CN101800505B - Method for controlling rotary speed of magnetically suspended flywheel - Google Patents

Abstract

The invention relates to a method for controlling a rotary speed of a magnetically suspended flywheel. The method comprises the following steps of: according to a feedback value of the rotary speed of the magnetically suspended flywheel, performing fuzzy adaptive kalman filtration of the feedback value of the rotary speed, performing rotary speed loop control of the magnetically suspended flywheel according to the rotary speed reference value and the filtered rotary speed value, adaptively adjusting the rotary speed loop control parameters according to the rotary speed reference value and the rotary speed deviation, and outputting the current reference value by the rotary speed loop; performing the current loop control according to the current reference value and the current feedback value; and finally, by adjusting the current value of a motor winding, realizing the high-precision control of the rotary speed of the magnetically suspended flywheel in the full-rotary speed range. The method belongs to the technical field of aerospace control, and can also be applied to the high-precision control of other dc brushless motors.

Description

A kind of method for controlling rotary speed of magnetically suspended flywheel

Technical field

The present invention relates to a kind of method for controlling rotary speed of magnetically suspended flywheel, be applicable to the High Accuracy Control of magnetically levitated flywheel rotating speed, belong to the technical field of Aerospace Control.

Background technology

Magnetically levitated flywheel is because of having no friction characteristics, makes it be easy to realize outstanding advantage such as high accuracy and long-life and the important development direction that becomes spacecraft attitude control executing mechanism such as space station, space maneuver platform and quick maneuvering satellite.Realize the high accuracy rotating speed control of magnetically levitated flywheel, high-precision speed feedback and rotating speed control are its necessary conditions.

At present, test the speed and mainly contain two kinds of methods: hall position transducer and photoelectric code disk position transducer.The problem that the hall position transducer tests the speed is that its signal output frequency is too low, and the rotating speed accuracy of detection is very poor, therefore, carries out the rotating speed High Accuracy Control and does not generally adopt the hall position transducer.The problem that adopts photoelectric code disk to carry out rotating speed detection existence is: when adopting photoelectric code disk to test the speed, because the photoelectric code disk output signal frequency is very high, receives forceful electric power easily and disturb, in addition, when the magnetically levitated flywheel rotor oscillation, deviation also appears in the rotating speed detected value.(the M/T method is meant in the process of testing the speed, and the tachometer pulse m1 that not only measures changes with the different of motor speed with high-frequency clock pulse m2 generally to carry out photoelectric code disk M/T method; And Measuring Time T also changes; Its clock equals each pulse signal cycle sum of optical pulse generator m1) test the speed and do not carry out handling, the rotating speed detected value has certain deviation, therefore; Carry out Filtering Processing to rotating speed, the general filtering method not character filter effect of consideration of noise or interference signal is relatively poor.

The High Accuracy Control that realizes magnetically levitated flywheel should guarantee that the reliability service of control program guarantees control precision again.There is perturbation in it with the slowspeed machine parameter at a high speed in the magnetically levitated flywheel running, and the system model when its control system model is with electric operation when the magnetically levitated flywheel running under braking is different.Adopt general PID control rotary speed precision can not reach requirement, adopt complicated control algolithm, reliability but can not guarantee.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiency of existing method to magnetically levitated flywheel rotating speed accuracy of detection and control performance; Propose a kind of high-precision method for controlling rotary speed of magnetically suspended flywheel, the high rotational speed control precision is all arranged in the full range of speeds of magnetically levitated flywheel.

Technical solution of the present invention is: a kind of method for controlling rotary speed of magnetically suspended flywheel, and according to given magnetically levitated flywheel speed command, the rotating-speed tracking given rotating speed value of control magnetically levitated flywheel, performing step is following:

(1) detects the flywheel tachometer value

Adopt photoelectric code disk to utilize the M/T method to test the speed; In the program of testing the speed, the photoelectric code disk signal is judged; Flip-flop number is counted after the high level of photoelectric code disk and low level keep certain hour, and to reduce the influence of high-frequency interferencing signal, photoelectric code disk umber of pulse that detects according to the M/T method at last and high frequency clock number are changed and promptly obtained current time magnetically levitated flywheel tachometer value n (k)=60f*m1/ [P* (m2+m3)]; Wherein, F is the frequency of high-frequency clock pulse, and P is the umber of pulse of sending in one week of code-disc, in official hour Tc (generally being the sampling period); Meter is got the pulse number m1 of photoelectric code disk and the pulse number m2 of high frequency clock respectively, and m3 is that Tc finishes the time interval of back to code-disc next pulse rising edge;

(2) said current time magnetically levitated flywheel tachometer value is carried out fuzzy self-adaption kalman filtering

At first, get state vector x according to the magnetically levitated flywheel motor model ₁(k)=and n (k), x ₂(k)=x ₁(k+1)-A*u (k), wherein, x ₁(k), x ₂(k) be the system mode vector, the current time magnetically levitated flywheel tachometer value that n (k) obtains for step (1), the control coefrficient of A for calculating according to system parameters, u (k) is system's output controlled quentity controlled variable.

Then system equation can be written as following state space equation formula:

$\left\{\begin{array}{c}\left[\begin{array}{c}{x}_1(k+1)\\ x_2(k+1)\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -D& -F\end{array}\right]*\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]+\left[\begin{array}{c}A\\ B-\mathrm{AF}\end{array}\right]*u\left(k\right)=G\left(k\right)+H*u\left(k\right)\\ n\left(k\right)\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]=C*x\left(k\right)\end{array}\right.$ , in the formula, D, F, A, B, G, H, C are constant matrices, and D, F, A, B are for converting system equation into the intermediate variable value of the control system parameter that obtains behind the state equation, and G is a sytem matrix, and H is an input matrix, C is an output matrix;

$G=\left[\begin{array}{cc}0& 1\\ -e^{d_{1}T}*e^{d_{2}T}& e^{d_{1}T}+e^{d_{2}T}\end{array}\right],$

$H=\begin{array}{}\end{array}\left[\begin{array}{c}\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_2*e^{d_{1}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{2}T}+d_1-d_2)}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)}\\ \frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}({\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{1}T}*e^{d_{2}T}-d_2*e^{d_{1}T}+d_2*e^{d_{2}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{1}T})}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)}-\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_2*e^{d_{1}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{2}T}+d_1-d_2)}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)}*(e^{d_{1}T}-e^{d_{2}T})\end{array}\right]$

C=[10], wherein, J is the magnetically levitated flywheel moment of inertia, k _eBe back EMF coefficient, B is a damping coefficient, and u is an electric power output voltage, and R is a motor windings resistance, and L is the motor windings inductance, d ₁, d ₂Be two of system features equations; E is the natural logrithm truth of a matter, and T is the sampling time.

The state estimation equation of kalman filter:

In the formula,

Be the state estimation value;

Be the state predicted value; K (k) is the filter gain matrix; The filter gain matrix K (k) of kalman filtering can be calculated as follows: K (k)=δ (k) * P (k/k-1) * C ^T* (C*P (k/k-1) * C ^T+ r (k)) ^-1, P (k/k-1)=G*P (k-1) * G ^T+ H*Q*H ^T, P (k)=(I-K (k) * C) * P (k/k-1)

Wherein,

C (k)=η (k)/τ (k), η (k)=E (k)-ε * r-C*G*C ^T, τ (k)=C*G*P (k) * G ^T* C ^T,

In the formula, δ (k) is the decline factor matrix, and P (k/k-1) is the one-step prediction mean square error, and C is an output matrix; P (k) is for estimating mean square error, and r (k) is the measuring noise square difference battle array, and G is a sytem matrix, and H is an input matrix; Q is a system noise variance battle array, and P (k) is for estimating mean square error, and K (k) is the filter gain matrix; Decline factor matrix δ (k) is confirmed that by softening factor ε and forgetting factor ρ e (k) is for the actual measurement rotating speed and estimate rotating speed deviation, e ₀Initial time rotating speed deviation, ε regulates through fuzzy self-adaption and confirms that c (k) is the decline amount, and E (k) is an error matrix, and η (k) is that current time square-error amount, τ (k) they are current time estimated bias amount of variation;

(3) carry out rotating speed control according to filtered tachometer value

The rotating speed control of magnetically levitated flywheel electric machine control system is through the outer shroud der Geschwindigkeitkreis; The double loop control of interior circular current ring realizes; Der Geschwindigkeitkreis and electric current loop all adopt and become the realization of integral PID control method, and wherein der Geschwindigkeitkreis is according to carrying out der Geschwindigkeitkreis control through filtered tachometer value and speed reference, and the der Geschwindigkeitkreis Control Parameter is carried out self adaptation according to rotating speed reference and rotating speed absolute value of the bias and regulated; Through der Geschwindigkeitkreis control output current reference value, be used for magnetically levitated flywheel motor windings Current Control; The current loop control program is carried out magnetically levitated flywheel motor windings Current Control according to the current reference value and the current feedback value of der Geschwindigkeitkreis output; The current loop control parameter will be according to magnetically levitated flywheel running status, reference rotation velocity value and current deviation absolute value real-time regulated, and electric current loop output controlled quentity controlled variable directly is used for the drive motors operation.

Fuzzy self-adaption kalman filtering parameter ε regulates through fuzzy self-adaption and confirms that method is following in the inventive method:

Fuzzy controller adopts single order T-S model, and what make controller is input as ζ=e (k) ², membership function is:

$\mathrm{\&mu;}=\left\{\begin{array}{cc}0& \mathrm{\&zeta;}\&le;{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\\ \frac{\mathrm{\&zeta;}-t_1}{t_2-t_1}& {\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;\mathrm{\&zeta;}\&le;t_2\\ 1& t_2\&le;\mathrm{\&zeta;}\&le;t_3\\ \frac{t_4-\mathrm{\&zeta;}}{t_4-t_3}& t_3\&le;\mathrm{\&zeta;}\&le;t_4\\ 0& t_4\&le;\mathrm{\&zeta;}\end{array}\right.,$ T wherein ₁, t ₂, t ₃, t ₄Be the point in the input parameter domain, fuzzy control rule

Then following:

Principle of the present invention is: in the magnetically levitated flywheel control procedure, because control system exists certainty to disturb and uncertain interference, constantly all cannot foresee for the frequency of disturbance, the size of disturbance, the generation of disturbance.But these disturbances have bigger influence to the performance of control system.Just must carry out Filtering Processing if obtain to control effect preferably to the speed feedback value.When magnetically levitated flywheel was operated in different rotating speeds, different running status (electronic, dynamic braking, plug braking), the rotating speed of flywheel was different, and the electric current of motor windings is different, and the disturbance size of generation is also inequality with frequency.Therefore filtering method is wanted and can be regulated filter factor according to the system noise self adaptation.The present invention adopts fuzzy self-adaption kalman filtering method, if less with the priori understanding that measures model to system model in filtering, will reduce the performance of kalman filtering, even can excitation filter disperse.Fuzzy self-adaption kalman filtering method is used the inconsistency that decline factor matrix δ (k) increases the predicted state vector, be the to fail calculating of matrix of the main difference of different fading memory algorithms.Filter is in the stabilized treatment state when δ (k)＜=1; When δ (k)=1, deteriorate to general kalman filtering method, filter is tending towards unstable when δ (k)＞=1.Adopt the defective of the normal value decline factor to be, in filtering owing to before the influence of data more and more littler, the precision of filter will descend.Therefore the decline factor that best method becomes when being exactly employing improves precision of filtering and dynamic property.The present invention regulates the size of the factor delta (k) that fails through detecting the deviation of surveying rotating speed and estimating rotating speed, thereby adjustment filter gain matrix K (k) reaches filter effect preferably.The filter gain matrix K (k) of kalman filtering can be calculated as follows:

K (k)=δ (k) * P (k/k-1) * C ^T* (C*P (k/k ^-1) * C ^T+ r (k)) ^-1, P (k/k-1)=G*P (k-1) * G ^T+ H*Q*H ^T, P (k)=(I-K (k) * C) * P (k/k-1) wherein,

C (k)=η (k)/τ (k), η (k)=E (k)-ε * r-C*G*C ^T, τ (k)=C*G*P (k) * G ^T* C ^T,

In the formula, δ (k) is the decline factor matrix, and P (k/k-1) is the one-step prediction mean square error, and C is an output matrix; P (k) is for estimating mean square error, and r (k) is the measuring noise square difference battle array, and G is a sytem matrix, and H is an input matrix; Q is a system noise variance battle array, and P (k) is for estimating mean square error, and K (k) is the filter gain matrix, and decline factor matrix δ (k) is confirmed by softening factor ε and forgetting factor ρ; E (k) is actual measurement rotating speed and estimation rotating speed deviation, e0 initial time rotating speed deviation, and ε regulates through fuzzy self-adaption and confirms; C (k) is the decline amount, and E (k) is an error matrix, and η (k) is that current time square-error amount, τ (k) are current time estimated bias amount of variation; Rule of thumb, the ρ value is 0.95, and ε regulates through fuzzy self-adaption and confirms;

Fuzzy self-adaption kalman filtering parameter ε regulates through fuzzy self-adaption and confirms that method is following:

Because the zeroth order model needs more complicated membership function and rule base, so the fuzzy controller of this control system adopts single order T-S model, because speed error can directly reflect the control precision of rotating speed, what make controller is input as ζ=e (k) ², choose simple and effective trapezoidal membership function, make membership function be:

$\mathrm{\&mu;}=\left\{\begin{array}{cc}0& \mathrm{\&zeta;}\&le;{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\\ \frac{\mathrm{\&zeta;}-t_1}{t_2-t_1}& {\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;\mathrm{\&zeta;}\&le;t_2\\ 1& t_2\&le;\mathrm{\&zeta;}\&le;t_3\\ \frac{t_4-\mathrm{\&zeta;}}{t_4-t_3}& t_3\&le;\mathrm{\&zeta;}\&le;t_4\\ 0& t_4\&le;\mathrm{\&zeta;}\end{array}\right.,$ T wherein ₁, t ₂, t ₃, t ₄Be the point in the input parameter domain, fuzzy control rule is following:

In the magnetically levitated flywheel control procedure; Because there is perturbation in system's controlling models when different running statuses and different rotating speeds value; Realize that high-precision rotating speed control must could realize the High Accuracy Control of magnetically levitated flywheel rotating speed according to magnetically levitated flywheel running status, reference rotation velocity value, speed feedback value, rotating speed deviate and current deviation value real-time regulated der Geschwindigkeitkreis, current loop control parameter and maximum duty cycle set-point.

Scheme of the present invention is compared with existing scheme, and major advantage is:

(1) traditional M/T rotating speed detection method is not anticipated tacho-pulse; The present invention judges the photoelectric code disk signal in the program of testing the speed; Flip-flop number is counted after the high level of photoelectric code disk and low level keep certain hour, to reduce the influence of high-frequency interferencing signal.

(2) traditional control method is directly utilized tachometer value, control poor-performing when there is fluctuation in rotating speed, and the present invention adopts fuzzy self-adaption kalman filtering method at first tachometer value to be carried out adaptive-filtering, and filtering interference signals carries out rotating speed control again.

(3) traditional control method is directly utilized fixing Control Parameter; Because there is perturbation in the high low speed parameter of magnetically levitated flywheel; The electrodynamic braking system model is different therefore relatively poor at full range of speeds control performance; The present invention adopts the method for parametric programming, to running status, reference rotation velocity, reference current, the current deviation value self adaptation adjustment Control Parameter of magnetically levitated flywheel.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a fuzzy self-adaption kalman filtering algorithm flow chart of the present invention;

Fig. 3 is a fuzzy membership function of the present invention;

Fig. 4 is a system construction drawing of the present invention.

Specific embodiments

As shown in Figure 1, in the practical implementation process, practical implementation step of the present invention is following:

At first, adopt fuzzy self-adaption kalman filtering method that the magnetically levitated flywheel tachometer value is carried out Real-Time Filtering.The der Geschwindigkeitkreis control program is regulated der Geschwindigkeitkreis Control Parameter, der Geschwindigkeitkreis output current ring reference current according to the reference rotation velocity value and through the filtered speed feedback value of fuzzy self-adaption kalman self adaptation.The current loop control program is confirmed the electric current loop maximum duty cycle based on the speed feedback value, and regulates current ring parameter and output current ring controlled quentity controlled variable based on speed reference, current deviation value self adaptation.Specifically may further comprise the steps:

(1) calculates the real-time tachometer value of magnetically levitated flywheel

Magnetically levitated flywheel adopts photoelectric code disk to test the speed, and speed-measuring method is the M/T method, and wherein choosing of timer will be confirmed according to the control precision and the dynamic response requirement of system in the M/T speed-measuring method; System's control precision requires high more, and the timer setting is long more, and the feedback speed precision is just high more, but the real-time of control is just relatively poor; It is short more that timer is provided with, and the real-time update property of speed feedback is just fast more, but the precision of speed feedback will be poor more; Consider that through compromise choosing the timer that tests the speed is 0.6s; The control frequency of der Geschwindigkeitkreis is 5KHz, because the frequency of photoelectric code disk signal is very high, is subject to disturb; When rotating speed is low; Therefore the photoelectric code disk counting error is bigger to the influence of control precision, in the program of testing the speed, the photoelectric code disk signal is judged, flip-flop number is counted behind the high level of photoelectric code disk and low level maintenance certain hour; To reduce the influence of high-frequency interferencing signal, photoelectric code disk umber of pulse that detects according to the M/T method at last and high frequency clock number are changed and are promptly obtained current time magnetically levitated flywheel tachometer value.

(2) the current time magnetically levitated flywheel speed feedback value that detects according to the M/T method is carried out filtering to reduce the influence of disturbing to the speed feedback value, and filtering clicks step and carries out:

A, set up the magnetically levitated flywheel equation of motion

At first, set up the magnetically levitated flywheel motor model: $\left\{\begin{array}{c}\frac{\mathrm{D\&omega;}}{\mathrm{Dt}}=\frac{1}{J}{k}_{e}i-\frac{B}{J}\mathrm{\&omega;}\\ \frac{\mathrm{Di}}{\mathrm{Dt}}=\frac{1}{L}u-\frac{R}{L}i-\frac{k_e}{L}\mathrm{\&omega;}\end{array}\right.---\left(1\right)$

Wherein, ω magnetically levitated flywheel angular speed, J are the magnetically levitated flywheel moment of inertia, k _eBe back EMF coefficient, B is a damping coefficient, and u is an electric power output voltage, and R is a motor windings resistance, and L is the motor windings inductance, and the biography letter that can get flywheel angular speed and electric power output voltage is:

$\frac{\mathrm{\&omega;}\left(s\right)}{U\left(s\right)}=\frac{k_e}{J*L*s^2+R*J*s+{k_e}^2}---\left(2\right)$

The system that further can release flywheel rotating speed and electric power output voltage passes letter:

$\frac{N\left(s\right)}{U\left(s\right)}=\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}}{s^2+\frac{R}{L}s+\frac{{k_e}^2}{J*L}},$ Order $a=\frac{30*k_e}{J*L*\mathrm{\&pi;}},$ $b=\frac{R}{L},$ $c=\frac{{k_e}^2}{J*L}---\left(3\right)$

System's biography letter is carried out the z conversion to be got

$\frac{N\left(z\right)}{U\left(z\right)}=Z\left[\frac{1-e^{-\mathrm{Ts}}}{s}\frac{a}{s^2+\mathrm{bs}+c}\right]=\frac{A*z+B}{z^2+F*z+D}---\left(4\right)$

Wherein,

$A=\frac{a*(d_2*e^{d_{1}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{2}T}+d_1-d_2)}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)},$ $B=\frac{a*({\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*{e^{d_{1}T}*e^{d_2}}^T-d_2*e^{d_{1}T}*e^{d_{2}T}+d_2*e^{d_{2}T}-d_1{e}^{d_{1}T})}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)},$ $F=-e^{d_{1}T}-e^{d_{2}T},$ $D=e^{d_{1}T}{e}^{d_{2}T},$ T is the sampling period.Get state vector x ₁(k)=and n (k), x ₂(k)=x ₁(k+1)-A*u (k), wherein, x ₁(k), x ₂(k) be the system mode vector, the current time magnetically levitated flywheel tachometer value that n (k) obtains for step (1), the control coefrficient of A for calculating according to system parameters, u (k) is system's output controlled quentity controlled variable.

Then system equation can be written as following state space equation formula:

$\left\{\begin{array}{c}\left[\begin{array}{c}{x}_1(k+1)\\ x_2(k+1)\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -D& -F\end{array}\right]*\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]+\left[\begin{array}{c}A\\ B-\mathrm{AF}\end{array}\right]*u\left(k\right)=G\left(k\right)+H*u\left(k\right)\\ n\left(k\right)\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]=C*x\left(k\right)\end{array}\right.$ In the formula, D, F, A, B, G, H, C are constant matrices, and D, F, A, B are for converting system equation into the intermediate variable value of the control system parameter that obtains behind the state equation, and G is a sytem matrix, and H is an input matrix, and C is an output matrix.

$G=\left[\begin{array}{cc}0& 1\\ -e^{d_{1}T}*e^{d_{2}T}& e^{d_{1}T}+e^{d_{2}T}\end{array}\right],$

$H=\begin{array}{}\end{array}\left[\begin{array}{c}\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_2*e^{d_{1}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{2}T}+d_1-d_2)}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)}\\ \frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}({\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{1}T}*e^{d_{2}T}-d_2*e^{d_{1}T}+d_2*e^{d_{2}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{1}T})}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)}-\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_2*e^{d_{1}T}-{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*e^{d_{2}T}+d_1-d_2)}{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1*d_2*(d_1-d_2)}*(e^{d_{1}T}-e^{d_{2}T})\end{array}\right]$

C=[1 0], wherein, J is the magnetically levitated flywheel moment of inertia, k _eBe back EMF coefficient, B is a damping coefficient, and u is an electric power output voltage, and R is a motor windings resistance, and L is the motor windings inductance, d ₁, d ₂Be two of system features equations; E is the natural logrithm truth of a matter, and T is the sampling time.

B, the magnetic suspension tachometer value is carried out fuzzy self-adaption kalman filtering

Adopt fuzzy self-adaption kalman filtering method that the actual measurement tachometer value is carried out Real-Time Filtering, to reduce the fluctuation of speed, the state estimation equation of kalman filter:

In the formula,

Be the state estimation value;

Be the state predicted value; K (k) is the filter gain matrix; The filter gain matrix K (k) of kalman filtering can be calculated as follows: K (k)=δ (k) * P (k/k-1) * C ^T* (C*P (k/k-1) * C ^T+ r (k)) ^-1, P (k/k-1)=G*P (k-1) * G ^T+ H*Q*H ^T, P (k)=(I-K (k) * C) * P (k/k-1)

Wherein,

C (k)=η (k)/τ (k), η (k)=E (k)-ε * r-C*G*C ^T, τ (k)=C*G*P (k) * G ^T* C ^T,

In the formula, δ (k) is the decline factor matrix, and P (k/k-1) is the one-step prediction mean square error, and C is an output matrix; P (k) is for estimating mean square error, and r (k) is the measuring noise square difference battle array, and G is a sytem matrix, and H is an input matrix; Q is a system noise variance battle array, and P (k) is for estimating mean square error, and K (k) is the filter gain matrix; Decline factor matrix δ (k) is confirmed that by softening factor ε and forgetting factor ρ e (k) is for the actual measurement rotating speed and estimate rotating speed deviation, e ₀Initial time rotating speed deviation, c (k) is the decline amount, and E (k) is an error matrix, and η (k) is that current time square-error amount, τ (k) they are current time estimated bias amount of variation; ε regulates through fuzzy self-adaption and confirms that method is following:

Fuzzy controller adopts single order T-S model, and what make controller is input as ζ=e (k) ², membership function is:

$\mathrm{\&mu;}=\left\{\begin{array}{cc}0& \mathrm{\&zeta;}\&le;{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\\ \frac{\mathrm{\&zeta;}-t_1}{t_2-t_1}& {\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000054075800021.png,HSA00000054075800031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\&le;\mathrm{\&zeta;}\&le;t_2\\ 1& t_2\&le;\mathrm{\&zeta;}\&le;t_3\\ \frac{t_4-\mathrm{\&zeta;}}{t_4-t_3}& t_3\&le;\mathrm{\&zeta;}\&le;t_4\\ 0& t_4\&le;\mathrm{\&zeta;}\end{array}\right.,$ T wherein ₁, t ₂, t ₃, t ₄Be the point in the input parameter domain, fuzzy control rule

Then following:

(3) carry out rotating speed control according to filtered tachometer value

The rotating speed control of magnetically levitated flywheel electric machine control system is through the outer shroud der Geschwindigkeitkreis; The double loop control of interior circular current ring, der Geschwindigkeitkreis and electric current loop all adopt and become the realization of integral PID control method, and wherein der Geschwindigkeitkreis is according to carrying out der Geschwindigkeitkreis control through filtered tachometer value and speed reference; The der Geschwindigkeitkreis Control Parameter is carried out self adaptation according to rotating speed reference and rotating speed absolute value of the bias and is regulated; Control program is at first judged the scope of speed reference, and Control Parameter is different when speed reference is different, when speed reference is big; The proportionality coefficient of der Geschwindigkeitkreis is bigger, otherwise less.Further judge the size of rotating speed absolute value of the bias, the der Geschwindigkeitkreis proportionality coefficient is bigger when the rotating speed absolute value of the bias is very big, and integral coefficient is zero or for very little, if absolute value of the bias has bigger integral coefficient can cause system overshoot bigger when big, the adjusting time is longer; With the rotating speed absolute value of the bias reduce proportionality coefficient is reduced, integral coefficient increases.The der Geschwindigkeitkreis pid algorithm adopts the proportional integral algorithm; Its controller form is:

the present invention set five different rotating speed Error Absolute Value scopes, be respectively e_speed (speed error absolute value) ∈ {＞200 ∪ [200100] ∪ [10050] ∪ [501] ∪＜1}., the speed error absolute value sets kp=305, ki=0.00001 in being in maximum scope when (e_speed＞200); , the speed error absolute value sets kp=95, ki=0.01 in being in minimum scope when (e_speed＜1); When the speed error absolute value is between two limiting error scopes, kp, the value of ki is between the value of border.

Der Geschwindigkeitkreis control output current reference value is used for magnetically levitated flywheel motor windings Current Control; The current loop control program is carried out magnetically levitated flywheel motor windings Current Control according to the current reference value and the current feedback value of der Geschwindigkeitkreis output; The current loop control parameter will be according to magnetically levitated flywheel running status, reference rotation velocity value and current deviation real-time regulated, and electric current loop output controlled quentity controlled variable directly is used for the drive motors operation.Control program is at first judged the scope of speed reference, and Control Parameter is different when speed reference is different, and when speed reference was big, the proportionality coefficient of electric current loop was bigger, otherwise less.Further judge the size of current deviation absolute value, the electric current loop proportionality coefficient is bigger when the current deviation absolute value is very big, and integral coefficient is zero or for very little, if absolute value of the bias has bigger integral coefficient can cause system overshoot bigger when big, the adjusting time is longer; With the current deviation absolute value reduce proportionality coefficient is reduced, integral coefficient increases.The electric current loop pid algorithm adopts the proportional integral algorithm, and its controller form is:

adopts the integral-separated PI implementation in DSP.The present invention sets five different current error absolute value scopes and is respectively e_cur (current error absolute value) ∈ {＞1 ∪ [0.60.3] ∪ [0.30.1] ∪ [0.10.05] ∪＜0.01} is as setting kp=1200 when (e_speed＞1) in the current error absolute value the is in maximum scope, ki=0.01; , the current error absolute value sets kp=20, ki=10 in being in minimum scope when (e_speed＜0.01); When the current error absolute value is between two limiting error scopes, kp, the value of ki is between the value of border.

For preventing the overcurrent in the running, the maximum duty cycle to electric current loop in the magnetically levitated flywheel running limits, and the maximum duty cycle of electric current loop carries out real-time regulated according to flywheel running status and rotating speed.Maximum duty cycle is less when rotating speed is low, improves maximum duty cycle gradually with the rising of rotating speed.

When satisfying given different reference rotation velocity, control system can both reach reference rotation velocity more accurately with higher dynamic responding speed, and the current loop control parameter will be according to reference rotation velocity value and current deviation absolute value real-time regulated; The current loop control program is carried out electric current loop PID computing according to the reference current value and the current feedback value of der Geschwindigkeitkreis output, and output current ring controlled quentity controlled variable.

Be illustrated in figure 2 as the algorithm flow chart of fuzzy self-adaption kalman filtering.At first; Confirm the initial value of state vector and mean square error according to the initial condition of system; The state initial value of choosing in the embodiment of the invention

step transition matrix

measures battle array

measuring noise square difference battle array r (k)=10000, and system noise variance battle array

is calculated each intermediate variable according to flow chart shown in Figure 2.By formula K (k)=δ (k) * P (k/k-1) * C ^T(C*P (k/k-1) * C ^T+ r (k)) ^-1Calculation of filtered gain K (k); Calculate estimated bias e (k) according to speed feedback value and rotating speed estimated value; According to the state predicted value

With filter gain matrix K (k) by formula

Computing mode is estimated

Calculate mean square error P (k) with one-step prediction mean square error P (k/k-1) according to formula P (k)=(I-K (k) * C) * P (k/k-1) by filter gain matrix K (k); Adopt the method adjustment parameter ε of fuzzy control according to estimated bias e (k), and pass through ε value adjustment decline factor delta (k), by system equation

Obtain the one-step prediction value of state

By P (k+1/k)=G*P (k) * G ^T+ H*Q*H ^TObtain one-step prediction mean square error P (k+1/k), and through the state estimation equation Obtain the filter value of actual speed.

Be illustrated in figure 3 as the fuzzy parameter of the present invention membership function of adjusting.Fuzzy membership function is obtained by control magnetically levitated flywheel experience, adopts fuzzy controller to adopt single order T-S model in the present invention, and what make controller is input as ζ=e (k) ², membership function is taken as trapezoidal function, and expression formula is:

T wherein ₁, t ₂, t ₃, t ₄Be the point among the input parameter domain T, wherein fuzzy domain is T ∈ [0 20], has 3 fuzzy control rules following:

Be illustrated in figure 4 as system construction drawing of the present invention.The present invention adopts der Geschwindigkeitkreis, the control of electric current loop dicyclo for the high accuracy that realizes the flywheel rotating speed.Der Geschwindigkeitkreis is interior ring for the outer shroud electric current loop; The PID control method is adopted in der Geschwindigkeitkreis control; The der Geschwindigkeitkreis Control Parameter is regulated according to speed reference and rotating speed deviate, and der Geschwindigkeitkreis proportionality coefficient given when speed reference is big is bigger, and integral coefficient is less to reduce system overshoot; Proportionality coefficient is bigger when rotating speed absolute value of the bias value is big equally, and integral coefficient is less; When speed reference and rotating speed absolute value of the bias value hour, proportionality coefficient is less, integral coefficient is more greatly to improve control precision.Der Geschwindigkeitkreis output current reference value, electric current loop is according to current reference value and current feedback value output current ring controlled quentity controlled variable, to carry out current loop control.

Electric current loop adopts the PID control method; When satisfying given different reference rotation velocity; Control system can both reach reference rotation velocity more accurately with higher dynamic responding speed, and the current loop control parameter will be according to magnetically levitated flywheel running status, reference rotation velocity value and current deviation absolute value real-time regulated; Electric current loop proportionality coefficient given when speed reference is big is bigger; Integral coefficient is less, and proportionality coefficient is bigger when current deviation absolute value value is big equally to reduce system overshoot, and integral coefficient is less; When speed reference and current deviation absolute value value hour, proportionality coefficient is less, integral coefficient is more greatly to improve control precision.Through electric current loop PID control output current ring controlled quentity controlled variable, the operation of driven magnetic suspending flywheel motor.

For preventing the overcurrent in the running, the maximum duty cycle to electric current loop in the magnetically levitated flywheel running limits, and the maximum duty cycle of electric current loop carries out real-time regulated according to flywheel running status and rotating speed.Maximum duty cycle is less when rotating speed is low, improves maximum duty cycle gradually with the rising of rotating speed.

The content of not doing in the present disclosure to describe in detail belongs to this area professional and technical personnel's known prior art.

Claims (2)

1. method for controlling rotary speed of magnetically suspended flywheel is characterized in that performing step is following:

(1) detects the flywheel tachometer value

Adopt photoelectric code disk to utilize the M/T method to test the speed; In the program of testing the speed, the photoelectric code disk signal is judged; Flip-flop number is counted after the high level of photoelectric code disk and low level keep certain hour, and to reduce the influence of high-frequency interferencing signal, photoelectric code disk umber of pulse that detects according to the M/T method at last and high frequency clock number are changed and promptly obtained current time magnetically levitated flywheel tachometer value n (k)=60f*m1/ [P* (m2+m3)]; Wherein, F is the frequency of high-frequency clock pulse, and P is the umber of pulse of sending in one week of code-disc, in official hour Tc; Meter is got the pulse number m1 of photoelectric code disk and the pulse number m2 of high frequency clock respectively, and m3 is that Tc finishes the time interval of back to code-disc next pulse rising edge;

(2) said current time magnetically levitated flywheel tachometer value is carried out fuzzy self-adaption kalman filtering

At first, get state vector x according to the magnetically levitated flywheel motor model ₁(k)=and n (k), x ₂(k)=x ₁(k+1)-Au (k), wherein, x ₁(k), x ₂(k) be the system mode vector, the current time magnetically levitated flywheel tachometer value that n (k) obtains for step (1), the control coefrficient of A for calculating according to system parameters, u (k) is system's output controlled quentity controlled variable, then system equation can be written as following state space equation formula:

$\left\{\begin{array}{c}\left[\begin{array}{c}{x}_1(k+1)\\ x_2(k+1)\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -D& -F\end{array}\right]*\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]+\left[\begin{array}{c}A\\ B-A*F\end{array}\right]*u\left(k\right)=G*x\left(k\right)+H*u\left(k\right)\\ n\left(k\right)=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\end{array}\right]=C*x\left(k\right)\end{array}\right.,$ In the formula, D, F, A, B, G, H, C are constant matrices, and D, F, A, B are for converting system equation into the intermediate variable value of the control system parameter that obtains behind the state equation, and G is a sytem matrix, and H is an input matrix, and C is an output matrix;

$G=\left[\begin{array}{cc}0& 1\\ -e^{d_{1}T}*e^{d_{2}T}& e^{d_{1}T}+e^{d_{2}T}\end{array}\right],$

$H=\left[\begin{array}{c}\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_2*e^{d_{1}T}-d_1*e^{d_{2}T}+d_1-d_2)}{d_1*d_2*(d_1-d_2)}\\ \frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_1*e^{d_{1}T}*e^{d_{2}T}-d_2*e^{d_{1}T}*e^{d_{2}T}+d_2*e^{d_{2}T}-d_1*e^{d_{1}T})}{d_1*d_2*(d_1-d_2)}-\frac{\frac{30*k_e}{J*L*\mathrm{\&pi;}}(d_2*e^{d_{1}T}-d_1*e^{d_{2}T}+d_1-d_2)}{d_1*d_2*(d_1-d_2)}*(-e^{d_{1}T}-e^{d_{2}t})\end{array}\right]$

C=[1 0], wherein, J is the magnetically levitated flywheel moment of inertia, k _eBe back EMF coefficient, L is the motor windings inductance, d ₁, d ₂Be two of system features equations; E is the natural logrithm truth of a matter, and T is the sampling time;

The state estimation equation of kalman filter: $\hat{x}\left(k\right)=\hat{x}\left(k\right|k-1)+K\left(k\right)*[n\left(k\right)-C*\hat{x}\left(k\right|k-1)],$ In the formula,

Be the state estimation value;

Be the state predicted value; K (k) is the filter gain matrix; The filter gain matrix K (k) of kalman filtering can be calculated as follows: K (k)=δ (k) * P (k|k-1) * C ^T* (C*P (k|k-1) * C ^T+ r (k)) ^-1, P (k|k-1)=G*P (k-1) * G ^T+ H*Q*H ^T, P (k)=(I-K (k) * C) * P (k|k-1) wherein, $\mathrm{\&delta;}\left(k\right)=\left\{\begin{array}{cc}c\left(k\right),& c\left(k\right)>=1\\ 1& c\left(k\right)<1\end{array}\right.,$ C (k)=η (k)/τ (k), η (k)=E (k)-ε * r-C*G*C ^T, τ (k)=C*G*P (k) * G ^T* C ^T, $E\left(k\right)=\left\{\begin{array}{cc}{e_0}^2& k=0\\ \frac{[\mathrm{\&rho;}*E(k-1)+e{\left(k\right)}^2]}{1+\mathrm{\&rho;}}& k>=1\end{array}\right.,$ $e\left(k\right)=n\left(k\right)-\hat{n}\left(k\right|k-1),$ In the formula, δ (k) is the decline factor matrix, and P (k|k-1) is the one-step prediction mean square error, and C is an output matrix; P (k) is for estimating mean square error, and r is the measuring noise square difference battle array, and G is a sytem matrix, and H is an input matrix; Q is a system noise variance battle array, and P (k) is for estimating mean square error, and K (k) is the filter gain matrix; Decline factor matrix δ (k) is confirmed that by softening factor ε and forgetting factor ρ e (k) is for the actual measurement rotating speed and estimate rotating speed deviation, e ₀Initial time rotating speed deviation, ε regulates through fuzzy self-adaption and confirms that c (k) is the decline amount, and E (k) is an error matrix, and η (k) is that current time square-error amount, τ (k) they are current time estimated bias amount of variation;

(3) carry out rotating speed control according to filtered tachometer value

The rotating speed control of magnetically levitated flywheel electric machine control system is through the outer shroud der Geschwindigkeitkreis; The double loop control of interior circular current ring realizes; Der Geschwindigkeitkreis and electric current loop all adopt and become the realization of integral PID control method, and wherein der Geschwindigkeitkreis is according to carrying out der Geschwindigkeitkreis control through filtered tachometer value and speed reference, and the der Geschwindigkeitkreis Control Parameter is carried out self adaptation according to rotating speed reference and rotating speed absolute value of the bias and regulated; Der Geschwindigkeitkreis control output current reference value is used for magnetically levitated flywheel motor windings Current Control; The current loop control program is carried out magnetically levitated flywheel motor windings Current Control according to the current reference value and the current feedback value of der Geschwindigkeitkreis output; The current loop control parameter will be according to magnetically levitated flywheel running status, reference rotation velocity value and current deviation absolute value real-time regulated, and electric current loop output controlled quentity controlled variable directly is used for the drive motors operation.

2. a kind of method for controlling rotary speed of magnetically suspended flywheel according to claim 1 is characterized in that: the method that the said softening factor of step (2) ε confirms through the fuzzy self-adaption adjusting is following:

Fuzzy controller adopts single order T-S model, and what make controller is input as ζ=e (k) ², membership function is:

T wherein ₁, t ₂, t ₃, t ₄Be the point in the input parameter domain, fuzzy control rule is following:

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