CN105450120A - PMSM chaotic stabilized control method based on dynamic surface sliding mode - Google Patents

Abstract

The invention discloses a PMSM chaotic stabilized control method based on a dynamic surface sliding mode, comprising steps of establishing a PMSM chaotic model and initial condition determination, splitting the PMSM system into two subsystems for improving the control effect, calculating the tracking error of the control system, a sliding surface and differential calculus based on the dynamic surface sliding mode control method, estimating an unknown parameter based on an adaptive law and designing the controller input according to the unknown parameter. The invention provides a dynamic surface sliding mode control method for realizing the PMSM chaotic stabilized control, realizes the chaotic state of the system is stabilized to a balance point, and improves the control performance of the system.

Description

Based on the permagnetic synchronous motor chaos stabilized control method that dynamic surface sliding formwork controls

Technical field

The invention belongs to permagnetic synchronous motor control technology field, relate to a kind of permagnetic synchronous motor chaos stabilized control method controlled based on dynamic surface sliding formwork, particularly carry out the method for chaos point stabilization for the chaotic behavior in permagnetic synchronous motor.

Background technology

Permagnetic synchronous motor is the High Order Nonlinear System of a kind of typical multivariable, close coupling, controls to be widely used in contour performance system at such as robot, aviation aircraft and servo turntable.But research in recent years shows, permagnetic synchronous motor, under some special parameters and condition of work, there will be complicated irregular movement, i.e. chaotic behavior.The existence of chaotic behavior in permagnetic synchronous motor, not only can influential system run stability and fail safe, can system crash be caused under serious conditions.And in industrial automation is produced, stability and the fail safe of guarantee permagnetic synchronous motor system are most important.Therefore, based on the nonlinear essence of electric system, study its chaos phenomenon, seek effective chaotic control method and more and more come into one's own.For the control problem of permagnetic synchronous motor, many effective advanced control methods are introduced into, and as sliding formwork controls, Backstepping controls, dynamic surface control etc.Sliding formwork controls to be considered to an effective robust control method in and external disturbance uncertain at resolution system.The advantages such as sliding-mode control has that algorithm is simple, fast response time, to external world noise jamming and Parameter Perturbation strong robustness.It in parameter of electric machine change and still can keep satisfied performance when there is external disturbance.But sliding formwork controls demand fulfillment matching condition in the design process, the uncertainty of real system matching condition becomes the obstacle of sliding formwork control design case.

Summary of the invention

In order to suppress permagnetic synchronous motor occurs under particular job condition chaos phenomenon and the complexity explosion issues that the method for inversion is brought, the invention provides a kind of permagnetic synchronous motor chaos stabilized control method controlled based on dynamic surface sliding formwork, improve the project organization of controller, achieve permagnetic synchronous motor chaos to calm, each state variable of guarantee system all can realize tenacious tracking.

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

Based on the permagnetic synchronous motor chaos stabilized control method that dynamic surface sliding formwork controls, comprise the following steps:

Step 1, sets up permagnetic synchronous motor chaotic model;

Set up the chaotic model such as formula the permagnetic synchronous motor system shown in (1), initialization system state and relevant parameter;

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_d}{dt}=-{\tilde{i}}_d+\widetilde{\mathrm{\ω}}{\tilde{i}}_q+{\tilde{u}}_d\\ \frac{d{\tilde{i}}_q}{dt}=-{\tilde{i}}_q-\widetilde{\mathrm{\ω}}{\tilde{i}}_d+\mathrm{\γ}\widetilde{\mathrm{\ω}}+{\tilde{u}}_q\\ \frac{d\widetilde{\mathrm{\ω}}}{dt}=\mathrm{\σ}({\tilde{i}}_q-\widetilde{\mathrm{\ω}})-{\tilde{T}}_L\end{array}\right.---\left(1\right)$

Wherein, ω, i _q, i _dfor state variable, be respectively motor angular velocity, quadrature axis stator current and d-axis stator current; with for outside input, be respectively external loading torque, stator voltage quadrature axis component and direct axis component, meet σ and γ is all operational factors of system;

Using the angular speed of permagnetic synchronous motor as control object, bring initial condition into, formula (1) is expressed as:

$\left\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}\\ \frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}+u\\ y={\mathrm{\ω}}_r\end{array}\right.---\left(2\right)$

Wherein, u is control law, and y is output signal, ω _rthe expectation angular speed of motor;

Step 2, split system, avoids controller to suddenly change;

Controller u is added in second state parameter, obtains formula (3)

$\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}+u\\ \frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}\end{array}---\left(3\right)$

Formula (3) is split as following two subsystems:

$\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}+u\end{array}---\left(4\right)$

With

$\frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}---\left(5\right)$

Step 3, Controller gain variations;

3.1 definition tracking error e and dynamic surface s ₁for

$\{\begin{array}{c}e=\mathrm{\ω}-{\mathrm{\ω}}_r\\ s_1=e+\mathrm{\λ}\∫edt\end{array}---\left(6\right)$

Wherein, ω _rfor angular speed expected by motor, λ is constant, and λ > 0;

Carry out differentiate to it to obtain

$\{\begin{array}{c}\stackrel{\·}{e}=\stackrel{\·}{\mathrm{\ω}}-{\stackrel{\·}{\mathrm{\ω}}}_r=\mathrm{\σ}\left(i_q\mathrm{\ω}\right)-{\stackrel{\·}{\mathrm{\ω}}}_r\\ {\stackrel{\·}{s}}_1=\stackrel{\·}{e}+\mathrm{\λ}e=\mathrm{\σ}(i_q-\mathrm{\ω})+\mathrm{\λ}e\end{array}---\left(7\right)$

3.2 design virtual controlling amounts

${\stackrel{\‾}{i}}_{qr}=\mathrm{\ω}-k_1{s}_1-\mathrm{\λ}e/\mathrm{\σ}---\left(8\right)$

Wherein, k ₁for constant, and k ₁> 0;

A 3.3 definition new variables i _qrestimate allow by having the firstorder filter of little positive timeconstantτ 2:

${\mathrm{\τ}}_2{\stackrel{\·}{i}}_{qr}+i_{qr}={\stackrel{\‾}{i}}_{qr},i_{qr}\left(0\right)={\stackrel{\‾}{i}}_{qr}\left(0\right)---\left(9\right)$

3.4 definition, second error surface

s ₂＝i _q-i _qr(10)

Differentiate obtains

${\stackrel{\·}{s}}_2=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}-{\stackrel{\·}{i}}_{qr}+u---\left(11\right)$

3.5 CONTROLLER DESIGN input u:

$u=i_q+i_d\mathrm{\ω}-\widehat{\mathrm{\γ}}\mathrm{\ω}+{\stackrel{\·}{i}}_{qr}-k_2{s}_2---\left(12\right)$

Wherein, k ₂for constant, and k ₂> 0, be the estimated value of uncertain parameter γ, its adaptive updates rule is

$\stackrel{\·}{\widehat{\mathrm{\γ}}}={\mathrm{\ρS}}_2\mathrm{\ω}---\left(13\right)$

Wherein, ρ is the positive count that can adjust adaptive algorithm performance.

The present invention is based on dynamic surface Sliding Mode Adaptive Control method, for the chaotic behavior in permagnetic synchronous motor, realize the point stabilization of permagnetic synchronous motor chaos state, improve system control performance.

Technical conceive of the present invention is: for controlling the chaos phenomenon of permagnetic synchronous motor, the present invention is in conjunction with dynamic surface control and sliding mode control algorithm, propose the permagnetic synchronous motor chaotic control method controlled based on dynamic surface sliding formwork, this control method can make controlled permagnetic synchronous motor chaos state Asymptotic Stability in re-set target.In order to make chaotic systems state by balance point of calming further, we improve control strategy, permagnetic synchronous motor chaos system are divided into two subsystems, and only on first subsystem, increase controller.Simulation comparison shows, the dynamic surface sliding mode control strategy after improvement can not only effectively by three system mode controls to balance point, and than common dynamic face control method, there is response speed faster.The invention provides a kind of dynamic surface sliding-mode control that can realize permagnetic synchronous motor chaos point stabilization, realize chaotic systems state by balance point of calming.

Beneficial effect of the present invention is: the chaos phenomenon that under suppression particular job condition, permagnetic synchronous motor occurs and the complexity explosion issues that the method for inversion is brought, simplify Controller gain variations, realize the point stabilization of permagnetic synchronous motor chaos state, improve system control performance.

Accompanying drawing explanation

Fig. 1 is the controlled curve synoptic diagram of ω;

Fig. 2 is i _qcontrolled curve synoptic diagram;

Fig. 3 is i _dcontrolled curve synoptic diagram;

Fig. 4 is the effect curves schematic diagram of controller u;

Fig. 5 is the evaluated error of parameter curve synoptic diagram.

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 chaos stabilized control method controlled based on dynamic surface sliding formwork, comprises the following steps:

Step 1, sets up permagnetic synchronous motor chaotic model;

Set up the chaotic model such as formula the permagnetic synchronous motor system shown in (1), initialization system state and relevant parameter;

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_d}{dt}=-{\tilde{i}}_d+\widetilde{\mathrm{\ω}}{\tilde{i}}_q+{\tilde{u}}_d\\ \frac{d{\tilde{i}}_q}{dt}=-{\tilde{i}}_q-\widetilde{\mathrm{\ω}}{\tilde{i}}_d+\mathrm{\γ}\widetilde{\mathrm{\ω}}+{\tilde{u}}_q\\ \frac{d\widetilde{\mathrm{\ω}}}{dt}=\mathrm{\σ}({\tilde{i}}_q-\widetilde{\mathrm{\ω}})-{\tilde{T}}_L\end{array}\right.---\left(1\right)$

Wherein, ω, i _q, i _dfor state variable, be respectively motor angular velocity, quadrature axis stator current and d-axis stator current; with for outside input, be respectively external loading torque, stator voltage quadrature axis component and direct axis component, meet σ and γ is all operational factors of system;

Using the angular speed of permagnetic synchronous motor as control object, bring initial condition into, formula (1) is expressed as:

$\left\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}\\ \frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}+u\\ y={\mathrm{\ω}}_r\end{array}\right.---\left(2\right)$

Wherein, u is control law, and y is output signal, ω _rthe expectation angular speed of motor;

Step 2, split system, avoids controller to suddenly change;

Controller u is added in second state parameter, obtains formula (3)

$\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}+u\\ \frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}\end{array}---\left(3\right)$

Formula (3) is split as following two subsystems:

$\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}+u\end{array}---\left(4\right)$

With

$\frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}---\left(5\right)$

Step 3, Controller gain variations;

3.1 definition tracking error e and dynamic surface s ₁for

$\{\begin{array}{c}e=\mathrm{\ω}-{\mathrm{\ω}}_r\\ s_1=e+\mathrm{\λ}\∫edt\end{array}---\left(6\right)$

Wherein, ω _rfor angular speed expected by motor, λ is constant, and λ > 0;

Carry out differentiate to it to obtain

$\{\begin{array}{c}\stackrel{\·}{e}=\stackrel{\·}{\mathrm{\ω}}-{\stackrel{\·}{\mathrm{\ω}}}_r=\mathrm{\σ}\left(i_q\mathrm{\ω}\right)-{\stackrel{\·}{\mathrm{\ω}}}_r\\ {\stackrel{\·}{s}}_1=\stackrel{\·}{e}+\mathrm{\λ}e=\mathrm{\σ}(i_q-\mathrm{\ω})+\mathrm{\λ}e\end{array}---\left(7\right)$

3.2 design virtual controlling amounts

${\stackrel{\‾}{i}}_{qr}=\mathrm{\ω}-k_1{s}_1-\mathrm{\λ}e/\mathrm{\σ}---\left(8\right)$

Wherein, k ₁for constant, and k ₁> 0;

A 3.3 definition new variables i _qrestimate allow by having the firstorder filter of little positive timeconstantτ 2:

${\mathrm{\τ}}_2{\stackrel{\·}{i}}_{qr}+i_{qr}={\stackrel{\‾}{i}}_{qr},i_{qr}\left(0\right)={\stackrel{\‾}{i}}_{qr}\left(0\right)---\left(9\right)$

3.4 definition, second error surface

s ₂＝i _q-i _qr(10)

Differentiate obtains

${\stackrel{\·}{s}}_2=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}-{\stackrel{\·}{i}}_{qr}+u---\left(11\right)$

3.5 CONTROLLER DESIGN input u:

$u=i_q+i_d\mathrm{\ω}-\widehat{\mathrm{\γ}}\mathrm{\ω}+{\stackrel{\·}{i}}_{qr}-k_2{s}_2---\left(12\right)$

Wherein, k ₂for constant, and k ₂> 0, be the estimated value of uncertain parameter γ, its adaptive updates rule is

$\stackrel{\·}{\widehat{\mathrm{\γ}}}={\mathrm{\ρS}}_2\mathrm{\ω}---\left(13\right)$

Wherein, ρ is the positive count that can adjust adaptive algorithm performance.

When γ unknown parameters, the controller designed based on proposed dynamic surface sliding-mode method (DSC+SMC) and the control effects of the controller designed based on dynamic surface method (DSC) are carried out simulation comparison.For ease of comparing, in emulation, both initial condition and the setting of partial parameters are consistent, and namely the sampling time gets T _s=0.01, initial condition is i _d(0)=i _q(0)=ω (0)=0.01.Expectation target ω _r=0, controling parameters value is k ₁=0.5, k ₂=1, τ ₂=0.01.In addition, controling parameters λ=20 in DSC+SMC method.

Simulation result as Fig. 1-5, as shown in Figure 1, about 1.8s, DSC+SMC controls to have made system mode parameter ω arrive desired value, and just reaches desired value to about 3.2s, DSC ω, contrast known, under the effect based on DSC+SMC method design controller, ω convergence rate is faster.As shown in Figure 2, about 0.1s, system mode parameter i _qdesired value zero point is arrived under the controller action of DSC+SMC control methods design, and to about 2s, just by i under the controller action of DSC control methods design _qcurrent converges to desired value, so contrast known, under the effect based on DSC+SMC method design controller, i _qcontrolled response is quicker.As shown in Figure 3, about 4.8s, state parameter i _dconverge to 0, based on the controller of DSC+SMC design and the controller based on DSC design, to state parameter i _dcontrol effects substantially identical.As shown in Figure 4, the controller based on DSC+SMC design just completes control at about 0.1s, and just substantially completes control to the controller of about 1.5s, DSC method design.As shown in Figure 5, the evaluated error of about 1s parameter obtain elimination.Therefore, under the effect of the controller based on DSC+SMC method design, the response of controlled parameter is more quick, and control effects is better.

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.

Claims (1)

1., based on the permagnetic synchronous motor chaos stabilized control method that dynamic surface sliding formwork controls, it is characterized in that: described control method comprises the following steps:

Step 1, sets up permagnetic synchronous motor chaotic model;

Set up the chaotic model such as formula the permagnetic synchronous motor system shown in (1), initialization system state and relevant parameter;

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_d}{dt}=-{\tilde{i}}_d+\widetilde{\mathrm{\ω}}{\tilde{i}}_q+{\tilde{u}}_d\\ \frac{d{\tilde{i}}_d}{dt}=-{\tilde{i}}_q-\widetilde{\mathrm{\ω}}{\tilde{i}}_d+\mathrm{\γ}\widetilde{\mathrm{\ω}}+{\tilde{u}}_q\\ \frac{d\widetilde{\mathrm{\ω}}}{dt}=\mathrm{\σ}({\tilde{i}}_q-\widetilde{\mathrm{\ω}})-{\tilde{T}}_L\end{array}\right.---\left(1\right)$

Wherein, ω, i _q, i _dfor state variable, be respectively motor angular velocity, quadrature axis stator current and d-axis stator current; with for outside input, be respectively external loading torque, stator voltage quadrature axis component and direct axis component, meet σ and γ is all operational factors of system;

Using the angular speed of permagnetic synchronous motor as control object, bring initial condition into, formula (1) is expressed as:

$\left\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}\\ \frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}+u\\ y={\mathrm{\ω}}_r\end{array}\right.---\left(2\right)$

Wherein, u is control law, and y is output signal, ω _rthe expectation angular speed of motor;

Step 2, split system, avoids controller to suddenly change;

Controller u is added in second state parameter, obtains formula (3)

$\left\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}+u\\ \frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}\end{array}\right.---\left(3\right)$

Formula (3) is split as following two subsystems:

$\left\{\begin{array}{c}\frac{d\mathrm{\ω}}{dt}=\mathrm{\σ}(i_q-\mathrm{\ω})\\ \frac{{\mathrm{di}}_q}{dt}=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}+u\end{array}\right.---\left(4\right)$

With

$\frac{{\mathrm{di}}_d}{dt}=-i_d+i_q\mathrm{\ω}---\left(5\right)$

Step 3, Controller gain variations;

3.1 definition tracking error e and dynamic surface s ₁for

$\left\{\begin{array}{c}e=\mathrm{\ω}-{\mathrm{\ω}}_r\\ s_1=e+\mathrm{\λ}\∫edt\end{array}\right.---\left(6\right)$

Wherein, ω _rfor angular speed expected by motor, λ is constant, and λ > 0;

Carry out differentiate to it to obtain

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_1=\stackrel{\·}{\mathrm{\ω}}-{\stackrel{\·}{\mathrm{\ω}}}_r=\mathrm{\σ}(i_q-\mathrm{\ω})-{\stackrel{\·}{\mathrm{\ω}}}_r\\ {\stackrel{\·}{s}}_1=\stackrel{\·}{e}+\mathrm{\λ}e=\mathrm{\σ}(i_q-\mathrm{\ω})+\mathrm{\λ}e\end{array}\right.---\left(7\right)$

3.2 design virtual controlling amounts

${\stackrel{\‾}{i}}_{qr}=\mathrm{\ω}-k_1{s}_1-\mathrm{\λ}e/\mathrm{\σ}---\left(8\right)$

Wherein, k ₁for constant, and k ₁> 0;

A 3.3 definition new variables i _qrestimate allow by having the firstorder filter of little positive timeconstantτ 2:

${\mathrm{\τ}}_2{\stackrel{\·}{i}}_{qr}+i_{qr}={\stackrel{\‾}{i}}_{qr},i_{qr}\left(0\right)={\stackrel{\‾}{i}}_{qr}\left(0\right)---\left(9\right)$

3.4 definition, second error surface

s ₂＝i _q-i _qr(10)

Differentiate obtains

${\stackrel{\·}{s}}_2=-i_q-i_d\mathrm{\ω}+\mathrm{\γ}\mathrm{\ω}-{\stackrel{\·}{i}}_{qr}+u---\left(11\right)$

3.5 CONTROLLER DESIGN input u:

$u=i_q+i_d\mathrm{\ω}-\widehat{\mathrm{\γ}}\mathrm{\ω}+{\stackrel{\·}{i}}_{qr}-k_2{s}_2---\left(12\right)$

Wherein, k ₂for constant, and k ₂> 0, be the estimated value of uncertain parameter γ, its adaptive updates rule is

$\stackrel{\·}{\widehat{\mathrm{\γ}}}={\mathrm{\ρS}}_2\mathrm{\ω}---\left(13\right)$

Wherein, ρ is the positive count that can adjust adaptive algorithm performance.