CN103728883B - The control method of active control type magnetic suspension system free of position sensor - Google Patents

The control method of active control type magnetic suspension system free of position sensor Download PDF

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CN103728883B
CN103728883B CN201410018572.2A CN201410018572A CN103728883B CN 103728883 B CN103728883 B CN 103728883B CN 201410018572 A CN201410018572 A CN 201410018572A CN 103728883 B CN103728883 B CN 103728883B
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electromagnet
suspension system
magnetic suspension
magnet coil
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CN103728883A (en
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于占东
赵旭东
尹珅
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Bohai University
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Abstract

The control method of active control type magnetic suspension system free of position sensor, belongs to the control technology field of magnetic suspension system.The present invention, in order to solve the existence of existing active control type magnetic suspension system due to position transducer, causes the problem of the poor robustness of system.It obtains the electric current of the magnet coil of magnetic suspension system by current sensor collection, AD converter is adopted to be converted to current digital signal by gathering the current analog signal obtained, position estimation unit obtains the position signalling of the suspension of magnetic suspension system by calculating according to described current digital signal, the position signalling of suspension and the desired locations signal pre-seted are made comparisons, obtain position error signal, after controller processes this position error signal, obtain the control signal to pwm signal generator, the voltage pulse signal that this control signal makes pwm signal generator produce corresponding dutycycle controls magnet coil.The present invention is used for the control of magnetic suspension system.

Description

The control method of active control type magnetic suspension system free of position sensor
Technical field
The present invention relates to the control method of active control type magnetic suspension system free of position sensor, belong to the control technology field of magnetic suspension system.
Background technology
Magnetic levitation technology is the good characteristic such as noise is little, pollution-free, mechanical contact owing to having, and has broad application prospects, it can eliminate frictional resistance, extension device serviceable life and reduce energy loss.Along with the development of control theory, electronic technology, electromagnetic theory and novel Electromagnetic Material, magnetic levitation technology have also been obtained significant progress.In recent years, magnetic levitation technology is widely used in a lot of fields, as magnetic suspension train, magnetic suspension bearing, high speed magnetic suspension motor etc.
Sensor is one of core component of existing active control type magnetic suspension system, due to the existence of position transducer, the cost of system and installation difficulty is raised.Meanwhile, the linearity, sensitivity, resolution etc. of position transducer are subject to the interference of the factor such as environment temperature and electromagnetic noise, and the control performance of system is affected, and this robustness that result also in magnetic suspension system is poor.These problems all greatly limit magnetic levitation technology application industrially.
Summary of the invention
The present invention seeks to, in order to solve the existence of existing active control type magnetic suspension system due to position transducer, to cause the problem of the poor robustness of system, provide a kind of control method of active control type magnetic suspension system free of position sensor.
The control method of active control type magnetic suspension system free of position sensor of the present invention, it obtains the electric current of the magnet coil of magnetic suspension system by current sensor collection, AD converter is adopted to be converted to current digital signal by gathering the current analog signal obtained, position estimation unit obtains the position signalling of the suspension of magnetic suspension system by calculating according to described current digital signal, the position signalling of suspension and the desired locations signal pre-seted are made comparisons, obtain position error signal, after controller processes this position error signal, obtain the control signal to pwm signal generator, this control signal makes pwm signal generator produce the voltage pulse signal of corresponding dutycycle, this voltage pulse signal realizes the control to magnet coil by driving circuit, and then the position control realized the suspension of magnetic suspension system.
The position signalling of suspension and the desired locations signal pre-seted, are made comparisons by calculating the position signalling of the suspension obtaining magnetic suspension system according to described current digital signal by described position estimation unit, and the detailed process obtaining position error signal is:
The electromagnet inductance L of magnetic suspension system is:
In formula, N is the number of turn of magnet coil, for the equivalent magnetic resistance of electromagnet system be made up of electromagnet and magnet coil;
Electromagnet inductance L is relevant to the width of air gap x between electromagnet and suspension, and the estimated value of electromagnet inductance L obtains by experiment, and its acquisition process is:
Width of air gap x between power taking magnet and suspension is a constant value, applies the excitation voltage of PWM form to magnet coil, and make electromagnet produce exciting curent, now, the differential equation in electromagnet system loop is:
d dt i = 1 L ( - Ri + ∂ L ∂ x wi + v ) ,
In formula, i is the electric current of magnet coil, and R is the resistance of magnet coil, and w is the movement velocity of suspension, and v is the excitation voltage of magnet coil,
The above-mentioned differential equation is simplified, obtains:
d dt i = 1 L ( - Ri + v ) ,
Again by the excitation voltage of PWM form modulation period with the voltage switching moment for boundary, be divided into positive electricity nip and negative electricity nip, respectively multiple repairing weld is carried out to the electric current of magnet coil at each positive electricity nip and negative voltage district, according to the current value that sampling obtains, above formula both sides integration is obtained:
i ( t ) = i ( t s ) + 1 L ∫ t s t ( - Ri + v ) dt ,
In formula, t sfor carrying out the initial time of current measurement,
By above formula discretize, and utilize least square method, calculate the estimated value obtaining electromagnet inductance L;
Repeat the process that above-mentioned electromagnet inductance L estimated value obtains by experiment, and each time different constant value is chosen to the width of air gap x between electromagnet from suspension, obtain the corresponding relation curve of width of air gap x and electromagnet inductance L, again according to this corresponding relation curve, obtain the width of air gap x corresponding with the estimated value of the electromagnet inductance L that computing obtains, this width of air gap x and the expectation width of air gap value pre-seted are compared, obtain the position error signal of suspension, using the position error signal that this position error signal finally obtains as evaluation unit.
After controller processes this position error signal, obtain and to the detailed process of the control signal of pwm signal generator be:
Controller adopts PID control method, and its transport function K (s) is:
K ( s ) = K a ( 1 + T d s ) ( 1 + 1 T i s ) ,
K in formula afor gain term, T dfor derivative time constant, T ifor integration time constant;
Transport function K (s) is inputted to the position error signal of evaluation unit output, transport function K (s) then exports the control signal to pwm signal generator, and this control signal is the control signal to pwm signal generator that controller exports.
Derivative time constant T d=0.028.
Gain term K a=2.2.
Integration time constant T i=1/12.
Advantage of the present invention: the present invention using electromagnet both as topworks, provides the electromagnetic force needed for magnetic levitation after being removed by the sensor being used for measuring position in existing active control type magnetic suspension system; Again as detecting unit, detect the position of suspended matter.The integrated design of this magnetic suspension system can reduce the complexity of magnetic suspension system, and improve the reliability of system, its robustness is good, also reduces the cost of magnetic suspension system simultaneously.It is by the estimation to coil inductance, the width of air gap of indirect detection suspension.Coil inductance is by the electric current of sampling coil and voltage signal estimation.
Accompanying drawing explanation
Fig. 1 is the control block diagram of the control method of active control type magnetic suspension system free of position sensor of the present invention;
Fig. 2 is the structural representation of electromagnet system and suspension;
Fig. 3 is the equivalent magnetic circuit modeling of Fig. 2; F in figure mfor electromagnetic force, f lfor gravity;
Fig. 4 is the circuit theory diagrams that driving circuit adopts bridge drive circuit;
Fig. 5 is the oscillogram that the magnet coil controlled by PWM is in periodic charging and discharging state;
Fig. 6 is the curve map in the magnetic field that electromagnet produces; L in figure cthe inductance of electromagnet during for only considering DC component, L oduring for considering the exchange current in electromagnet, the inductance of electromagnet;
Fig. 7 is the corresponding relation curve map of electromagnet coil current sampled value and voltage; Be presented in the PWM cycle in figure, system divides two groups of electromagnet currents of sampling, and when positive voltage, is designated as I district in figure, moment of current sample be from arrive when negative voltage, in figure, be designated as II district, moment of current sample be from arrive bring disturbance in order to avoid power device switches to current sample, during current sample, circumvent the switch area of power device.By the sampling time according to AD conversion period discrete, just the time can be obtained arrive with sampling number arrive and the time arrive with sampling number arrive corresponding relation;
Fig. 8 is electromagnet inductance characteristic curve map;
Fig. 9 is the process flow diagram realizing inductance estimation in the inventive method;
Figure 10 is T2/T4 interruption subroutine process flow diagram in Fig. 9;
Figure 11 is T3 interruption subroutine process flow diagram in Fig. 9;
Figure 12 is the experiment curv figure of the position signalling of electromagnet inductance and suspension.
Embodiment
Embodiment one: present embodiment is described below in conjunction with Fig. 1, the control method of active control type magnetic suspension system free of position sensor described in present embodiment, it obtains the electric current of the magnet coil 7 of magnetic suspension system by current sensor 1 collection, AD converter 2 is adopted to be converted to current digital signal by gathering the current analog signal obtained, position estimation unit 3 obtains the position signalling of the suspension of magnetic suspension system by calculating according to described current digital signal, the position signalling of suspension and the desired locations signal pre-seted are made comparisons, obtain position error signal, after controller 4 processes this position error signal, obtain the control signal to pwm signal generator 5, this control signal makes pwm signal generator 5 produce the voltage pulse signal of corresponding dutycycle, this voltage pulse signal realizes the control to magnet coil 7 by driving circuit 6, and then the position control realized the suspension of magnetic suspension system.
Embodiment two: present embodiment is described below in conjunction with Fig. 1 to Figure 12, present embodiment is described further embodiment one, position estimation unit 3 described in present embodiment obtains the position signalling of the suspension of magnetic suspension system by calculating according to described current digital signal, the position signalling of suspension and the desired locations signal pre-seted are made comparisons, the detailed process obtaining position error signal is:
The electromagnet inductance L of magnetic suspension system is:
In formula, N is the number of turn of magnet coil 7, for the equivalent magnetic resistance of electromagnet system be made up of electromagnet and magnet coil;
Electromagnet inductance L is relevant to the width of air gap x between electromagnet and suspension, and the estimated value of electromagnet inductance L obtains by experiment, and its acquisition process is:
Width of air gap x between power taking magnet and suspension is a constant value, applies the excitation voltage of PWM form to magnet coil 7, and make electromagnet produce exciting curent, now, the differential equation in electromagnet system loop is:
d dt i = 1 L ( - Ri + ∂ L ∂ x wi + v ) ,
In formula, i is the electric current of magnet coil 7, and R is the resistance of magnet coil 7, and w is the movement velocity of suspension, and v is the excitation voltage of magnet coil 7,
The above-mentioned differential equation is simplified, obtains:
d dt i = 1 L ( - Ri + v ) ,
Again by the excitation voltage of PWM form modulation period with the voltage switching moment for boundary, be divided into positive electricity nip and negative electricity nip, respectively multiple repairing weld is carried out to the electric current of magnet coil 7 at each positive electricity nip and negative voltage district, according to the current value that sampling obtains, above formula both sides integration is obtained:
i ( t ) = i ( t s ) + 1 L ∫ t s t ( - Ri + v ) dt ,
In formula, t sfor carrying out the initial time of current measurement,
By above formula discretize, and utilize least square method, calculate the estimated value obtaining electromagnet inductance L;
Repeat the process that above-mentioned electromagnet inductance L estimated value obtains by experiment, and each time different constant value is chosen to the width of air gap x between electromagnet from suspension, obtain the corresponding relation curve of width of air gap x and electromagnet inductance L, again according to this corresponding relation curve, obtain the width of air gap x corresponding with the estimated value of the electromagnet inductance L that computing obtains, this width of air gap x and the expectation width of air gap value pre-seted are compared, obtain the position error signal of suspension, using the position error signal that this position error signal finally obtains as evaluation unit 3.
Embodiment three: present embodiment is described below in conjunction with Fig. 1 to Figure 12, present embodiment is described further embodiment two, after controller 4 described in present embodiment processes this position error signal, obtain and to the detailed process of the control signal of pwm signal generator 5 be:
Controller 4 adopts PID control method, and its transport function K (s) is:
K ( s ) = K a ( 1 + T d s ) ( 1 + 1 T i s ) ,
K in formula afor gain term, T dfor derivative time constant, T ifor integration time constant;
Transport function K (s) is inputted to the position error signal of evaluation unit 3 output, transport function K (s) then exports the control signal to pwm signal generator 5, and this control signal is the control signal to pwm signal generator 5 that controller 4 exports.
In present embodiment, differential term mainly ensures that system has enough dampings, mainly acts on the Mid Frequency of system; The object adding integration control is the gain in order to improve low-frequency range, and the effect of integration decays along with the increase of frequency, and the stability of the delayed phase brought to make integration item not influential system, makes integration rule just attenuate before reaching Mid Frequency.
Principle of work of the present invention: the mathematical model of magnetic suspension system sensor and actuator integrated design:
Electromagnet model: composition graphs 2 and Fig. 3, the equivalent magnetic resistance that can be obtained whole system by the equivalent magnetic circuit modeling of Fig. 3 is:
Wherein for effective magnetic resistance of electromagnet, for effective magnetic resistance of suspension, for the effective magnetic resistance of air gap, for leakage flux magnetic resistance;
Can by the magnetic flux phi of magnet coil 7 by ohm's law for magnetic circuit fcfor:
Θ is mmf, Θ=Ni.
The magnetic linkage ψ of magnet coil 7 is:
By Ohm law, Faraday's electromagnetic induction law, have
di dt = 1 L ( x ) ( - Ri - ∂ L ( x ) ∂ x wi + v ) ,
By the energy storage formula of inductance, the electromagnetic force of maglev ball system is:
F ( x , i ) = ∂ W m ( x , i ) ∂ x = 1 2 ∂ L ( x ) ∂ x i 2
In formula, W m(x, i) represents the energy in magnetic field,
As shown in Figure 4, system adopts PWM full-bridge circuit to control the electric current of magnet coil to driving circuit 6, and it is high that this circuit has switching frequency, and system inertia is less, and fast-response can wait advantage well.In a PWM cycle, the polarity of output voltage can produce one-shot change, and output voltage is:
v ( t ) = v bat k T pwm < t &le; ( k + &chi; ) T pwm - v bat ( k + &chi; ) T pwm < t &le; ( k + 1 ) T pwm ,
In formula, χ represents the dutycycle of PWM, T pwmrepresent the cycle of PWM, k is number of samples.
So the average voltage at magnet coil two ends is:
v &OverBar; = 2 v bat ( &chi; - 1 2 ) ,
Therefore, the amplitude of the average voltage of magnet coil and polarity all can be controlled by dutycycle χ.
The magnet coil controlled by PWM is in periodic charging and discharging state, and therefore the electric current of coil is in periodically rising and decline state, as shown in Figure 5.
The relative permeability μ of electromagnet and suspension rby modulating frequency T pwmimpact very large, along with the increase of frequencies omega, relative permeability μ rreduce gradually, as ω → ∞, μ r→ 1.PWM voltage driven electromagnet can produce a D.C. magnetic field and superpose the magnetic field of a little alternation, and the magnetic field of this alternation can change the relative permeability of iron core, and then changes the inductance of coil, as shown in Figure 6.
Design of Observer and Controller gain variations mathematical model:
Controller gain variations is the position in order to control suspension, and the frequency of positioner is much smaller than the frequencies omega of the PWM of voltage v pWM=2 π/T pWM, therefore the position of suspension is primarily of the mean value of voltage v control, and the vibration being changed the position of suspended substance caused by PWM can be ignored.So electromagnetic force suffered by suspension is only and DC excitation, namely during ω=0, the inductance of coil is relevant, namely ignores the magnetic resistance of suspension and iron core, only calculates the magnetic resistance of air gap, so
f m = 1 2 &PartialD; L C ( x ) &PartialD; x i 2 ,
Wherein, L cthe inductance of magnet coil during (x) expression ω=0.
The design of observer is completely different from the design of controller, and Design of Observer mainly utilizes the current waveform produced by PWM voltage to estimate the inductance of coil, and then obtains the position of suspension.In this case, need to set up the mathematical model of current i based on time t, inductance L ocalculating depend primarily on ω=ω pWMtime relative permeability μ r, PWM.
So by inductance L othe mathematical model estimated is:
d dt i = 1 L O ( x ) ( - Ri + &PartialD; L O ( x ) &PartialD; x wi + v ) ,
The mathematical model of Controller gain variations is:
d dt i = 1 L C ( x ) ( - Ri + &PartialD; L C ( x ) &PartialD; x wi + v ) d dt x = w d dt w = 1 m ( mg + 1 2 &PartialD; L C ( x ) &PartialD; x i 2 + f l ) ,
Because the value of the large multiparameter of maglev ball system can not obtain directly and accurately, so the parameter of above-mentioned two formula be can not determine, and relative permeability μ raccurately can not obtain with the funtcional relationship of frequencies omega, therefore adopt method below to carry out parameter estimation to inductance.
For electromagnet, have according to Faraday's electromagnetic induction law:
d dt i = 1 L ( - Ri + &PartialD; L &PartialD; x wi + v ) ,
Suppose that following condition is set up:
1, the internal resistance R of electromagnet remains unchanged;
2, in a pulse width modulation cycle, inductance is 0 to the partial derivative of position;
3, electromagnet current waveform is triangular wave;
4, the voltage of magnet driver direct supply does not fluctuate;
Then above formula can be reduced to:
d dt i = 1 L ( - Ri + v ) .
By the switching instant of v, a modulation period is divided into two parts, positive electricity nip and negative electricity nip shown in Fig. 7.In each voltage zone respectively to electromagnet current signal multiple repairing weld.Bridge circuit switch device switches district is avoided during sampling.Above formula both sides integration can be obtained
i ( t ) = i ( t 0 ) + 1 L &Integral; t 0 t ( - Ri + v ) dt ,
Utilize least square method can obtain the estimated value of inductance.
Obtain electromagnet inductance-air gap characteristic: instantaneous inductor L (x) in magnet coil is about the function of suspension to the air gap x on electromagnet pole surface, and becomes nonlinear relation with it, as shown in Figure 8.
Magnetic suspension system is non-linear as seen from Figure 8.The relation of the instantaneous inductor that electromagnet produces after being energized and air gap x is as follows:
L ( x ) = L 1 + L 0 1 + x a ,
In formula:
L 1for the static inductance of magnet coil when air gap is infinite distance;
L 0for the inductance increased in coil when suspension and electromagnet air gap are zero;
A is constant.
Above-mentioned curve can be obtained by metering system in actual position estimation.Namely when suspension is determined, by changing size of gaps, utilize inductance algorithm for estimating to obtain inductance value simultaneously.Thus draw electromagnet inductance-air gap characteristic.
Magnetic suspension system sensor and the design of actuator integrated apparatus:
Magnetic levitation sensor-actuator integrated apparatus can adopt Infineon XE164FN single-chip microcomputer to be the control system of core.Hardware circuit comprises minimum system, PWM bridge drive circuit, current sampling circuit and AD7655 analog to digital conversion circuit.
Convert the voltage and current signal of coil to digital signal by AD7655 analog to digital converter, then bring the inductance that algorithm for estimating calculates coil into, and then estimate the position of suspension.The position-sensor-free method of estimation based on least square method is adopted to realize the process flow diagram of coil inductance estimation as shown in Figure 9.
The cycle match of T12 interrupts and comparison match interrupts controlling current sample, enters the calculating that timer T3 interrupts carrying out inductance method of estimation after having sampled.The comparison match IE timer T4 of T12, carries out the subsynchronous sampling of N by the interrupt routine control AD7655 of T4 to the electric current of positive voltage section.The cycle match IE timer T2 of T12, carries out the subsynchronous sampling of M by T2 control AD7655 to the electric current of negative voltage section.Timer T2/T4 interruption subroutine is similar, and its software flow pattern as shown in Figure 10.
Enter T3 after having sampled to interrupt, as shown in figure 11, obtain the inductance mean value estimating coil, after computation of table lookup, just obtain the location estimation of suspension.
Experiment adopts electromagnet core material to be siliconized plate, and model is EI96, and coil turn is 575, and coil resistance is 3.866 ohm.The system PWM cycle is set to 1ms, and namely modulating frequency is 1KHz, and Dead Time is set to 1 μ s.The sampling resistor that the output of current sensor adds one 50 ohm converts voltage signal to, and the current signal input AD7655 current waveform after amplifying circuit and filtering circuit can be approximated to be triangular wave.
Embodiment four: present embodiment is described further embodiment three, derivative time constant T described in present embodiment d=0.028.
Embodiment five: present embodiment is described further embodiment four, gain term K described in present embodiment a=2.2.
Embodiment six: present embodiment is described further embodiment five, integration time constant T described in present embodiment i=1/12.

Claims (5)

1. the control method of an active control type magnetic suspension system free of position sensor, it obtains the electric current of the magnet coil (7) of magnetic suspension system by current sensor (1) collection, AD converter (2) is adopted to be converted to current digital signal by gathering the current analog signal obtained, position estimation unit (3) obtains the position signalling of the suspension of magnetic suspension system by calculating according to described current digital signal, the position signalling of suspension and the desired locations signal pre-seted are made comparisons, obtain position error signal, after controller (4) processes this position error signal, obtain the control signal to pwm signal generator (5), this control signal makes pwm signal generator (5) produce the voltage pulse signal of corresponding dutycycle, this voltage pulse signal realizes the control to magnet coil (7) by driving circuit (6), and then the position control realized the suspension of magnetic suspension system,
It is characterized in that, described position estimation unit (3) obtains the position signalling of the suspension of magnetic suspension system by calculating according to described current digital signal, the position signalling of suspension and the desired locations signal pre-seted are made comparisons, the detailed process obtaining position error signal is:
The electromagnet inductance L of magnetic suspension system is:
In formula, N is the number of turn of magnet coil (7), for the equivalent magnetic resistance of electromagnet system be made up of electromagnet and magnet coil;
Electromagnet inductance L is relevant to the width of air gap x between electromagnet and suspension, and the estimated value of electromagnet inductance L obtains by experiment, and its acquisition process is:
Width of air gap x between power taking magnet and suspension is a constant value, applies the excitation voltage of PWM form to magnet coil (7), and make electromagnet produce exciting curent, now, the differential equation in electromagnet system loop is:
d d t i = 1 L ( - R i + &part; L &part; x w i + v ) ,
In formula, i is the electric current of magnet coil (7), and R is the resistance of magnet coil (7), and w is the movement velocity of suspension, and v is the excitation voltage of magnet coil (7),
The above-mentioned differential equation is simplified, obtains:
d d t i = 1 L ( - R i + v ) ,
Again by the excitation voltage of PWM form modulation period with the voltage switching moment for boundary, be divided into positive electricity nip and negative electricity nip, respectively multiple repairing weld is carried out to the electric current of magnet coil (7) at each positive electricity nip and negative voltage district, according to the current value that sampling obtains, above formula both sides integration is obtained:
i ( t ) = i ( t s ) + 1 L &Integral; t s t ( - R i + v ) d t ,
In formula, t sfor carrying out the initial time of current measurement,
By above formula discretize, and utilize least square method, calculate the estimated value obtaining electromagnet inductance L;
Repeat the process that above-mentioned electromagnet inductance L estimated value obtains by experiment, and each time different constant value is chosen to the width of air gap x between electromagnet from suspension, obtain the corresponding relation curve of width of air gap x and electromagnet inductance L, again according to this corresponding relation curve, obtain the width of air gap x corresponding with the estimated value of the electromagnet inductance L that computing obtains, this width of air gap x and the expectation width of air gap value pre-seted are compared, obtain the position error signal of suspension, using the position error signal that this position error signal finally obtains as evaluation unit (3).
2. the control method of active control type magnetic suspension system free of position sensor according to claim 1, is characterized in that,
After controller (4) processes this position error signal, obtain and to the detailed process of the control signal of pwm signal generator (5) be:
Controller (4) adopts PID control method, and its transport function K (s) is:
K ( s ) = K a ( 1 + T d s ) ( 1 + 1 T i s ) ,
K in formula afor gain term, T dfor derivative time constant, T ifor integration time constant;
The position error signal that evaluation unit (3) exports is inputted to transport function K (s), transport function K (s) then exports the control signal to pwm signal generator (5), and this control signal is the control signal to pwm signal generator (5) that controller (4) exports.
3. the control method of active control type magnetic suspension system free of position sensor according to claim 2, is characterized in that, derivative time constant T d=0.028.
4. the control method of active control type magnetic suspension system free of position sensor according to claim 3, is characterized in that, gain term K a=2.2.
5. the control method of active control type magnetic suspension system free of position sensor according to claim 4, is characterized in that, integration time constant T i=1/12.
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