CN105811826A - Novel reaching law sliding mode control method for induction machine - Google Patents

Abstract

Disclosed is a novel reaching law sliding mode control method for an induction machine. The novel reaching law sliding mode control is characterized in that a PI controller of a rotating speed outer ring is replaced by a novel reaching law sliding mode controller with higher robustness and rapidness in a classical vector control system, namely on the basis of a speed outer ring and a speed inner ring; and the input of the novel reaching law sliding mode controller is a difference between a given rotating speed w<*> and an actual feedback rotating speed w of the induction machine. According to the method, the novel reaching law sliding mode control method is applied to the vector control system of the induction machine, so that the rapidness and the robustness of the induction machine control system are improved; meanwhile, buffeting of the system caused by the conventional sliding mode system can be effectively reduced; the control method is verified through simulation verification; and the verification result proves that the control method has relatively high robustness, stability and rapidness, as well as wide industrial application prospect.

Description

A kind of novel Reaching Law sliding-mode control of induction machine

Technical field

The present invention relates to a kind of novel Reaching Law sliding-mode control of induction machine.

Background technology

Induction conductivity has that simple in construction, firm and durable, conveyance capacity are big, easily safeguards and the advantage such as cheap, is widely used in modern AC drive system.But it is the multi-variable system of a high-order, non-linear, close coupling, therefore realizes high dynamic performance relative difficulty.Control research worker for induction machine has been proposed that a lot of control method, such as Self Adaptive Control, neutral net etc., but because method comparison complexity seldom has in the engineer applied being applied in reality.Adaptive control technology can when running situation changes the relevant parameter of identification, amendment system runs program, with the improvement system control performance when control object and service condition change, but this control algolithm is computationally intensive, it is achieved high dynamic performance relative difficulty；Nerve network controller adjusts parameter because of needs unceasing study, so needing speed microprocessor quickly, hardware realizes relatively difficult.

Sliding mode variable structure control has strong robustness, realizes simple advantage, when the parameter of electric machine changes and disturbance occurs, still can guarantee that satisfied performance, thus be subject to increasing Chinese scholars and pay attention to, but the discontinuity due to its control action, it is easy to make system produce to buffet, leverages it and control effect.And the amplitude scaled versions relation that the amplitude buffeted perturbs with disturbance and model parameter.In electric machine control system, buffeting can produce pulsation thrust, the stationarity of influential system and positioning precision, increases energy loss.Application saturation function replaces switch function, and emulation shows that it weakens buffeting to a certain extent, but reduces robustness simultaneously.Therefore, how to solve the buffeting of Sliding mode variable structure control, be effectively improved Immunity Performance and the dynamic responding speed of inductive motor control system, be a sliding moding structure technical problem anxious to be resolved being applied to inductive motor control system field.

Summary of the invention

It is an object of the invention to provide a kind of novel Reaching Law sliding-mode control of induction machine, to improve Immunity Performance and the dynamic responding speed of inductive motor control system.

The present invention adopts the following technical scheme that realization: a kind of novel Reaching Law sliding-mode control of induction machine, is realize on the basis of traditional Induction Motor Vector Control System, and described Induction Motor Vector Control System includes speed outer shroud and current inner loop；The current signal of described current inner loop is three electric currents being detected induction machine by Hall element, and testing result is converted to the electric current i under biphase rest frame through 3/2 conversion_α,i_β；Described speed outer shroud is the rotary speed actual value speed feedback value as speed outer shroud of Negotiation speed sensor detection induction machine, and poor with speed preset value, output torque current set-point i after a novel Reaching Law sliding mode controller regulates_q ^*；Current value i under biphase rest frame_α,i_βThe feedback excitation electric current i obtained under rotor coordinate in feedback circuit is converted through Park_dWith feedback calculating torque electric current i_q, adopt given exciting current i_d ^*With feedback excitation electric current i_dMake difference and obtain the output voltage u under biphase rotating coordinate system through electric current loop pi regulator_d；Torque current set-point i_q ^*With feedback calculating torque electric current i_qAfter comparing, after electric current loop pi regulator regulates, obtain the q axle output voltage u of two cordic phase rotators_q, u_qWith u_dTwo phase voltage u under convert to static two phase coordinate system after Park inverse transformation_α、u_β, pass through u_α、u_βVoltage vector can be calculated, obtain sector, voltage vector place by the azimuth and vector size judging voltage vector, further across the adjustment of SVPWM module, send PWM ripple, thus drive motor work；

Described novel Reaching Law sliding mode controller design is:

$\stackrel{\&CenterDot;}{s}=-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)---\left(1\right)$

In formula, s is sliding-mode surface；A > 1,0 < β < 1, k₁>0,k₂>0；Design sliding formwork switching function s=x₁+cx₂, wherein, x₁=ω^*-ω,State variable for induction machine system；State equation according to induction machine, asks local derviation to have s:

$\stackrel{\&CenterDot;}{s}=c{\stackrel{\&CenterDot;}{x}}_1+{\stackrel{\&CenterDot;}{x}}_2=-A{\stackrel{\&CenterDot;}{i}}_{qs}+{\mathrm{cx}}_2---\left(2\right)$

In formula, A=3p²ψ_r/ 2J, wherein ψ_rFor rotor magnetic linkage, P is motor number of pole-pairs, and J is rotary inertia, i_qsFor induction machine stator electric current q axle component, selectionFor the double; two power Reaching Laws in convergence method, can obtain:

$-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)={\mathrm{cx}}_2-A{\stackrel{\&CenterDot;}{i}}_{qs}---\left(3\right)$

By the i in formula (3)_qsAs torque current set-point i_q ^*, formula (3) controlled quentity controlled variable i can be obtained_q ^*Expression formula be:

${i_q}^{*}=\frac{1}{A}\&Integral;({\mathrm{cx}}_2+k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}(s)+k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}(s\left)\right)dt---\left(4\right)$

In formula, s is sliding-mode surface, a > 1,0 < β < 1, k₁>0,k₂>0。

The torque current set-point i calculated by formula (4)_q ^*With feedback calculating torque electric current i_qAfter comparing, after electric current loop pi regulator regulates, the q axle output voltage u of two cordic phase rotators can be obtained_q。

The primary object of the present invention is in that the PI controller that conventional vector controls system medium speed outer shroud is substituted by novel Reaching Law sliding mode controller, when being applied to system because of traditional Sliding mode variable structure control, the time delay of switching switch and the factor such as error of Spatial lag, state-detection is controlled due to sliding formwork, easily making control system produce chattering phenomenon, this is extremely harmful to Mechatronic Systems.Therefore, the present invention proposes a kind of Control of Induction Motors method based on novel Reaching Law sliding formwork, adopting Reaching Law sliding formwork to control is effective one of method weakening buffeting, and double; two power Reaching Law is no matter away from sliding mode or being respectively provided with Fast Convergent ability in the space of sliding mode.Theory analysis shows, this pair of power Reaching Law has Second Order Sliding Mode characteristic, and when system exists uncertain, system mode and derivative thereof can rapidly converge in balance zero neighborhood of a point.

There is advantages that

1, the present invention is by adopting novel Reaching Law sliding mode controller to replace the PI controller of induction Motor Vector Control medium speed outer shroud, have that convergence rate is slow for tradition Reaching Law in sliding formwork control, time length and buffet the deficiencies such as serious, it is proposed to a kind of design utilizing novel Reaching Law to improve system mode convergence rate.

2, the present invention proposes the induction machine method for controlling number of revolution based on novel Reaching Law sliding formwork, while eliminating controlled quentity controlled variable buffeting, it is achieved that the Fast Convergent of motor speed, and load disturbance has stronger robustness.

Accompanying drawing explanation

Fig. 1 is Control of Induction Motors vector method block diagram；

Fig. 2 is that the novel Reaching Law sliding formwork of the present invention controls and the induction machine of conventional PI control emulates speed waveform curve；

Fig. 3 is the induction machine torque profile curve that novel Reaching Law sliding formwork controls with conventional PI control.

In Fig. 1,1. controlling inverter, 2. induction machine module, 3. current signal detection circuit, 4.Clark converts, and 5.Park converts, 6. speed measuring coder, 7. novel Reaching Law sliding mode controller, 8. anti-Park conversion, 9.SVPWM module.

Detailed description of the invention

A kind of novel Reaching Law sliding-mode control of induction machine, it is realize on the basis of traditional vector control system, Induction Motor Vector Control System mainly includes speed outer shroud and current inner loop two parts, the current signal of electric current loop is by three electric currents of Hall element detection motor, and testing result is converted to the electric current i under biphase rest frame through 3/2 conversion_α,i_β, speed outer shroud is the rotary speed actual value speed feedback value as speed outer shroud of Negotiation speed sensor detection induction machine, and poor with speed preset value, output torque current set-point i after novel Reaching Law sliding mode controller regulates_q ^*, current value i under static two phase coordinate systems_α,i_βThe feedback excitation electric current i obtained under rotor coordinate in feedback circuit is converted through Park_dWith feedback torque electric current i_q, i_d ^*With i_dMake difference and obtain the output voltage u under biphase rotating coordinate system through electric current loop pi regulator_d, torque current i_q ^*With feedback calculating torque electric current i_qAfter comparing, after overcurrent PI regulates, obtain the q axle output voltage u of two cordic phase rotators_q, u_qWith u_dTwo phase voltage u under convert to static two phase coordinate system after Park inverse transformation_α、u_β, pass through u_α、u_βVoltage vector can be calculated, obtain sector, voltage vector place by the azimuth and vector size judging voltage vector, further across the adjustment of SVPWM module, send PWM ripple, thus drive motor work.

As follows based on induction machine novel Reaching Law sliding mode controller design, designing novel sliding formwork Reaching Law is:

$\stackrel{\&CenterDot;}{s}=-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)---\left(1\right)$

In formula, s is sliding-mode surface；A > 1,0 < β < 1, k₁>0,k₂>0.When system mode is away from sliding mode (| s | > 0), in formula (1), Section 1 plays a leading role；When system mode is close to sliding mode (| s | < 1), the Section 2 of formula (1) plays a leading role, therefore adopt novel Reaching Law to be possible not only to effectively eliminate buffeting, and away from or all there is convergence rate faster during close to sliding mode.There is Second Order Sliding Mode Control characteristic after limited convergence time, namely simultaneouslyWhen there is external disturbance, s andAll converge in the bounded field of balance zero point.

In order to reduce the buffeting of the novel Reaching Law System with Sliding Mode Controller of induction machine, and improving velocity of approach, the present invention designs sliding formwork switching function s=x₁+cx₂, wherein, x₁=ω^*-ω,State variable for induction machine system.State equation according to induction machine, asks local derviation to have s:

$\stackrel{\&CenterDot;}{s}=c{\stackrel{\&CenterDot;}{x}}_1+{\stackrel{\&CenterDot;}{x}}_2=-A{\stackrel{\&CenterDot;}{i}}_{qs}+{\mathrm{cx}}_2---\left(2\right)$

In formula, A=3p²ψ_r/ 2J, wherein ψ_rFor rotor magnetic linkage, P is motor number of pole-pairs, and J is rotary inertia, i_qsFor induction machine stator electric current q axle component, selectionFor the double; two power Reaching Laws in convergence method, can obtain:

$-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)={\mathrm{cx}}_2-A{\stackrel{\&CenterDot;}{i}}_{qs}---\left(3\right)$

By the i in formula (3)_qsAs torque current set-point i_q ^*, formula (3) controlled quentity controlled variable i can be obtained_q ^*Expression formula be:

${i_q}^{*}=\frac{1}{A}\&Integral;({\mathrm{cx}}_2+k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}(s)+k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}(s\left)\right)dt---\left(4\right)$

The torque current set-point i calculated by formula (4)_q ^*With feedback calculating torque electric current i_qAfter comparing, after electric current loop pi regulator regulates, the q axle output voltage u of two cordic phase rotators can be obtained_q。

According to the accessibility that sliding formwork controls, because a > 1,0 < β < 1, k₁>0,k₂> 0, therefore to ensure that formula (5) is set up, can ensure that sliding formwork motion can at Finite-time convergence.

$s\stackrel{\&CenterDot;}{s}=s\&lsqb;-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)\&rsqb;=-k_1{\left|s\right|}^{1+\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{1+\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)<0---\left(5\right)$

Assuming system initial state s (0) > 1, point two phase analysis s can at Finite-time convergence.

1) s (0) to s=1, now, because of a > 1,0 < β < 1, so in formula (1) the 1st play a leading role, effect much larger than the 2nd, such that it is able to ignore the impact of the 2nd, formula (1) can dissolve for:

$\stackrel{\&CenterDot;}{s}=k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)---\left(6\right)$

Formula (6) both sides integration can be obtained s^1-α=-(1-α) k₁t+s(0)^1-α, thus can calculate s (0) to s=1 required time is t₁=1-s (0)^(1-α)/k₁(α-1)。

2) s=1 to s=0.Same because of a > 1,0 < β < 1, so in formula (3) the 2nd play a leading role, effect much larger than the 1st, such that it is able to ignore the impact of the 1st, in like manner can calculate the time obtained needed for s=1 to s=0 is t₂=1/k₂(1-β).Therefore convergence time is the summation of two convergence stage each convergence times.That is:

$t=t_1+t_2=t_1=\frac{1-s{\left(0\right)}^{1-\mathrm{\&alpha;}}}{k_1(\mathrm{\&alpha;}-1)}+\frac{1}{k_2(1-\mathrm{\&beta;})}---\left(7\right)$

When s (0) < when-1, equally possible is divided into two convergence stages to carry out convergence time research.System mode convergence time is:

$t=t_1+t_2=t_1=\frac{1+s{\left(0\right)}^{1-\mathrm{\&alpha;}}}{k_1(\mathrm{\&alpha;}-1)}+\frac{1}{k_2(1-\mathrm{\&beta;})}---\left(8\right)$

So may certify that as s=0

In order to prove when system exists uncertain external interference, s andCan be converged in a neighborhood of (0,0).Consider uncertain system:

$\stackrel{\&CenterDot;}{s}=-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)+d\left(t\right)---\left(9\right)$

Assume | d (t) |≤δ, δ > 0 it is normal number, definition Lyapunove function is:

$V=\frac{1}{2}{s}^2---\left(10\right)$

Held time derivation by Lyapunov's stability criterion formula (9) and formula (10) substituted into:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=\stackrel{\&CenterDot;}{s}\&CenterDot;s=s\&lsqb;-k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)+d\left(t\right)\&rsqb;\\ =-k_1{\left|s\right|}^{1+\mathrm{\&alpha;}}-k_2{\left|s\right|}^{1+\mathrm{\&beta;}}+sd\left(t\right)\&le;-k_1{\left|s\right|}^{1+\mathrm{\&alpha;}}-k_2{\left|s\right|}^{1+\mathrm{\&beta;}}+\left|s\right|\left|d\left(t\right)\right|\end{array}---\left(11\right)$

Can be calculated by shifting onto:

$\left|s\right|\&le;min({\left(\frac{\mathrm{\&delta;}}{k_2}\right)}^{1/\mathrm{\&beta;}},{\left(\frac{\mathrm{\&delta;}}{k_1}\right)}^{1/\mathrm{\&alpha;}})---\left(12\right)$

State can also be obtained equallyFor:

$\begin{array}{c}\left|\stackrel{\&CenterDot;}{s}\right|\&le;k_1{\left|s\right|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)+k_2{\left|s\right|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)+d\left(t\right)\&le;k_1{\left|s\right|}^{\mathrm{\&alpha;}}+k_2{\left|s\right|}^{\mathrm{\&beta;}}+d\left|d\left(t\right)\right|\&le;\\ k_1\min {({\left(\frac{\mathrm{\&delta;}}{k_1}\right)}^{1/\mathrm{\&alpha;}},{\left(\frac{\mathrm{\&delta;}}{k_2}\right)}^{1/\mathrm{\&beta;}})}^{\mathrm{\&alpha;}}+k_2\min {({\left(\frac{\mathrm{\&delta;}}{k_1}\right)}^{1/\mathrm{\&alpha;}},{\left(\frac{\mathrm{\&delta;}}{k_2}\right)}^{1/\mathrm{\&beta;}})}^{\mathrm{\&beta;}}+\mathrm{\&delta;}\\ =\min (\mathrm{\&delta;},k_1{\left(\frac{\mathrm{\&delta;}}{k_2}\right)}^{\mathrm{\&alpha;}/\mathrm{\&beta;}})+\min (k_2{\left(\frac{\mathrm{\&delta;}}{k_1}\right)}^{\mathrm{\&beta;}/\mathrm{\&alpha;}},\mathrm{\&delta;})+\mathrm{\&delta;}\end{array}---\left(13\right)$

Therefore may certify that state s andAll restrain.

Control method of the present invention improves that the convergence rate that tradition sliding formwork controls is slow, time length and buffet the deficiencies such as serious, has and controls effect preferably.

While the rapidity improving electric machine control system and robustness, also effectively reduce the buffeting that tradition sliding formwork controls to bring to system simultaneously, improve the stability of system, effectively improve the dynamic and static runnability of system.

In order to verify the feasibility based on novel Reaching Law sliding-mode control of proposition, having emulated based on MATLAB software herein, the parameter of electric machine is: rated power P_N=7.5kW, rated voltage U_N=380V, rated current I_N=15.4A, rated frequency f_N=50Hz, stator resistance R_s=0.594 Ω, rotor resistance R_r=0.406 Ω, stator inductance L_s=28.878mH, inductor rotor L_r=28.878mH, mutual inductance L_m=26.527mH, rotary inertia J=0.02kg m², number of pole-pairs P=2, rated speed n_N=1440r/min.

Fig. 2 gives the Emulation of Electrical Machinery speed waveform that when given rotating speed is 1500r/min, novel Reaching Law sliding formwork controls and PI controls.Motor is the load of impact 10N m when 3s, can be seen that the PI speed overshoot controlled is about 60r/min, regulating time is 0.2s, and novel Reaching Law sliding formwork controls speed overshoot and is about 30r/min, regulating time is only 0.15s, it can be seen that novel Reaching Law sliding formwork controls there is dynamic property faster.System is when 3s after system shock load, and PI controls after the adjustment time of 0.1s stable, and motor speed loss is 30r/min, and novel Reaching Law sliding formwork controls after the adjustment of 0.05s stable, and loading rear motor motor speed loss is 20r/min.

Fig. 3 is given rotating speed is motor torque simulation waveform during 1500r/min, it can be seen that PI controls torque after electric motor starting and arrives stable state after 0.2s, and novel Reaching Law sliding formwork arrives steady statue through 0.15s after controlling starting；System is when 3s after the load of impact 10N m, and the torque that PI controls just arrives steady statue after 0.4s, and the torque that novel Reaching Law sliding formwork controls arrives stable state after the adjustment of 0.1s.By simulation result it can be seen that the Control of Induction Motors strategy based on novel Reaching Law sliding formwork has good effect, having speed responsive faster compared with pi regulator, steady-state behaviour is also better, and has good robustness when motor shock load.

Claims (1)

1. the novel Reaching Law sliding-mode control of induction machine, it is characterised in that being realize on the basis of traditional Induction Motor Vector Control System, described Induction Motor Vector Control System includes speed outer shroud and current inner loop；The current signal of described current inner loop is three electric currents being detected induction machine by Hall element, and testing result is converted to the electric current i under biphase rest frame through 3/2 conversion_α,i_β；Described speed outer shroud is the rotary speed actual value speed feedback value as speed outer shroud of Negotiation speed sensor detection induction machine, and poor with speed preset value, output torque current set-point i after a novel Reaching Law sliding mode controller regulates_q ^*；Current value i under biphase rest frame_α,i_βThe feedback excitation electric current i obtained under rotor coordinate in feedback circuit is converted through Park_dWith feedback calculating torque electric current i_q, adopt given exciting current i_d ^*With feedback excitation electric current i_dMake difference and obtain the output voltage u under biphase rotating coordinate system through electric current loop pi regulator_d；Torque current set-point i_q ^*With feedback calculating torque electric current i_qAfter comparing, after electric current loop pi regulator regulates, obtain the q axle output voltage u of two cordic phase rotators_q, u_qWith u_dTwo phase voltage u under convert to static two phase coordinate system after Park inverse transformation_α、u_β, pass through u_α、u_βVoltage vector can be calculated, obtain sector, voltage vector place by the azimuth and vector size judging voltage vector, further across the adjustment of SVPWM module, send PWM ripple, thus drive motor work；

Described novel Reaching Law sliding mode controller design is:

$\stackrel{\&CenterDot;}{s}=-k_1|s{|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2|s{|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)---\left(1\right)$

In formula, s is sliding-mode surface；A > 1,0 < β < 1, k₁>0,k₂>0；Design sliding formwork switching function s=x₁+cx₂, wherein, x₁=ω^*-ω,State variable for induction machine system；State equation according to induction machine, right_sLocal derviation is asked to have:

$\stackrel{\&CenterDot;}{s}=c{\stackrel{\&CenterDot;}{x}}_1+{\stackrel{\&CenterDot;}{x}}_2=-A{\stackrel{\&CenterDot;}{i}}_{qs}+{\mathrm{cx}}_2---\left(2\right)$

In formula, A=3p²ψ_r/ 2J, wherein ψ_rFor rotor magnetic linkage, P is motor number of pole-pairs, and J is rotary inertia, i_qsFor induction machine stator electric current q axle component, selectionFor the double; two power Reaching Laws in convergence method, can obtain:

$-k_1|s{|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)-k_2|s{|}^{\mathrm{\&beta;}}\mathrm{sgn}\left(s\right)={\mathrm{cx}}_2-A{\stackrel{\&CenterDot;}{i}}_{qs}---\left(3\right)$

By the i in formula (3)_qsAs torque current set-point i_q ^*, formula (3) controlled quentity controlled variable i can be obtained_q ^*Expression formula be:

${i_q}^{*}=\frac{1}{A}\&Integral;({\mathrm{cx}}_2+k_1|s{|}^{\mathrm{\&alpha;}}\mathrm{sgn}\left(s\right)+k_2\left|s{|}^{\mathrm{\&beta;}}\mathrm{sgn}\right(s\left)\right)dt---\left(4\right)$

In formula, s is sliding-mode surface, a > 1,0 < β < 1, k₁>0,k₂>0。