≤d, d are normal number；

Construct virtual master function:

If error variance e₃(k)=x₃(k)-x_2c(k), then Δ V₂(k) it indicates are as follows:

It is obtained by Young inequality:

Therefore, bringing formula (11) into formula (10) can obtain:

C.3. by the 3rd equation of discrete dynam ic m odeX formula (3):

x₃(k+1)=(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)+b₄Δ_tu_q(k), error change can be acquired Amount:

Choose liapunov functionTo V₃(k) ask difference that can obtain:

Wherein, f₃(k)=(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)-x_2c(k+1)；

By RBF neural approximation theory it is found that for arbitrarily small positive number ε₃, there is always a nerve network systemsSo that

Wherein δ₃Indicate approximate error, and meet inequality | δ₃|≤ε₃, | | W₃| | it is vector W₃Norm, thus:

Wherein, S₃(Z₃It (k)) is basis function vector, Z₃(k)=[x₂(k),x₃(k),x₄(k),x_2c(k+1)]^T；

Choose the u in control input_qIt (k) is practical control law and adaptive lawAre as follows:

Wherein, γ₃, λ₃For normal number,For η₃Estimated value, definition | | W₃| |=η₃And η₃> 0, defined variable η₃ Evaluated error beFormula (7), (12), (15) are substituted into formula (14) and obtained:

C.4. remember systematic error variable e₄(k)=x₄(k), liapunov function is chosenP It is a normal number；By the 4th expression formula of discrete dynam ic m odeX formula (3):

x₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k), error variance can be acquired:

e₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Seek V₄(k) difference can obtain:

Wherein, f₄(k)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k), by RBF neural approximation theory it is found that right In arbitrarily small positive number ε₄, there is always a nerve network systemsSo that Wherein, δ₄Indicate approximate error, and meet inequality | δ₄|≤ε₄, wherein | | W₄| | it is vector W₄Norm, thus:

Wherein, S₄(Z₄It (k)) is basis function vector, Z₄(k)=[x₂(k),x₃(k),x₄(k)]^T；

Choose the u in control input_dIt (k) is practical control law and adaptive lawAre as follows:

Wherein, γ₄, λ₄For normal number,For η₄Estimated value, definition | | W₄| |=η₄, and η₄> 0, defined variable η₄ Evaluated error beFormula (19), which are substituted into formula (18), to be obtained:

D. stability analysis is carried out to the permasyn morot neural network Backstepping Controller of foundation

It chooses Li Ya and composes promise husband function are as follows:

Ask difference that can obtain V (k):

According to above-mentioned formulaWithWhen kth+1 time of progress evaluated error Formula can be obtained when samplingAnd adaptive lawM=3,4, and have:

By Young inequality and | | S_m(Z_m(k))||²< l_m, m=3,4, l_mThe number of nodes for indicating nerve network system, can :

DefinitionM is any positive number, because | x_jc(k)-α_j(k)|≤τ_j, j=1,2, according to formula (20), and Formula (22) to formula (26), which is substituted into formula (21), to be obtained:

Wherein, l₃, l₄Respectively indicate nerve network systemWithNumber of nodes；

Wherein,

τ₁,τ₂It is the constant greater than zero；

Select suitable parameter P and sampling period Δ_t, make its satisfaction If selection parameter meetsM=3,4, then only It wantsWithIt sets up, then can obtain Δ V (k)≤0；

It is further known that for arbitrarily small positive number σ,It sets up.

The present invention has the advantage that

(1) the present invention is directed discrete-time system, with higher compared to the control method of continuous time system Stability and realizability.

(2) present invention approaches the nonlinear terms of output voltage using the adaptive Backstepping of neural network, and building is same The adaptive Backstepping Controller of neural network for walking motor, efficiently solves the problems, such as nonlinear Control present in system, and And the controller simple structure is easy, realizes convenient, design rationally, has stronger anti-disturbance ability.

(3) present invention uses command filtering technology, efficiently avoids " calculating explosion " problem in traditional Backstepping；Together The controller of the adaptive Backstepping technical construction of Shi Yingyong neural network can enable tracking error converge to one of origin In sufficiently small neighborhood, reach more accurate control precision；

The adaptive contragradience algorithm of neural network itself can be realized by software programming, and can be saved to motor The setting of parameter is easy to directly control permasyn morot, reduces cost, safe and reliable, has wide application Prospect.

(4) present invention does not need the difference according to permasyn morot and modifies the parameter of controller, can be in principle It realizes the stability contorting to the synchronous motor of all models and power, reduces in control process to synchronous motor parameter Measurement, conducive to the quick response for realizing permanent-magnet synchronous motor rotor rotational speed regulation.

Detailed description of the invention

Fig. 1 is in the present invention by permasyn morot neural network Backstepping Controller, coordinate transform and SVPWM inverter The schematic diagram of the composite controlled object of composition；

Rotor angle after permasyn morot neural network Backstepping Controller control in Fig. 2 present invention based on command filtering The tracking analogous diagram of position and rotor angle location setting value；

Fig. 3 is rotor after the permasyn morot neural network Backstepping Controller in the present invention based on command filtering controls The tracking error analogous diagram of Angle Position and rotor angle location setting value；

Fig. 4 is permanent magnetism after the permasyn morot neural network Backstepping Controller in the present invention based on command filtering controls Synchronous motor d axis stator voltage analogous diagram；

Fig. 5 is permanent magnetism after the permasyn morot neural network Backstepping Controller in the present invention based on command filtering controls Synchronous motor q axis stator voltage analogous diagram.

Specific embodiment

With reference to the accompanying drawing and specific embodiment invention is further described in detail:

As shown in connection with fig. 1, a kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering, uses Component include permasyn morot neural network contragradience discrete controller 1, coordinate transformation unit 2,3 and of SVPWM inverter Rotation speed detection unit 4 and current detecting unit 5.Rotation speed detection unit 4 and current detecting unit 5 are mainly for detection of permanent-magnet synchronous The current value and revolving speed correlated variables of motor, it is same by permanent magnetism by the electric current and speed variable of actual measurement as input It walks electronic machine neural network contragradience discrete controller 1 and carries out voltage control, be ultimately converted to three-phase electric control synchronous motor Revolving speed, in order to design a significantly more efficient controller, it is very necessary for establishing permasyn morot dynamic model.

In Fig. 1, ω_γ(k) refer to rotor velocity, U_α(k),U_β(k) refer to and obtained after the transformation of α β o coordinate system The voltage arrived, U, V, W refer to three-phase alternating voltage.

A kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering, includes the following steps:

A. the dynamic model of permasyn morot is established

Under synchronous rotary d-q coordinate, the dynamic model expression of permasyn morot are as follows:

Wherein, Θ is permanent-magnet synchronous motor rotor angle position, ω is permanent-magnet synchronous motor rotor angular speed, J is Rotary inertia, T_LIt is magnetic linkage, the n that permanent magnet generates for load torque, Φ_pFor number of magnetic pole pairs, i_qFor q axis stator current, i_dFor d Axis stator current, u_qFor permasyn morot q axis stator voltage, u_dFor permasyn morot d axis stator voltage, L_dAnd L_q For stator inductance, the R under d-q coordinate system_sIt is coefficient of friction for permasyn morot stator equivalent resistance, B.

For the dynamic model for simplifying permasyn morot, it is defined as follows variable:

Then the discrete dynam ic m odeX of permasyn morot indicates are as follows:

Wherein, x₁(k+1) rotor angular position of kth+1 time sampling is indicated.

x₂(k+1) rotor velocity of kth+1 time sampling is indicated.

x₃(k+1) the q axis stator current of kth+1 time sampling is indicated.

x₄(k+1) it is expressed as the d axis stator current of kth+1 time sampling；Δ_tIndicate the sampling period.

B. according to Backstepping principle, a kind of discrete controlling party of synchronous motor neural network contragradience based on command filtering is designed Method, above-mentioned discrete dynam ic m odeX is simplified to two independent subsystems, i.e., by state variable x₁(k),x₂(k) and control inputs u_q (k) form subsystem and by state variable x₄(k) and control inputs u_d(k) subsystem formed.Wherein:

First subsystem are as follows:

Second subsystem are as follows: x₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)。

Use RBF neural Approximation of Continuous Functions f (Z (k)) below: Rⁿ→R；F (Z (k))=W^TS(Z(k))。

Wherein,It is input vector, q is neural network input dimension, R^qFor real vector collection.

W=[W₁,...,W_l]^T∈R^lIt is weight vectors, neural network node number l is positive integer, and l > 1, R^lFor real number to Quantity set.

RⁿRefer to that n Wei Shishuoxiangliangji, R refer to set of real numbers；Wherein, W₁,...,W_lRefer to the weight of weight vectors W.

S (Z (k))=[s₁(Z(k)),...,s_l(Z(k))]^T∈R^lFor basis function vector, wherein s_i(Z (k)) is used as height This function, form are as follows:

Wherein, μ_i=[μ_i1,...,μ_iq]^TIt is the center of acceptance region, and η_iIt is then the width of Gaussian function.

And when neural network node number l is sufficiently large, RBF neural, which is approached, compactsOn arbitrary continuation function f (Z (k)) arrives arbitrary accuracy ε > 0.

Definition command filter are as follows:

Wherein, ζ, ω_nFor command filtering device parameter.

z_j,1(k)=x_jc(k),J=1,2.

x_jc(k) and x_jc(k+1) kth time of j-th of command filtering device and the output signal of kth+1 time sampling are indicated.

z_j,1(k),z_j,2It (k) is the output signal of the kth of command filtering device time sampling.

z_j,1(k+1),z_j,2It (k+1) is the output signal of kth+1 time sampling of command filtering device.

α_jIt (k) is the input signal of the kth of j-th of command filtering device time sampling.

If input signal α_j(k) for all constant k >=0, so that | α_j(k+1)-α_j(k)|≤ρ₁And | α_j(k+ 2)-2α_j(k+1)+α_j(k)|≤ρ₂It sets up, then can obtain, to arbitrary constant, τ_j> 0, there are ω_n> 0 and ζ ∈ (0,1] so that |z_j,1(k)-α_j(k)|≤τ_j, Δ z_j,1(k)=| z_j,1(k+1)-z_j,1(k) | it is bounded.

Wherein, ρ₁And ρ₂It is normal number, α_j(k+1) the input letter of kth+1 time sampling of j-th of command filtering device is indicated Number, α_j(k+2) input signal of kth+2 times samplings of j-th of command filtering device is indicated；Z simultaneously_j,1(0)=α_j(0), z_j,2(0) =0 is the initial value of command filtering device, α_j(0) original input signal of command filtering device is indicated.

It is as follows to define systematic error variable:

Wherein, x_dIt (k) is desired position signal, x_1c(k)、x_2cIt (k) is the output signal of command filtering device.

It c.1. is to ensure x₁(k) desired position signal x can effectively be tracked_d(k), Liapunov control function is chosen such as Under:

According to the 1st EQUATION x in discrete dynam ic m odeX formula (3)₁(k+1)=x₁(k)+Δ_tx₂(k) error can be acquired Variable are as follows:

e₁(k+1)=x₁(k+1)-x_d(k+1)=x₁(k)+Δ_tx₂(k)-x_d(k+1)。

Ask difference that can obtain formula (5):

By x₂(k) it is considered as the control input of first subsystem, x_dIt (k+1) is the desired locations signal of kth+1 time sampling, If error variance e₂(k)=x₂(k)-x_1c(k), virtual master function is constructedThen obtain:

C.2. according to the 2nd equation in discrete dynam ic m odeX formula (3):

x₂(k+1)=a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L, error variance can be acquired:

e₂(k+1)=a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L-x_1c(k+1)。

Select liapunov function:Then to V₂(k) ask difference that can obtain:

The load torque T in permasyn morot real work_LThere are upper limit d, therefore | T_L|≤d, d are normal number.

Construct virtual master function:

If error variance e₃(k)=x₃(k)-x_2c(k), then Δ V₂(k) it indicates are as follows:

It is obtained by Young inequality:

Therefore, bringing formula (11) into formula (10) can obtain:

C.3. by the 3rd equation of discrete dynam ic m odeX formula (3):

x₃(k+1)=(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)+b₄Δ_tu_q(k), error change can be acquired Amount:

Choose liapunov functionTo V₃(k) ask difference that can obtain:

Wherein, f₃(k)=(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)-x_2c(k+1)。

By RBF neural approximation theory it is found that for arbitrarily small positive number ε₃, there is always a nerve network systemsSo that

Wherein δ₃Indicate approximate error, and meet inequality | δ₃|≤ε₃, | | W₃| | it is vector W₃Norm, thus:

Wherein, S₃(Z₃It (k)) is basis function vector, Z₃(k)=[x₂(k),x₃(k),x₄(k),x_2c(k+1)]^T。

Choose the u in control input_qIt (k) is practical control law and adaptive lawAre as follows:

Wherein, γ₃, λ₃For normal number,For η₃Estimated value, definition | | W₃| |=η₃And η₃> 0, defined variable η₃ Evaluated error beFormula (7), (12), (15) are substituted into formula (14) and obtained:

C.4. remember systematic error variable e₄(k)=x₄(k), liapunov function is chosenP It is a normal number；By the 4th expression formula of discrete dynam ic m odeX formula (3):

x₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k), error variance can be acquired:

e₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Seek V₄(k) difference can obtain:

Wherein, f₄(k)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k), by RBF neural approximation theory it is found that right In arbitrarily small positive number ε₄, there is always a nerve network systemsSo that Wherein, δ₄Indicate approximate error, and meet inequality | δ₄|≤ε₄, wherein | | W₄| | it is vector W₄Norm, thus:

Wherein, S₄(Z₄It (k)) is basis function vector, Z₄(k)=[x₂(k),x₃(k),x₄(k)]^T。

Choose the u in control input_dIt (k) is practical control law and adaptive lawAre as follows:

Wherein, γ₄, λ₄For normal number,For η₄Estimated value, definition | | W₄| |=η₄, and η₄> 0, defined variable η₄ Evaluated error beFormula (19), which are substituted into formula (18), to be obtained:

D. stability analysis is carried out to the permasyn morot neural network Backstepping Controller of foundation

It chooses Li Ya and composes promise husband function are as follows:

Ask difference that can obtain V (k):

According to above-mentioned formulaWithWhen kth+1 time of progress evaluated error Formula can be obtained when samplingAnd adaptive lawM=3,4.And have:

By Young inequality and | | S_m(Z_m(k))||²< l_m, m=3,4, l_mThe number of nodes for indicating nerve network system, can :

DefinitionM is any positive number, because | x_jc(k)-α_j(k)|≤τ_j, j=1,2, according to formula (20), and Formula (22) to formula (26), which is substituted into formula (21), to be obtained:

Wherein, l₃, l₄Respectively indicate nerve network systemWithNumber of nodes.

Wherein,

τ₁,τ₂It is the constant greater than zero.

Select suitable parameter P and sampling period Δ_t, make its satisfaction If selection parameter meetsM=3,4, then only It wantsWithIt sets up, then can obtain Δ V (k)≤0.

It is further known that for arbitrarily small positive number σ,It sets up.

It is available in control law u by analyzing above_q(k),u_d(k) under the action of, the tracking error of system can be converged to One of origin sufficiently under neighborhood in, and guarantee other signal boundeds.

E. the permasyn morot neural network contragradience discrete controller established is emulated under virtual environment, Verify the feasibility of proposed permasyn morot adaptive neural network backstepping control method.Permasyn morot mind Through network contragradience discrete controller designed by Discrete Control Method, for the input quantity to discrete dynamic system into Row control,

PMSM Control System and related load parameter are as follows:

J=0.0003978kgm²；B=0.001158Nm/ (rad/s)；

R_s=0.68 Ω；L_d=0.00285H；L_q=0.00315H；n_p=3；Φ=0.1245H；

Select control law parameter are as follows:

λ₃=0.87, λ₄=0.0021, γ₃=0.98, γ₄=0.25, ζ=2.0, ω_n=200；

The neural network subordinating degree function of selection are as follows:

Wherein, μ₁……μ₉Be expressed as the output valve of hidden layer neuron, Z (k) indicate the input of neural network to Amount.

Desired position signal and sampling period are respectively as follows:

x_d(k)=2cos (0.5 π k Δ_t)；Δ_t=0.0025s.

Corresponding simulation result is as shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5.It can be seen from the simulation result of Fig. 2 and Fig. 3 originally The tracking effect of inventive method is ideal, fast response time, and the method for the present invention is corresponding it can be seen from the simulation result of Fig. 4 and Fig. 5 Permasyn morot neural network contragradience discrete controller effect it is ideal, fluctuate small, fast response time.

The method of the present invention for permasyn morot variable is more, coupling is strong, and be highly susceptible to external loading with And the problem of motor relevant parameter variation influence, a kind of neural network is devised based on command filtering technology and Backstepping principle Adaptive controller, nerual network technique are used for the design of controller for approaching unknown nonlinear terms, adaptive Backstepping, Command filtering technology is for solving the problems, such as " calculating explosion ".In addition, the present invention is supplemented with the complete control lacked in conventional method The part of device design increases Liapunov stability analysis；After being controlled to adjust by controller, motor running can be fast Speed reaches stable state, is more suitable for needing the control object of fast dynamic response, simulation result shows this new controller gram It has taken the influence of parameter inaccuracy and ensure that ideal control effect, realized the quickly and stably tracking to position.

Certainly, described above is only that presently preferred embodiments of the present invention is answered the present invention is not limited to enumerate above-described embodiment When explanation, anyone skilled in the art is all equivalent substitutes for being made, bright under the introduction of this specification Aobvious variant, all falls within the essential scope of this specification, ought to be by protection of the invention.

Claims (1)

1. a kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering, which is characterized in that

Include the following steps:

A. the dynamic model of permasyn morot is established

Under synchronous rotary d-q coordinate, the dynamic model expression of permasyn morot are as follows:

Wherein, Θ is permanent-magnet synchronous motor rotor angle position, ω is permanent-magnet synchronous motor rotor angular speed, J is rotation Inertia, T_LIt is magnetic linkage, the n that permanent magnet generates for load torque, Φ_pFor number of magnetic pole pairs, i_qFor q axis stator current, i_dIt is fixed for d axis Electron current, u_qFor permasyn morot q axis stator voltage, u_dFor permasyn morot d axis stator voltage, L_dAnd L_qFor d-q Stator inductance, R under coordinate system_sIt is coefficient of friction for permasyn morot stator equivalent resistance, B；

For the dynamic model for simplifying permasyn morot, it is defined as follows variable:

Then the discrete dynam ic m odeX of permasyn morot indicates are as follows:

Wherein, x₁(k+1) rotor angular position of kth+1 time sampling is indicated；

x₂(k+1) rotor velocity of kth+1 time sampling is indicated；

x₃(k+1) the q axis stator current of kth+1 time sampling is indicated；

x₄(k+1) it is expressed as the d axis stator current of kth+1 time sampling；Δ_tIndicate the sampling period；

B. according to Backstepping principle, a kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering is designed, Above-mentioned discrete dynam ic m odeX is simplified to two independent subsystems, i.e., by state variable x₁(k),x₂(k) and control inputs u_q(k) The subsystem of composition and by state variable x₄(k) and control inputs u_d(k) subsystem formed；Wherein:

First subsystem are as follows:

Second subsystem are as follows: x₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Use RBF neural Approximation of Continuous Functions f (Z (k)) below: Rⁿ→R；F (Z (k))=W^TS(Z(k))；

Wherein,It is input vector, q is neural network input dimension, R^qFor real vector collection；

W=[W₁,...,W_l]^T∈R^lIt is weight vectors, neural network node number l is positive integer, and l > 1, R^lFor real vector Collection；

RⁿRefer to that n Wei Shishuoxiangliangji, R refer to set of real numbers；Wherein, W₁,...,W_lIt is the weight of weight vectors W；

S (Z (k))=[s₁(Z(k)),...,s_l(Z(k))]^T∈R^lFor basis function vector, wherein s_i(Z (k)) is used as Gaussian function Number, form are as follows:

Wherein, μ_i=[μ_i1,...,μ_iq]^TIt is the center of acceptance region, and η_iIt is then the width of Gaussian function；

And when neural network node number l is sufficiently large, RBF neural, which is approached, compactsOn arbitrary continuation function f (Z (k)) arbitrary accuracy ε > 0 is arrived；

Definition command filter are as follows:

Wherein, ζ, ω_nFor command filtering device parameter；

z_j,1(k)=x_jc(k),

x_jc(k) and x_jc(k+1) kth time of j-th of command filtering device and the output signal of kth+1 time sampling are indicated；

z_j,1(k),z_j,2It (k) is the output signal of the kth of command filtering device time sampling；

z_j,1(k+1),z_j,2It (k+1) is the output signal of kth+1 time sampling of command filtering device；

α_jIt (k) is the input signal of the kth of j-th of command filtering device time sampling；

If input signal α_j(k) for all constant k >=0, so that | α_j(k+1)-α_j(k)|≤ρ₁And | α_j(k+2)-2α_j (k+1)+α_j(k)|≤ρ₂It sets up, then can obtain, to arbitrary constant, τ_j> 0, there are ω_n> 0 and ζ ∈ (0,1] so that | z_j,1 (k)-α_j(k)|≤τ_j, Δ z_j,1(k)=| z_j,1(k+1)-z_j,1(k) | it is bounded；

Wherein, ρ₁And ρ₂It is normal number, α_j(k+1) input signal of kth+1 time sampling of j-th of command filtering device, α are indicated_j (k+2) input signal of kth+2 times samplings of j-th of command filtering device is indicated；Z simultaneously_j,1(0)=α_j(0), z_j,2(0)=0 it is The initial value of command filtering device, α_j(0) original input signal of command filtering device is indicated；

It is as follows to define systematic error variable:

Wherein, x_dIt (k) is desired position signal, x_1c(k)、x_2cIt (k) is the output signal of command filtering device；

It c.1. is to ensure x₁(k) desired position signal x can effectively be tracked_d(k), it is as follows to choose Liapunov control function:

According to the 1st EQUATION x in discrete dynam ic m odeX formula (3)₁(k+1)=x₁(k)+Δ_tx₂(k) error variance can be acquired Are as follows:

e₁(k+1)=x₁(k+1)-x_d(k+1)=x₁(k)+Δ_tx₂(k)-x_d(k+1)；

Ask difference that can obtain formula (5):

By x₂(k) it is considered as the control input of first subsystem, x_dIt (k+1) is the desired locations signal of kth+1 time sampling, if accidentally Poor variable e₂(k)=x₂(k)-x_1c(k), virtual master function is constructedThen obtain:

C.2. according to the 2nd equation in discrete dynam ic m odeX formula (3):

x₂(k+1)=a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L, error variance can be acquired:

e₂(k+1)=a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L-x_1c(k+1)；

Select liapunov function:Then to V₂(k) ask difference that can obtain:

The load torque T in permasyn morot real work_LThere are upper limit d, therefore | T_L|≤d, d are normal number；

Construct virtual master function:

If error variance e₃(k)=x₃(k)-x_2c(k), then Δ V₂(k) it indicates are as follows:

It is obtained by Young inequality:

Therefore, bringing formula (11) into formula (10) can obtain:

C.3. by the 3rd equation of discrete dynam ic m odeX formula (3):

x₃(k+1)=(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)+b₄Δ_tu_q(k), error variance can be acquired:

Choose liapunov functionTo V₃(k) ask difference that can obtain:

Wherein, f₃(k)=(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)-x_2c(k+1)；

By RBF neural approximation theory it is found that for arbitrarily small positive number ε₃, there is always a nerve network systemsSo that

Wherein δ₃Indicate approximate error, and meet inequality | δ₃|≤ε₃, | | W₃| | it is vector W₃Norm, thus:

Wherein, S₃(Z₃It (k)) is basis function vector, Z₃(k)=[x₂(k),x₃(k),x₄(k),x_2c(k+1)]^T；

Choose the u in control input_qIt (k) is practical control law and adaptive lawAre as follows:

Wherein, γ₃, λ₃For normal number,For η₃Estimated value, definition | | W₃| |=η₃And η₃> 0, defined variable η₃Estimation Error isFormula (7), (12), (15) are substituted into formula (14) and obtained:

C.4. remember systematic error variable e₄(k)=x₄(k), liapunov function is chosenP is one Normal number；By the 4th expression formula of discrete dynam ic m odeX formula (3):

x₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k), error variance can be acquired:

e₄(k+1)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Seek V₄(k) difference can obtain:

Wherein, f₄(k)=(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k), by RBF neural approximation theory it is found that for appointing The positive number ε for anticipating small₄, there is always a nerve network systemsSo thatIts In, δ₄Indicate approximate error, and meet inequality | δ₄|≤ε₄, wherein | | W₄| | it is vector W₄Norm, thus:

Wherein, S₄(Z₄It (k)) is basis function vector, Z₄(k)=[x₂(k),x₃(k),x₄(k)]^T；

Choose the u in control input_dIt (k) is practical control law and adaptive lawAre as follows:

Wherein, γ₄, λ₄For normal number,For η₄Estimated value, definition | | W₄| |=η₄, and η₄> 0, defined variable η₄Estimate Counting error isFormula (19), which are substituted into formula (18), to be obtained:

D. stability analysis is carried out to the permasyn morot neural network Backstepping Controller of foundation

It chooses Li Ya and composes promise husband function are as follows:

Ask difference that can obtain V (k):

According to above-mentioned formulaWithWhen kth+1 time sampling for carrying out evaluated error When can obtain formulaAnd adaptive lawAnd have:

By Young inequality and | | S_m(Z_m(k))||²< l_m, m=3,4, l_mThe number of nodes for indicating nerve network system, can obtain:

DefinitionM is any positive number, because | x_jc(k)-α_j(k)|≤τ_j, j=1,2, according to formula (20), and will be public Formula (22) to formula (26) substitute into formula (21) and can obtain:

Wherein, l₃, l₄Respectively indicate nerve network systemWithNumber of nodes；

Wherein,

τ₁,τ₂It is the constant greater than zero；

Select suitable parameter P and sampling period Δ_t, make its satisfaction If selection parameter meetsSo only It wantsWithIt sets up, then can obtain Δ V (k)≤0；

It is further known that for arbitrarily small positive number σ,It sets up.