CN103248290A - Grey sliding mode control method for dual-redundancy brushless direct current motor of electric brake of airplane - Google Patents

Abstract

The invention provides a grey sliding mode control method for a dual-redundancy brushless direct current motor of an electric brake of an airplane. The grey sliding mode control method comprises the following steps of calculating a brake pressure error, establishing a sliding mode line, calculating current-sharing current output of two motor windings, acquiring current feedback signals of the two motor windings, and calculating a current error signal; performing current-sharing ring PID control and driving the dual-redundancy brushless direct current motor to work; and establishing a grey model, calculating a neighbor mean generation sequence and a middle matrix, and calculating predicted pressure of a brake system at the next moment. By the grey sliding mode control method, the reliability of the brake system is improved, the current of the two motor windings is balanced, a problem of force fight is solved, the robustness of the electric brake system of the airplane is improved and the buffeting brought by sliding mode control is inhibited.

Description

The grey sliding-mode control that is used for the two margin brushless DC motors of aircraft electric brake

Technical field

The present invention relates to a kind of grey sliding-mode control of motor.

Background technology

Airplane brake system is the subsystem that has relatively independent function on the aircraft, and its effect is outstanding, and reliability requirement is very high.Full electric brake acting device non-skid property is good, the braking efficiency height, and maintenanceability is strong.At present, electric brake control system achievement in research has: the article " design of the full electric brake driver of aircraft and key technology research " that is published in " computer measurement and control " be a kind of be the technology of the controller of brake system major control chip based on CPLD and DSP.But its start motor is single remaining motor, and reliability is not high; Be published in the article " the two full electric brake driving governor of the remaining design and research of aircraft " of " small and special electric machine ", adopt two remaining designs, but its control method is still continued to use classical PID control, and not high for non-linear stronger system's control precision, the brake system robustness is not strong.

Summary of the invention

In order to overcome the deficiencies in the prior art, the invention provides a kind of grey sliding-mode control for the two margin brushless DC motors of aircraft electric brake, improve reliability and the system robustness of brake system.

The scheme that the present invention solves the prior art problem may further comprise the steps:

The first step, controller receive given brake pressure P _GvAnd prediction brake pressure

In second step, calculate the brake pressure error

In the 3rd step, set up the sliding formwork line

Wherein,

Next moment pressure of system for gray model GM (1,1) prediction;

The 4th step, the current-sharing electric current output of calculating two motor windings

Wherein:

$\left\{\begin{array}{c}{\hat{i}}_1=[\mathrm{Jc}{\stackrel{\·}{P}}_{\mathrm{gv}}-\mathrm{Jc\ω}+J{\stackrel{\·\·}{P}}_{\mathrm{gv}}+\mathrm{B\ω}+T_L+\mathrm{J\ξsgn}\left(s\right)+\mathrm{Jks}]/2K_T\\ {\hat{i}}_2=[\mathrm{Jc}{\stackrel{\·}{P}}_{\mathrm{gv}}-\mathrm{Jc\ω}+J{\stackrel{\·\·}{P}}_{\mathrm{gv}}+\mathrm{B\ω}+T_L+\mathrm{J\ξsgn}\left(s\right)+\mathrm{Jks}]/2K_T\end{array}\right.$

In the formula: J is load rotating inertia, and B is the coefficient of viscosity, and ω is motor angular velocity, T _LBe load torque, K _TBe winding average torque coefficient, ξ＞0, k＞0;

The 5th goes on foot, and gathers the current feedback signal i of two motor windings respectively ₁And i ₂, calculate current error signal

And $e_{i2}={\hat{i}}_2-i_2;$

The 6th step, carry out flow equalizing ring PID control, drive two margin brushless DC machine operation;

In the 7th step, set up gray model GM (1,1):

x ⁽⁰⁾(k)+az ⁽¹⁾(k)＝b

The corresponding albefaction equation of system is:

$\frac{x^{\left(1\right)}\left(t\right)}{\mathrm{dt}}+a{x}^{\left(1\right)}\left(t\right)=b$

Wherein, parameter-a is the development coefficient, and parameter b is the grey actuating quantity,

Continuous acquisition t-4 ..., t is corresponding motor output pressure P (t-4) constantly ..., P (t) constitutes non-negative sequence

X ⁽⁰⁾＝(P(t-4),P(t-3),P(t-2),P(t-1),P(t))；

X ⁽⁰⁾The 1-AGO sequence be: X ⁽¹⁾=(x ⁽¹⁾(1), x ⁽¹⁾(2), x ⁽¹⁾(3), x ⁽¹⁾(4), x ⁽¹⁾(5))

Wherein, $x^{\left(1\right)}\left(k\right)=\underset{i=t-4}{\overset{t-5+k}{\mathrm{\Σ}}}{\mathrm{\θ}}^{\left(0\right)}\left(i\right),k=\mathrm{1,2},...,5;$

In the 8th step, calculate X ⁽¹⁾Neighbour's average formation sequence: Z ⁽¹⁾=(z ⁽¹⁾(2), z ⁽¹⁾(3), z ⁽¹⁾(4), z ⁽¹⁾(5)), wherein, $z^{\left(1\right)}\left(k\right)=\frac{1}{2}(x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}(k-1)),k=2,...,5;$

In the 9th step, calculate intermediary matrix Y, B ^T

Y＝[θ(t-3),θ(t-2),θ(t-1),θ(t)] ^T

$B^T=\left[\begin{array}{cccc}{-z}^{\left(1\right)}\left(2\right)& -z^{\left(1\right)}(3& -z^{\left(1\right)}\left(4\right)& -z^{\left(1\right)}\left(5\right)\\ 1& 1& 1& 1\end{array}\right]$

Then the parameter of grey systems GM (1,1) is: [a, b] ^T=(B ^TB) ^-1B ^TY;

In the tenth step, calculate brake system t+1 forecast pressure constantly:

$\hat{P}(t+1)=[P(t-4)-\frac{b}{a}]e^{-5a}(1-e^a);$ Go to the first step.

The invention has the beneficial effects as follows: with two margin brushless DC motors as the start motor, improve the reliability of brake system, proposed a kind of sliding formwork sharing control strategy, balance motor two cover winding currents, solution power dispute problem improves aircraft electric brake system robustness simultaneously.In order to suppress the buffeting that sliding formwork control brings, introduce the gray model prediction, eliminate and buffet.

Description of drawings

Fig. 1 is the control procedure flow chart.

Embodiment

The present invention is further described below in conjunction with accompanying drawing and example.

As shown in Figure 1, as the present invention includes following steps:

The first step, controller receive given brake pressure P _GvAnd prediction brake pressure

Went to for second step.

In second step, calculate the brake pressure error

Went to for the 3rd step.

In the 3rd step, set up the sliding formwork line

Wherein,

Next moment pressure of system for gray model GM (1,1) prediction; Went to for the 4th step.

In the 4th step, calculate the output of current-sharing electric current

Wherein:

$\left\{\begin{array}{c}{\hat{i}}_1=[\mathrm{Jc}{\stackrel{\·}{P}}_{\mathrm{gv}}-\mathrm{Jc\ω}+J{\stackrel{\·\·}{P}}_{\mathrm{gv}}+\mathrm{B\ω}+T_L+\mathrm{J\ξsgn}\left(s\right)+\mathrm{Jks}]/2K_T\\ {\hat{i}}_2=[\mathrm{Jc}{\stackrel{\·}{P}}_{\mathrm{gv}}-\mathrm{Jc\ω}+J{\stackrel{\·\·}{P}}_{\mathrm{gv}}+\mathrm{B\ω}+T_L+\mathrm{J\ξsgn}\left(s\right)+\mathrm{Jks}]/2K_T\end{array}\right.$

In the formula: J is load rotating inertia,

Be the subdifferential to setting pressure,

Be the second differential of setting pressure, B is the coefficient of viscosity, and ω is motor angular velocity, T _LBe load torque, K _TBe winding average torque coefficient, ξ＞0, k＞0; Went to for the 5th step.

In the 5th step, gather motor winding 1 current feedback signal i respectively ₁And motor winding 2 current feedback signal i ₂, calculate current error signal And Went to for the 6th step.

The 6th step, carry out flow equalizing ring PID control, drive two margin brushless DC machine operation; Went to for the 7th step.

In the 7th step, set up gray model GM (1,1):

x ⁽⁰⁾(k)+az ⁽¹⁾(k)＝b

The corresponding albefaction equation of system is:

$\frac{x^{\left(1\right)}\left(t\right)}{\mathrm{dt}}+a{x}^{\left(1\right)}\left(t\right)=b$

Wherein, parameter-a has reflected the developing state of grey systems GM (1,1) for the development coefficient, and parameter b is the grey actuating quantity, be from background value, excavate data.

Continuous acquisition t-4 ..., t is corresponding motor output pressure P (t-4) constantly ..., P (t) constitutes non-negative phase-sequence

X ⁽⁰⁾＝(P(t-4),P(t-3),P(t-2),P(t-1),P(t))。

X ⁽⁰⁾The 1-AGO sequence be: X ⁽¹⁾=(x ⁽¹⁾(1), x ⁽¹⁾(2), x ⁽¹⁾(3), x ⁽¹⁾(4), x ⁽¹⁾(5))

Wherein, $x^{\left(1\right)}\left(k\right)=\underset{i=t-4}{\overset{t-5+k}{\mathrm{\Σ}}}{\mathrm{\θ}}^{\left(0\right)}\left(i\right),k=\mathrm{1,2}.,.5;$ Went to for the 8th step.

In the 8th step, calculate X ⁽¹⁾Neighbour's average formation sequence: Z ⁽¹⁾=(z ⁽¹⁾(2), z ⁽¹⁾(3), z ⁽¹⁾(4), z ⁽¹⁾(5)) wherein, $z^{\left(1\right)}\left(k\right)=\frac{1}{2}(x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}(k-1),k=2,...,;$ Went to for the 9th step.

In the 9th step, calculate intermediary matrix Y, B ^T

Wherein,

Y＝[θ(t-3),θ(t-2),θ(t-1),θ(t)] ^T

$B^T=\left[\begin{array}{cccc}{-z}^{\left(1\right)}\left(2\right)& -z^{\left(1\right)}(3& -z^{\left(1\right)}\left(4\right)& -z^{\left(1\right)}\left(5\right)\\ 1& 1& 1& 1\end{array}\right];$

In the tenth step, the parameter of calculating grey systems GM (1,1) is:

[a, b] ^T=(B ^TB) ^-1B ^TY; Went to for the 11 step.

In the 11 step, calculate brake system t+1 forecast pressure constantly:

$\hat{P}(t+1)=[P(t-4)-\frac{b}{a}]e^{-5a}(1-e^a);$ Go to the first step.

Claims (1)

1. a grey sliding-mode control that is used for the two margin brushless DC motors of aircraft electric brake is characterized in that comprising the steps:

The first step, controller receive given brake pressure P _GvAnd prediction brake pressure

In second step, calculate the brake pressure error

In the 3rd step, set up the sliding formwork line

The 4th step, the current-sharing electric current output of calculating two motor windings

Wherein:

$\left\{\begin{array}{c}{\hat{i}}_1=[\mathrm{Jc}{\stackrel{\·}{P}}_{\mathrm{gv}}-\mathrm{Jc\ω}+J{\stackrel{\·\·}{P}}_{\mathrm{gv}}+\mathrm{B\ω}+T_L+\mathrm{J\ξsgn}\left(s\right)+\mathrm{Jks}]/2K_T\\ {\hat{i}}_2=[\mathrm{Jc}{\stackrel{\·}{P}}_{\mathrm{gv}}-\mathrm{Jc\ω}+J{\stackrel{\·\·}{P}}_{\mathrm{gv}}+\mathrm{B\ω}+T_L+\mathrm{J\ξsgn}\left(s\right)+\mathrm{Jks}]/2K_T\end{array}\right.$

In the formula: J is load rotating inertia, and B is the coefficient of viscosity, and ω is motor angular velocity, T _LBe load torque, K _TBe winding average torque coefficient, ξ＞0, k＞0;

The 5th goes on foot, and gathers the current feedback signal i of two motor windings respectively ₁And i ₂, calculate current error signal

And $e_{i2}={\hat{i}}_2-i_2;$

The 6th step, carry out flow equalizing ring PID control, drive two margin brushless DC machine operation;

In the 7th step, set up gray model GM (1,1):

x ⁽⁰⁾(k)+az ⁽¹⁾(k)＝b

The corresponding albefaction equation of system is:

$\frac{x^{\left(1\right)}\left(t\right)}{\mathrm{dt}}+a{x}^{\left(1\right)}\left(t\right)=b$

Wherein, parameter-a is the development coefficient, and parameter b is the grey actuating quantity,

Continuous acquisition t-4 ..., t is corresponding motor output pressure P (t-4) constantly ..., P (t) constitutes non-negative sequence

X ⁽⁰⁾＝(P(t-4),P(t-3),P(t-2),P(t-1),P(t))；

X ⁽⁰⁾The 1-AGO sequence be: X ⁽¹⁾=(x ⁽¹⁾(1), x ⁽¹⁾(2), x ⁽¹⁾(3), x ⁽¹⁾(4), x ⁽¹⁾(5))

Wherein, $x^{\left(1\right)}\left(k\right)=\underset{i=t-4}{\overset{t-5+k}{\mathrm{\Σ}}}{\mathrm{\θ}}^{\left(0\right)}\left(i\right),k=\mathrm{1,2},...,5;$

In the 8th step, calculate X ⁽¹⁾Neighbour's average formation sequence: Z ⁽¹⁾=(z ⁽¹⁾(2), z ⁽¹⁾(3), z ⁽¹⁾(4), z ⁽¹⁾(5)), wherein, $z^{\left(1\right)}\left(k\right)=\frac{1}{2}(x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}(k-1)),k=2,...,5;$

In the 9th step, calculate intermediary matrix Y, B ^T

Y＝[θ(t-3),θ(t-2),θ(t-1),θ(t)] ^T

$B^T=\left[\begin{array}{cccc}{-z}^{\left(1\right)}\left(2\right)& -z^{\left(1\right)}(3& -z^{\left(1\right)}\left(4\right)& -z^{\left(1\right)}\left(5\right)\\ 1& 1& 1& 1\end{array}\right]$

Then the parameter of grey systems GM (1,1) is: [a, b] ^T=(B ^TB) ^-1B ^TY;

In the tenth step, calculate brake system t+1 forecast pressure constantly:

$\hat{P}(t+1)=[P(t-4)-\frac{b}{a}]e^{-5a}(1-e^a);$ Go to the first step.

Images