EP0137093A2 - Method of measuring the voltage induced in the coil of a stepping motor by the rotation of its rotor - Google Patents

Abstract

The method comprises measuring the voltage induced during the driving pulse in the coil by rotation of the rotor, and interrupting the drive pulse in dependence on the measurement made. The device for carrying out this method comprises a circuit for measuring the induced voltage, a circuit for comparison with a reference value and a circuit for calculating the duration of the drive pulse.

Description

The present invention relates to a method of measuring the voltage induced in the coil of a stepping motor by the rotation of its rotor in response to the application to the coil of a supply voltage.

Stepper motors are used in many devices where a mechanical member has to be moved a determined amount in response to an electrical signal. They are used in particular in electronic timepieces. In these, the time display hands must be moved by a specified amount in response to very precise period pulses provided by a time base.

In these timepieces, most of the energy supplied by the electrical power source, which is generally a battery, is consumed by the stepping motor. The volume available in these timepieces being very limited, it is important to limit as much as possible the consumption of this engine to increase the lifespan of the battery or, for a given lifespan, to be able to decrease its volume .

In most timepieces today, the duration of the driving pulses sent at regular intervals to the motor is fixed. This duration is chosen so as to guarantee the proper functioning of the motor even in the worst conditions, that is to say with a low battery voltage, during the drive of the calendar mechanism, in the presence of shock or field external magnetic, etc. As these bad conditions occur only rarely, the engine is most often supercharged.

It is possible to significantly reduce the energy consumption of the motor by adapting the energy supplied by the pulses power to the momentary load it must drive and to the supply voltage.

One solution to this problem consists in providing a pulse-forming circuit capable of producing pulses of different durations and a device which detects the rotation or the absence of rotation of the motor. The duration of the driving pulses sent to the motor is gradually reduced until a step not taken is detected. A catch-up pulse is then sent to the motor and the energy of the normal driving pulses is fixed at a higher value. This value is maintained for a certain time. If the engine has been running normally during this period, the pulse duration is further reduced. Such a solution does not allow permanent and rapid adaptation of the driving pulses to the motor load. In addition, this slow adaptation and the sending of catch-up pulses in the event of non-rotation means that the energy consumption is higher than necessary.

To avoid this drawback, it is known to provide devices which adapt the duration of each driving pulse to the load that the motor must drive in response to this driving pulse.

US Patent 3,500,103 describes a device which detects the movement of the movable member of the motor via the voltage induced in a detection coil separate from the drive coil and which interrupts the drive pulse when the movable member reaches either a position or a determined speed.

American patent 3,855,781 proposes solutions according to which the position of the rotor is detected by measuring the voltage induced in an auxiliary coil or created by the deformation of a piezoelectric sensor when the teeth of one of the wheels of the gear train driven by the motor. This voltage is used to interrupt the driving pulse.

The devices described in the two above patents require additional elements to operate, which makes their implementation expensive and complicated.

French patent 2,200,675 proposes to detect the current variation in the motor control coil and to interrupt the driving pulse when this current passes through a minimum. The limits of this detection are imposed by the shape of the current which depends on the time constant of the circuit, on the induced electromotive force, as well as on the load of the motor. In some cases, the minimum current can disappear, which makes the servo device ineffective.

Furthermore, American patent 4,114,364 describes a circuit for controlling the duration of the driving pulses at the load of the motor, which comprises means for detecting the current in the control coil and means for interrupting the pulse when this current reaches a value equal to the ratio between the supply voltage of the coil and its resistance in direct current, that is to say when the rotor has completed its pitch. Provision is also made for interrupting the pulse before the current has reached this value.

All the devices described above use the measurement of a physical quantity such as the speed or the position of the rotor or such that the current flowing in the coil. This measurement is used directly or by comparison with a reference value to control the interruption of the driving pulse. However, none of these physical quantities gives an absolute indication of the exact instant when this driving impulse must be interrupted so that the energy consumption of the motor is truly minimal. All these devices therefore cause the interruption of the motor pulse at an arbitrarily chosen instant and which is generally not the optimum instant. In practice, these devices must take into account safety factors such that, most of the time, the motor consumes too much energy or does not operate safely.

This drawback is avoided by the method according to the invention, which consists in measuring the voltage induced in the motor coil by the movement of the rotor, and in interrupting the driving pulse in dependence on this measurement of induced voltage.

où U r est cette tension induite, i est le courant qui circule dans la bobine, C le couple fourni par le moteur et w la vitesse angulaire du rotor.This tension induced in the coil by the movement of the rotor is closely related to the mechanical energy supplied by the motor, by the relation

where U r is this induced voltage, i is the current flowing in the coil, C the torque supplied by the motor and w the angular speed of the rotor.

The second term in the above equation represents the total mechanical energy supplied by the motor during one of its steps, and the first term represents the electrical energy which is transformed, by the motor, into this mechanical energy.

The above relationship shows that the voltage U induced in the coil by the rotation of the rotor is directly related to the mechanical energy supplied by the motor. The current i which is also involved in this relationship, as well as all the other physical quantities which can be measured on a rotating motor, also depend on factors not related to this mechanical energy, such as the voltage of the power source and the ohmic resistance of the coil. It follows that the measurement of the induced voltage U constitutes the most adequate method for determining with precision and security the optimal instant of interruption of the driving pulse.

It should be noted that the voltage induced in the coil by the movement of the rotor constitutes only part of the overall induced voltage which is cited in French patent 2,200,675 and the maximum of which coincides with the minimum of the current flowing in the coil. , when this minimum exists. The other part of the global induced voltage consists of the self-induction voltage created in the coil by the variations of the current which circulates there.

Since this self-induction voltage is not directly linked to the energy supplied by the motor, the overall induced voltage does not constitute an adequate quantity for determining the optimum moment of interruption of the driving pulse. Added to this is the fact, already mentioned, that the current in the coil does not always have a minimum. In addition, this minimum, when present, is not sharp enough for it to be detected with precision.

• - La figure 1 représente le schéma équivalent d'un moteur pas-à-pas;
• - La figure 2a illustre la variation du courant dans la bobine du moteur dans deux cas de charge de ce moteur;
• - La figure 2b illustre la variation de la tension induite dans la bobine par la rotation du rotor dans les mêmes cas de charge;
• - La figure 3 illustre la variation de la durée de l'impulsion motrice minimum et du temps mis par la tension induite pour atteindre un seuil déterminé en fonction de la charge entraînée par le moteur;
• - La figure 4 est un schéma bloc d'un exemple de dispositif selon l'invention;
• - La figure 5 illustre le fonctionnement du dispositif de la figure 4;
• - La figure 6 est un schéma d'un premier exemple de circuit de mesure de la tension induite dans la bobine par la rotation du rotor;
• - La figure 7 illustre le principe de fonctionnement du circuit de la figure 6;
• - La figure 8 illustre le fonctionnement du circuit de la figure 6;
• - La figure 9 est un schéma d'un deuxième exemple de circuit de mesure de la tension induite dans la bobine par la rotation du rotor;
• - La figure 10 illustre le fonctionnement du circuit de la figure 9;
• - La figure 11 est un schéma d'un troisième exemple de circuit de mesure de la tension induite dans la bobine par la rotation du rotor;
• - La figure 12 est un schéma d'un premier exemple de circuit utilisant la mesure de la tension induite dans la bobine par la rotation du rotor pour interrompre l'impulsion motrice;
• - La figure 13 illustre le fonctionnement du circuit de la figure 12;
• - La figure 14 est un schéma d'un deuxième exemple de circuit utilisant la mesure de la tension induite dans la bobine par la rotation du rotor pour interrompre l'impulsion motrice; et
• - La figure 15 illustre le fonctionnement du circuit de la figure 14.

The invention will now be described in more detail using the drawing in which:

• - Figure 1 shows the equivalent diagram of a stepping motor;
• - Figure 2a illustrates the variation of the current in the motor coil in two cases of load of this motor;
• - Figure 2b illustrates the variation of the voltage induced in the coil by the rotation of the rotor in the same load cases;
• - Figure 3 illustrates the variation of the duration of the minimum driving pulse and the time taken by the induced voltage to reach a threshold determined according to the load driven by the motor;
• - Figure 4 is a block diagram of an exemplary device according to the invention;
• - Figure 5 illustrates the operation of the device of Figure 4;
• - Figure 6 is a diagram of a first example of a circuit for measuring the voltage induced in the coil by the rotation of the rotor;
• - Figure 7 illustrates the operating principle of the circuit of Figure 6;
• - Figure 8 illustrates the operation of the circuit of Figure 6;
• - Figure 9 is a diagram of a second example of a circuit for measuring the voltage induced in the coil by the rotation of the rotor;
• - Figure 10 illustrates the operation of the circuit of Figure 9;
• - Figure 11 is a diagram of a third example of a circuit for measuring the voltage induced in the coil by the rotation of the rotor;
• - Figure 12 is a diagram of a first example of a circuit using the measurement of the voltage induced in the coil by the rotation of the rotor to interrupt the driving pulse;
• - Figure 13 illustrates the operation of the circuit of Figure 12;
• - Figure 14 is a diagram of a second example of a circuit using the measurement of the voltage induced in the coil by the rotation of the rotor to interrupt the driving pulse; and
• - Figure 15 illustrates the operation of the circuit of Figure 14.

Figure 1 shows the equivalent diagram of a stepping motor. The coil of this motor is represented by a coil 1, of inductivity L and zero resistance, and by a resistance 2, of value R equal to the resistance of the motor coil. The voltage source induced in the coil by the rotation of the rotor is symbolized by a voltage source 3. The value of this induced voltage is designated by U.

The curves 4 and 5 of FIG. 2a, which are well known, illustrate the variation of the current i in the motor coil as a function of time, during the driving pulse, in cases where the load driven by the motor is low, respectively strong.

The curves 6 and 7 of FIG. 2b illustrate, in the same load cases, the variation of the voltage U, measured by a device which will be described later.

Curves 4 and 5 show that, just after the instant t ₀ of activation of the driving pulse, the current in the coil increases according to an exponential law, with a time constant equal to L / R, independently of the load. that the motor should drive. The rotor is still stationary and the voltage U is zero r (Figure 2b).

At time t _l , the rotor begins to rotate. The source 3 begins to supply the voltage U induced by the rotation of the rotor, and the current i in the coil therefore ceases to have an exponential variation. It follows a curve which depends on the load driven by the motor, and of which curves 4 and 5 are two examples. The voltage U follows a curve which also depends on the load driven by the motor. Curve 6 in Figure 2b corresponds to curve 4 in Figure 2a, and curve 7 in curve 5. Whatever the load driven by the motor, the voltage U _r goes through a maximum, before going through zero the moment the rotor passes through its equilibrium position with current, that is to say the position which it ends up taking, after a few oscillations, if the driving pulse is not interrupted.

The voltage U then oscillates around zero until the rotor comes to a stop.

There are several possibilities of exploiting the information provided by the measurement of the voltage U. This, like the other physical quantities which can be measured on the motor, does not present any particular point which coincides exactly with the moment when the driving impulse must be interrupted for the consumption of the motor to be minimum.

However, measurements have shown that whatever information is extracted from the measurement, this information is very directly linked to the optimum duration of the motor pulse. The law which links this information and this duration is always a simple law, which makes it possible to easily exploit the information extracted from the measurement of the voltage U.

r

Among the information that can be extracted from the measurement of the voltage U, one can cite the position in time or the amplitude of the maximum of this voltage U, the time taken by this voltage U _r to reach a certain threshold on its flank amount or on its falling edge, its derivative or its integral, etc. Tests have shown that the information given by the time taken by the voltage U _r to reach a certain threshold is the easiest to extract from the measurement of the voltage U _r and to use to determine the optimum duration of the driving pulse. .

où T01 est la durée minimum de l'impulsion motrice pour une charge nulle et a la pente de la droite.FIG. 3 illustrates the variation of the minimum duration Tl of the driving pulse necessary to turn an engine as a function of the torque C that this engine must provide. This variation is substantially linear and has a fairly low dispersion for a given type of engine. It can be expressed by the relation

where T01 is the minimum duration of the driving pulse for a zero load and has the slope of the line.

où T02 est le temps mis par la tension U_r pour atteindre la tension de seuil U en l'absence de charge et b est la pente de la droite.The variation of the time T2 put by the voltage U _r to reach a determined threshold U has also been reported in this figure 3. It is also substantially linear and can be expressed by the relation

where T02 is the time taken by the voltage U _r to reach the threshold voltage U in the absence of load and b is the slope of the line.

It is interesting to note that, in a fairly wide range of values of the threshold voltage U _s , the relationship between T2 and C remains linear. The terms T02 and b depend of course on the voltage U chosen. s

The relationship between times T1 and T2 is also linear and is given by the equation:

avec

In this equation, the terms a, b, TOI and T02 are constants for a given type of motor and for a determined threshold voltage U _s . It can therefore be written in the form

with

The terms k and K can be easily calculated from the measurement of times T01 and T02 and times T1 and T2 for a known load. Once they have been determined, for a type of engine, they can be used in the control circuit of this type of engine, the diagram of which gives the diagram. Figure 5 shows the variation of the signals at some points in this figure 4.

In FIG. 4, the reference 8 designates a circuit whose output delivers a signal S8 to a control circuit 9 each time that the motor 10 must advance by one step.

Circuit 8 can be constituted, by way of nonlimiting example, by the oscillator and the frequency division chain of an electronic watch, and it can be arranged so as to deliver periodic signals having various frequencies. These signals will be described later.

In response to the signal S8, the control circuit 9 delivers a driving pulse I to the motor 10. In the case where this motor 10 is a stepping motor as it is commonly used in watches, the correct polarity of the driving pulse 1 is also determined by the circuit 9.

A measurement circuit 11 is connected to the motor 10. It is arranged, in a manner which examples will be given later, to deliver a voltage U _m proportional to the voltage U induced in the motor coil by the rotation of the rotor.

The measured voltage U _m is applied to a detector circuit 12 which delivers a signal S12 at the instant when this voltage U _m exceeds a judiciously chosen reference voltage U '.

A calculation circuit 13, of which exemplary embodiments will be described later, delivers a signal S13 a certain time after having received the signal S12. The instant when this signal S13 is delivered depends on the time which has elapsed between the start of the driving pulse and the appearance of the signal S12, and on the two constants k and K which are also provided, in an adequate form, to the calculation circuit 13. The signal S13 is used by the control circuit 9 to interrupt the driving pulse I.

FIG. 6 gives the block diagram of an example of a circuit 11 for measuring the voltage U. This circuit 11, like the other circuits which will be described later, is supplied by a voltage source, not shown. This source delivers a positive voltage + U _a and a negative voltage -U _a with respect to a midpoint which is grounded to the circuit. The voltage -U _a is intended, in particular, to supply the differential amplifiers used in these circuits.

This FIG. 6 shows the motor 10 connected, in a conventional manner, in a bridge of four MOS transistors 14, 15, 16 and 17 forming part of the control circuit 9 of FIG. 4. The transistors 14 and 15, of type p, have their sources connected to the positive pole tU _a of the power source, not shown. Transistors 16 and 17, of type n, have their source connected to the ground of the circuit, through a measurement resistor 18, of low value, forming part of the measurement circuit 11 of FIG. 4. The drains of transistors 14 and 16 are connected to one of the terminals of the motor 10, and the drains of the transistors 15 and 17 to the other.

The control electrodes of the four transistors 14 to 17 are connected to a logic circuit, not shown in this figure 6, which delivers the logic signals necessary for the control of these transistors. An example of this logic circuit will be given later.

The measurement circuit 11 includes an amplifier 20 whose input is connected to point 19 common to the sources of the transistors 16 and 17 and to the resistor 18. The gain of this amplifier 20 is chosen so that its output voltage U20 is equal at the supply voltage + U _a when the current i flowing in the motor coil is equal to U _a / R.

The output of this amplifier 20 is connected to the input of a transmission gate 21, and to the inverting input of a differential amplifier 22. The transmission gate 21 is controlled by a logic signal 21C which is supplied, by example, by circuit 8 in FIG. 4, which will be described later.

The output of this transmission gate 21 is connected to the junction point 23 of a resistor 24, having a value R24, and of a capacitor 25 having a capacitance C25. Point 23 is also connected, through an amplifier 26, to the non-inverting input of the differential amplifier 22.

The sole purpose of the amplifier 26 is to reduce the load that the input of the amplifier 22 would constitute for the R-C circuit 24-25. The gain of this amplifier 26 is chosen to be equal to 1.

où L et R sont, comme ci-dessus, l'inductivité et la résistance de la bobine du moteur.The circuit formed by the resistor 24 and the capacitor 25 is connected between the + U terminal of the power source and the ground. The value R24 of resistance 24 and the capacity C25 of capacitor 25 are chosen so that

where L and R are, as above, the inductance and resistance of the motor coil.

When the signal 21C is in the "0" state, the transmission gate 21 is in its blocking state. The voltage at point 23 therefore varies exponentially, towards its asymptotic value, which is equal to the supply voltage + U, with the same time constant t = R24.C25 as the current which would circulate in the motor coil if the rotor was blocked, that is to say if the voltage U _r was zero.

When the transmission gate 21 is in its conductive state, the voltage at point 23 is equal to the output voltage of the amplifier 20.

Figure 7 illustrates the operating principle of this circuit. In this FIG. 7, the curve 27 represents the variation, during a driving pulse, of the output voltage U20 of the amplifier 20. This curve 27 is an image of the current i which flows in the coil of the motor 10.

As long as the transmission gate 21 remains conductive, the voltage U23 at point 23 follows the same curve 27. The voltage U22 at the output of the differential amplifier 22 therefore remains zero. If, at any time t _x , the gate 21 becomes blocking, the voltage U20 continues to follow the curve 27. The voltage U23, on the other hand, begins to follow the curve 28, which is the exponential curve passing through the point X, of time constant τ = R24.C25 and of asymptotic value equal to + U. This curve 28 is exactly the same as that which the voltage U20 would follow if, at time t _x , the rotor was suddenly blocked, which would cancel the voltage U. It is therefore the image of the current i 'which would flow, under these conditions, in the motor coil.

The voltages U20 and U23 being applied to the reverse and direct inputs of the differential amplifier 22, the output voltage U22 of the latter therefore has the value U23 - U20.

We will show below that, for a short time after gate 21 has become blocking, this voltage U22 = U23 - _U20 is proportional to the voltage U _rx , i.e. to the value of the induced voltage in the motor coil by the rotation of the rotor at time t. x

qui se déduit facilement du circuit de la figure 1 dans le cas où la tension +U_a est appliquée au moteur par son circuit de commande, non représenté dans cette figure 1.The voltage U20 is proportional to the current i which flows in the coil during a driving pulse. In general, this current i can be expressed by the relation

which is easily deduced from the circuit of FIG. 1 in the case where the voltage + U _a is applied to the motor by its control circuit, not shown in this FIG. 1.

Au point X, cette pente est donnée par :

où U rx et i_x sont respectivement les valeurs de U_r et de i au point X.At each point on curve 27, the slope is given by the following equation, which is easily deduced from equation (2):

At point X, this slope is given by:

where U rx and i _x are respectively the values of U _r and i at point X.

où C1 est une constante d'intégration qui peut se calculer en tenant compte de la condition

The tangent 29 to the curve 27 at point X therefore has the equation

where C1 is an integration constant which can be calculated taking into account the condition

Au point Y, pour lequel t = t , on trouve :

All calculations made, the equation of the tangent 29 becomes:

At point Y, for which t = t, we find:

We have seen above that if, at time t, the rotor was suddenly blocked, which would cancel the voltage U _r , the current i flowing in the coil would follow, after this time t, an exponential curve whose curve 28 is a picture. In this case, equation (2) above would become:

où At = t - t . y xThe same reasoning as above shows that the ordinate i "y of the point Z located at t = t _y on the tangent 30 to the exponential 28 is equal to

where At = t - t. yx

ou encore

By subtracting equation (4) above from this equation (6), we find

or

We therefore see that at each point X of curve 27, the voltage U _rx induced in the coil by the rotation of the rotor is proportional to the segment Y - Z, for a given measurement time At = t - t.

y x

In particular, for Δt ₌ t, U _rx is equal to the length of the segment Z '- Y' in Figure 7, where Y 'and Z' are the points of the tangents 29 and 30 located on the abscissa (t _x + τ ). The ordinate of point Z 'is equal to U _{a /} R which is the asymptotic value of the exponential 28.

If At is chosen sufficiently small, the tangents 29 and 30 can be confused with curves 27 and 28. The current i ' _y can be replaced by the current i and the current i " _y by the current which would circulate in the coil at l 'instant t if the induced voltage U was canceled at time t. rx

où J est un facteur de proportionnalité qui dépend de la valeur de la résistance 18 et du gain de l'amplificateur 22, et U23_y et U20_y sont les valeurs des tensions U23 et U20 à l'instant t .If we remember that the voltage U20 is proportional to the current i and that the voltage U23 is proportional to the current which would circulate in the coil after the instant t _x if the induced voltage were canceled at this instant t, we see that the equation (7) above can be written

where J is a proportionality factor which depends on the value of the resistor 18 and the gain of the amplifier 22, and U23 _y and U20 _y are the values of the voltages U23 and U20 at time t.

Figures 8a and 8b illustrate the operation of the circuit of Figure 6 when the transmission gate 21 is controlled by a signal 21C such as that shown in Figure 8c.

In the present example, the transmission gate 21 is conductive when the signal 21C is in the logic state "1", and blocked when this signal 21C is in logic state "0". The control signal 21C is constituted, for example, by pulses having a period of approximately 250 micro-seconds which are in the logic state "1" for a few microseconds, and in state "0" the rest of the time. The transmission gate 21 therefore becomes conductive for a few microseconds every 250 microseconds, and it is blocking the rest of the time.

In FIG. 8a, the curve 31 again represents the voltage U20, which is an image of the current i in the coil. The sawtooth curve 32 which is superposed on it represents the voltage U23. Indeed, each time the transmission gate 21 becomes conductive, that is to say when the signal 21C is in the state "1", the voltage U23 becomes equal to the voltage U20. When the transmission door 21 is blocking, that is to say when the signal 21C is in the "0" state, the voltage U23 varies according to a curve such as the exponential curve 28 shown in FIG. 7.

The sawtooth curve 33 of FIG. 8b represents, on a different scale from that of FIG. 8a, the output voltage U22 of the differential amplifier 22. This voltage U22 is equal to zero each time the transmission gate 21 is conductive, and it is equal to the difference of the voltages U23 and U20 when the transmission door 21 is blocked. As the time intervals during which the transmission door 21 is blocked are equal to each other, the curve 34, which is the envelope of the curve 33, is an image of the voltage U induced in the motor coil by the rotation of the rotor.

This envelope 34 could be obtained by filtering the voltage U22 in a low-pass filter. The output signal of this filter could be amplified in an amplifier, the gain of which would be chosen taking into account all the proportionality factors introduced into the circuit of FIG. 6 by the choice of the measurement resistance 18, of the gain of the amplifier 20 and the period of the control signal 21C. The output signal from this amplifier would then be equal to the induced voltage U. But this filtering and this amplification are not necessary. The voltage U22 itself can be directly used as the measurement voltage U in the circuit of FIG. 4. The voltage U 'at which the voltage U _m is compared in circuit 12 of FIG. 4 must of course be chosen taking into account the proportionality factors above.

It should be noted that the voltage U22 is independent of the supply voltage U, since the voltages U23 and U20 are both proportional to this voltage U.

En termes de tension, cette équation peut s'écrire :

La figure 7 montre que :

L'équation (8) ci-dessus peut donc s'écrire :

The difference of the currents i "and i 'which it has been shown above is proportional to the voltage U _rx induced in the motor coil by the rotation of the rotor at time t (see Figure 7), can be written as follows:

In terms of tension, this equation can be written:

Figure 7 shows that:

Equation (8) above can therefore be written:

This expression shows that the voltage U, which is proportional to (U _z - U _y ), can be measured without the voltage U itself having to be measured.

Figure 9 shows the block diagram of a measurement circuit 11 (Figure 4) providing a voltage U _ml proportional to U _rx based on equation (9) above.

In this FIG. 9, the resistor 18 for measuring the current flowing in the motor (not shown in this FIG. 9) and the amplifier 20 whose output voltage is an image of this current are identical to the resistor 18 and to the amplifier 20 of FIG. 6.

The output of amplifier 20 is connected, via diary of a transmission gate 61 to a first terminal of a capacitor 62 of capacitance C62, and to the non-inverting input of a differential amplifier 63. The second terminal of the capacitor 62 is connected to the ground of the circuit.

The output of amplifier 63 is connected to its inverting input. The gain of this amplifier is therefore equal to one. Its output is also connected, through two transmission doors 64 and 65, to the first terminals of two capacitors 66 and 67, of capacity C66 and C67.

The second terminal of the capacitor 66 is connected through a transmission gate 68 to the + U terminal of the power source and the second terminal of the capacitor 67 is connected to the output of the amplifier 20 by a transmission gate 69.

The first terminal of the capacitor 66 and the second terminal of the capacitor 67 are connected to a first output terminal of the circuit, designated by B1, by transmission gates 70, respectively 71. The second terminal of the capacitor 66 and the first terminal of the capacitor 67 are connected to a second output terminal of the circuit, designated by B2, by transmission doors 72, 73 respectively.

The transmission doors 61 and 70 to 73 are controlled together by a signal designated by C1, and the transmission doors 64, 65, 68 and 69 are controlled, also together, by a signal designated by C2.

These signals C1 and C2, which can be delivered, for example, by the circuit 8 of FIG. 4, and which are represented in FIG. 10, have identical periods of 0.5 milliseconds for example and equally short durations, compared to their period, 30 microseconds for example. Each of them appears in the middle of the other's period. FIG. 7 can also be used to understand the operation of the circuit of FIG. 9.

When, at an instant t _x the signal C1 puts the transmission gate 61 in its conductive state, the capacitor 62 charges at the voltage U _x which is proportional to the current i _x flowing at this instant in the coil. The voltage U appears at the output of the amplifier 63. The role of the transmission gates 70 to 73 which are also made conductive at this time will be discussed later.

At time t, the signal C2 makes the transmission doors 64, 65, 68 and 69 conductive. The voltage U _x memorized by the capacitor 62 and the amplifier 63 is therefore applied to the first terminal of the capacitor 66 and of the capacitor 67. At the same time, the voltage U _a is applied to the second terminal of the capacitor 66 and a proportional voltage to the current flowing at this instant t _y in the motor coil is applied to the second terminal of the capacitor 67. As the time Δt which separates the instants t _x and t _y is short, this voltage can be considered to be the voltage U _y of FIG. 7. At this instant t, the capacitor 66 therefore charges at a voltage U66 = U - U and the capacitor 67 charges at a voltage U67 = U - U.

et

The charges Q66 and Q67 stored in these capacitors are therefore respectively:

and

The following pulse C1 makes the transmission doors 70 to 73 conductive. During this pulse C1, the capacitors 66 and 67 are therefore connected in parallel with the output terminals B1 and B2 of the circuit. The voltage U _ml which then appears at these terminals is equal to:

, l'équation (10) peut s'écrire :

If capacitors 66 and 67 are chosen so that

, equation (10) can be written:

The expression between the brackets is proportional to the voltage U _rx (see equation 9 above). The voltage U _m1 is therefore also proportional to U.

It should be noted that, with this circuit, the voltage U _ml representative of the voltage U _r induced at the instant t _x in the coil by the rotation of the rotor only appears at the output of the circuit at an instant t _x + 2Δt . This delay is not annoying since Δt is short.

It should also be noted that either of the output terminals B1 and B2 can be grounded to the circuit without the operation of the latter being modified.

In the circuit of FIG. 6, the accuracy of the measured value depends directly on the accuracy of the value of the resistor 24 and of the capacitor 25. It is well known that it is difficult, in mass production, to obtain great precision for such elements. The circuit of FIG. 9 does not have this drawback. The precision of the measurement depends in fact only on the ratio of the capacities of the capacitors 66 and 67. However, even in mass production, this ratio can be guaranteed with very good precision.

. Dans cette expression, R représente la valeur de la résistance de mesure 18, et ∑R_T la somme des résistances internes des transistors conducteurs. Ces résistances étant différentes d'un transistor à l'autre et, en plus, variables en fonction du courant qui traverse les transistors, cette valeur U ' ne peut pas être déterminée avec exactitude.The circuit of FIG. 9, like that of FIG. 6 moreover, however has another small drawback. To make the above calculations and reasoning, it has been accepted that the transistors 14 to 17 of the motor control circuit (Figure 6) have no internal resistance when they are conductive. In reality, this internal resistance is not zero, and the asymptote of the exponential curves such as the curve 28 of FIG. 7 is not located at the ordinate U _a but at the ordinate

. In this expression, R represents the value of the measurement resistance 18, and ∑R _T the sum of the internal resistances of the conductive transistors. These resistances being different from one transistor to another and, moreover, variable as a function of the current flowing through the transistors, this value U ′ cannot be determined with accuracy.

The error in the measurement of the value of the voltage induced by the rotation of the rotor caused by the replacement of U 'by U is not very large. However, Figure 11 shows the diagram of a third measurement circuit which eliminates this source of error.

All of the elements described in connection with Figure 9 are retrou wind in Figure 11, with the exception of transmission doors 68 and 72 which are not shown in this diagram. In addition, the second terminal of the capacitor 66 and the output terminal B2 are connected directly to ground.

The output terminal BI of the circuit of FIG. 9 is connected to the inverting input of a differential amplifier 74. The non-inverting input of this amplifier 74 is connected to ground. The output of this amplifier 74 is connected to its inverting input by a capacitor 75 connected in parallel with a transmission gate 76. The output of the amplifier 74 is further connected, through a transmission gate 77, to the input non-inverting of a differential amplifier 78. A capacitor 79 and a transmission gate 80 are connected in parallel between this non-inverting input of amplifier 78 and ground.

The output of amplifier 78 constitutes the output of measurement circuit 11. This output is connected to the inverting input of amplifier 78 by a resistor 81 and to the ground of the circuit by a resistor 82. The non-input amplifier 78 is further connected by a transmission gate 83 to the non-inverting input of a differential amplifier 84. A capacitor 85 and a transmission gate 86 are connected in parallel between this input of the amplifier 84 and the mass.

The output of amplifier 84 is connected to its inverting input. The gain of this amplifier 84 is therefore equal to one. Its output is also connected, by a transmission gate 87, to a first terminal of a capacitor 88. The other terminal of this capacitor 88 is connected to ground. Finally, the first terminal of the capacitor 88 is connected by a transmission gate 89 to the inverting input of the amplifier 74.

The transmission doors 77 and 89 are controlled by the signal C1 described above, at the same time as the transmission doors 61, 70, 71 and 73. The transmission doors 76 and 87 are controlled by the signal C2 also described here above, like the transmission doors 64, 65 and 69. The transmission doors 80 and 86 are controlled by a signal C3 which can be, for example, delivered by the circuit 9 for controlling the motor 10 and which is at state "0" during motor pulses and state "1" the rest of the time. The doors 80 and 86 are therefore conductive between the driving pulses and blocked during these driving pulses. Finally, the transmission gate 83 is controlled by a signal C4 which is normally at "0" and which passes to the state "1" for a few microseconds approximately one millisecond after the start of the driving pulse. Signals C3 and C4 are also shown in Figure 10.

The operation of the circuit located between the output of the amplifier 20 and the terminal B1 is identical to that of the circuit of FIG. 9. However, the fact that the second terminal of the capacitor 66 is connected to the ground of the circuit and not to the voltage U _a , this capacitor 66 charges at voltage - U, and not at voltage (U _a - U _x ) in response to signal C2. The expression of the charge Q66 therefore becomes:

Equation (11) above in which the term U _a is replaced by 0 shows that the voltage U _m2 which would appear at terminal B1 in response to the signal C1 if the elements 74 to 89 did not exist would be:

A comparison of this equation (12) with equation (11) above shows that:

It should be noted that as long as the rotor is stationary, that is to say between the driving pulses and at the very beginning of these, the voltage U _ml is zero. The voltage U _m2r which would appear at terminal B1 under these conditions would therefore be:

• Entre les impulsions motrices, le signal C3 est à "1". Les condensateurs 79 et 85 sont donc court-circuités par les portes de transmission 80 et 86 qui sont conductrices. La sortie de l'amplificateur 78, qui est la sortie du circuit de mesure, et la sortie de l'amplificateur 84 sont au potentiel de la masse.

The operation of the circuit composed of elements 74 to 89 is as follows:

• Between the driving pulses, the signal C3 is at "1". The capacitors 79 and 85 are therefore short-circuited by the transmission doors 80 and 86 which are conductive. The output of amplifier 78, which is the output of the measurement circuit, and the output of amplifier 84 are at ground potential.

The capacitor 88 is discharged since the output of the amplifier 84, which is grounded, is connected to it at each pulse C2 by the transmission gate 87.

At each pulse C2, the capacitor 75 is also discharged through the transmission door 76 which short-circuits it. Immediately after each of these pulses C2, the output of the amplifier 74 is therefore also at ground potential.

si la porte de transmission 80 n'était pas conductrice. Le signe - qui apparaît dans cette équation résulte du fait que la borne B1 est reliée à l'entrée inverseuse de l'amplificateur 74.An instant At after each of these pulses C2, a pulse C1 makes the transmission gates 70, 71, 73, 77 and 89 conductive. The sum of the charges contained at this time in the capacitors 66, 67 and 88 is therefore transferred to the capacitor 75. The voltage U75 at the terminals of this capacitor would then be:

if the transmission door 80 was not conductive. The sign - which appears in this equation results from the fact that terminal B1 is connected to the inverting input of amplifier 74.

In reality, this voltage U75 remains zero as long as the signal C3 is in the state "1" and the charges Q66 and Q67 are transmitted to ground by this transmission gate 80. The charge Q88 of the capacitor 88 is in any case zero at this moment. The output of amplifier 78 therefore remains at ground potential.

At the start of each driving pulse, signal C3 goes to state "0" and stays there. The transmission doors 80 and 86 are therefore blocked.

Comme Q66 = C66 (-U ) et Q67 = C67 (U_x-U_y), on peut écrire :

A l'instant D de la dernière impulsion C1 précédant l'impulsion C4, cette tension U75 a la valeur

où U_xD et Uy_D sont les valeurs de U et de U_y à cet instant D.The process described above is repeated at the first pulse C1 which follows the start of the driving pulse but, this time, the capacitor 79 charges at the voltage U75 defined. above. The transmission gate 83 is still blocked, so that the output voltage of the amplifier 84 does not change, and that the capacitor 88 remains discharged. The voltage U75 above therefore becomes equal to

As Q66 = C66 (-U) and Q67 = C67 (U _x -U _y ), we can write:

At time D of the last pulse C1 preceding the pulse C4, this voltage U75 has the value

where U _xD and Uy _D are the values of U and U _y at this instant D.

The C4 pulse is produced approximately one millisecond after the start of the driving pulse, at a time when the rotor is still stationary. This pulse C4 briefly opens the transmission gate 83. The capacitor 85 is therefore charged at this voltage U75 _D which also appears at the output of the amplifier 84. The pulse C2 following this pulse C4 opens the transmission gate 87 and the capacitor 88 therefore also charges at voltage U75 _D. The electrical charge Q88 of the capacitor 88 therefore becomes equal to:

It should be noted that the capacitor 85 remains practically charged at the voltage U75 _D as long as the transmission gate 86 remains blocked, if the input resistance of the amplifier 84 is large, which is the case. Subsequent changes in the output voltage of amplifier 74 no longer have any influence on this voltage since the transmission gate 83 is permanently blocked again.

At each subsequent pulse C1, the capacitor 88 discharges into the capacitor 75, at the same time as the capacitors 66 and 67. The charge of the capacitor 75 therefore becomes

It should also be noted that, at each pulse C2, the capacitor 88 recharges at the voltage U75 _D which is memorized by the capacitor 85.

At any time after the pulse C4, we can therefore write:

,cette équation devient :

If C88 = C75, and if, as above,

, this equation becomes:

, peut donc s'écrire :

The voltage U75, which is equal to

, can therefore be written:

This voltage U75 is independent of the voltage U, or of the voltage U _a '. In addition, it is proportional to the voltage U _rx induced in the motor coil at time t _x by the rotation of the rotor. Indeed, at time D defined above, the voltage U _m2 given by equation (12) is written:

en fonction des caractéristiques des divers composants du circuit de la figure 11, notamment des capacités des divers condensateurs et des gains des amplificateurs.Equation (14) above can therefore be written:

as a function of the characteristics of the various components of the circuit of FIG. 11, in particular of the capacities of the various capacitors and of the gains of the amplifiers.

FIG. 12 shows an example of a circuit realizing the function of the circuits 9, 12 and 13 of FIG. 4. In this example, the circuit 12 is constituted by a simple differential amplifier 41. The voltage U, constituted by the output voltage of one of the circuits 11 described above, is applied to the non-inverting input of this amplifier 41, the inverting input of which receives a voltage U _s ′ chosen as explained above. This voltage U ′ can be supplied by a separate source or by a simple voltage divider connected to the terminals of the source supplying the entire circuit.

In this FIG. 12, the control circuit 9 of the motor 10 comprises the transistors 14 to 17 described in connection with FIG. 6. It also comprises a type D flip-flop 42 whose clock input Ck is connected to the output S8 of circuit 8 of FIG. 4. The input D of this flip-flop 42 is connected to its inverse output Q * so that it changes state each time the signal S8 passes from the logic state "0" in logic state "1". The direct output Q of the flip-flop 42 is connected to a first input of an AND gate 43 whose output is connected to the control electrodes of the transistors 14 and 16. The output Q * of the flip-flop 42 is connected to a first input of an AND gate 44, the output of which is connected to the control electrodes of the transistors 15 and 17.

The control circuit 9 also comprises a flip-flop 45, of type D, the clock input Ck of which is connected to the output S8 of the circuit 8 by means of an inverter 58.

The input D of this flip-flop 45 is permanently in the logic state "1", and its output Q is connected to the second input of the gates 43 and 44.

The calculation circuit 13 comprises a flip-flop 46, also of type D, whose clock input Ck is connected to the output S8 of circuit 8 and whose input D is permanently in the logic state "1 ". The outputs Q and Q ^* of the flip-flop 46 are respectively connected to the first inputs of two AND gates 47 and 48, the second inputs of which are connected, together, to the output Q of the flip-flop 45.

The rotor being stationary at time D, the voltage U _m2 is equal to the voltage U _{m2r '} defined by equation (13) above.

By replacing in equation (15), the term U _m2 by the value of U _m2r taken from this equation (13), we can write:

A comparison of this equation (16) with equation (11) above shows that:

Since the voltage U _m1 is proportional to the voltage U, the voltage U75 is also proportional.

alors U7_{5 =} U_m1.If the capacity C75 is chosen equal to C67

then U7 _{5 =} U _m1 .

It is quite clear, however, that another relationship can be chosen between the C75 capacity and the C67 and C88 capacities. Likewise, the gain of amplifiers 74 and 84 can be chosen different from one. In any case, the voltage U75 will remain proportional to U _m1 , and therefore to the voltage U induced at time t in the motor coil by the rotation of the rotor.

It should be noted that, since the non-inverting input of the amplifier 75 is connected to ground, the capacitors 66, 67 and 88 completely discharge in the capacitor 75 at each pulse C1. At each pulse C2, this capacitor 75 is short-circuited by the transmission gate 76 and the voltage U75 calculated above drops to zero. The capacitor 79 which is charged at this voltage U75 at each pulse CI ensures the storage of this voltage between two successive pulses C1. The voltage U75 memorized by the capacitor 79 is amplified by the amplifier 78 by a factor which can be freely set by choosing the ratio of the values of the resistors 81 and 82. The output voltage U78 of the amplifier 78 is also proportional at the voltage U, and can therefore constitute the voltage U _m applied to the comparison circuit 12 of FIG. 4. The reference voltage U _s ' applied in this case to this circuit 12 must obviously be chosen

The reset input R of the flip-flop 46 is connected to the output of the differential amplifier 41.

Three transmission doors 49, 50 and 51 have their control input respectively connected to the outputs of doors 47 and 48, and to the output Q * of the flip-flop 45. These transmission doors 49, 50 and 51 are similar to the door transmission 21 of FIG. 6. When their command input is in logic state "0", they are in their blocking state and when their command input is in logic state "1", they are in their state driver.

The transmission door 49 is connected between the positive pole + Uade the power source and a resistor 52, of value R52.

The transmission door 50 is connected between the negative pole -U of the power source and a resistor 53, of value R53.

Finally, the transmission door 51 is connected between a voltage U be which will be defined below, and a resistor 54, of value R54.

The second terminals of resistors 52, 53 and 54 are connected to each other and to the inverting input of a differential amplifier 55, the non-inverting input of which is connected to a determined voltage, which is that of ground in the present example. .

A capacitor 56, of capacity C56, is connected between the common point of the resistors 52 to 54 and the ground.

The output of the amplifier 55 is connected to a first input of an AND gate 57 whose second input is connected to the output Q * of the flip-flop 46. The output of this gate 57 is connected to the input R of resetting the flip-flop 45.

The operation of this circuit will now be explained, using the diagram in FIG. 13. At rest, the output Q of the flip-flops 45 and 46 is in the state "0". The output of doors 43, 44, 47 and 48 is therefore also at "0". The transistors 14 and 15 are therefore conductive, which short-circuits the coil of the motor 10. The transistors 16 and 17 are blocked. The transmission doors 49 and 50 are blocked, while the transmission door 51 is made conductive by the state "1" present at the output Q * of the flip-flop 45.

The voltage U56 across the capacitor 56 is therefore equal to the voltage U _b . If this voltage is positive, as in this example, the outputs of amplifier 55 and of gate 57 are at "0".

If the voltage U _b is negative, the output of the amplifier 55 and the output of the gate 57 are at "1".

As the rotor of the motor 10 is stationary, the voltage U22 is zero, and the output of the amplifier 41 is at "0".

We will admit, for this explanation, that the output Q of the flip-flop 42 is for the moment at "0" and that the signal S8 of output of circuit 8 takes the state "1" for a few microseconds each time the motor must take a step.

As soon as the signal S8 goes to "1", at time t, the outputs Q of the flip-flops 42 and 46 go to "1".

The output of gate 57 therefore changes to "0", even if the output of amplifier 55 is at "1" at this time.

When signal S8 returns to "0", a few microseconds later, the Q output of flip-flop 45 also changes to "1".

The output of gate 43 therefore also changes to "1". The transistor 14 is blocked and the transistor 16 becomes conductive. The current i begins to circulate in the coil of the motor 10, through the transistors 15 and 16. The voltage at point 19 begins to increase and act on the measurement circuit 11 as has been explained with reference to FIGS. 6, 9 or 12.

At the same time, the output Q * of the flip-flop 45 changes to "0", which blocks the transmission door 51. The output of the door 47 changes to "1", which makes the transmission door 49 conductive. The voltage + U a is therefore applied to the capacitor 56 through the resistor 52, and the voltage U56 begins to increase according to an exponential curve having a time constant il determined by the product R52.C56. To simplify the drawing, the variation of the voltage U56 has been represented, in FIG. 13, as a linear variation.

When at time t _d , the voltage U22 exceeds the threshold voltage U _s ', the output of the amplifier 41 changes to "1". The output Q of the flip-flop 46 therefore returns to "0", which causes the blocking of the transmission door 49. The value U _d reached by the voltage U56 at time t _d depends on the time T2 taken by the induced voltage U to reach the threshold voltage U, the value of the voltage U _b and the time constant τ1.

At the same instant t _of the output Q * d ₂ this flip-flop 46 goes to "1", which makes the transmission gate 50 conductive. The voltage -U a is therefore now applied to the capacitor 56 through the resistor 53. The voltage U56 therefore begins to decrease, from the value U _d , with a time constant 12 determined by the product R53.C56.

When at the instant t _i , this voltage U56 becomes equal to a determined voltage, which is the voltage of the ground in the present example, the output of the amplifier 55 changes to "1", which resets the flip-flop 45 in its rest state, that is to say with its Q output at "0" and its Q * output at "1". The output of the gate 43 therefore returns to "0", which blocks the transistor 16 and makes the transistor 14 conductive. The current i is therefore interrupted, and the rotor of the motor ends its pitch thanks to its inertia and thanks to a part energy that is stored, in the form of magnetic energy, in the inductance of the coil. The rotor is braked by the short circuit which is established through the transistors 14 and 15.

The time T3 taken by the voltage U56 to become equal to zero depends on the voltage U _d that it had reached at the instant t _d and on the time constant τ2.

The duration Tl of the driving pulse is equal to the sum of the durations T2 and T3. As T3 depends on the voltage U _of and this voltage U _{d itself} depends on the duration T2, we see that this duration Tl depends directly on the time T2 put by the voltage U induced in the motor coil by the rotation of the rotor to reach a predetermined U value.

Knowing by tests, as explained above, the duration TOI of the driving impulse necessary to run the motor without load, the time T02 put by the induced voltage U _r to reach the value U _s when the motor is also without load, and the coefficients a and b of the lines which represent the variation as a function of the motor load of the duration of the driving pulse and of the time taken by the voltage U _r to reach the threshold U _s , it is easy to determine the time constant t1 and t2 as well as the voltage U _b so that the relation (1) mentioned above is verified. It is therefore in the form of these parameters τ1, t2 and U _b that the constants k and K of this relation (1) are introduced in the present example of the calculation circuit 13. The voltage U _b can be chosen negative, if necessary, to take account of the sign of the constant K.

At time t _i , the state "0" of the output Q of the flip-flop 45 causes the blocking of the transmission gate 50. The state "1" of the output Q ^* of this flip-flop 45 makes the conductive transmission door 51. The voltage U _b is therefore again applied to the capacitor 56 through the resistor 54. The voltage U56 therefore increases again, until it reaches, after a certain time, the voltage ^U _b .

As soon as the voltage U56 becomes positive again, the output of the amplifier 55 returns to "0". This output therefore remains in state "1" only for a very short time.

A certain time after the instant t _d the voltage U22 falls below the voltage U s'. The output of amplifier 41 therefore returns to "0". This time, which plays no role in the operation of the circuit, depends on the mechanical load driven by the motor and on the value of the voltage U _s '.

When the signal S8 returns to "1", the process described above begins again, with the only difference that this time, it is the output Q * of the flip-flop 42, and therefore the output of the gate 44, which goes to "1". The transistor 15 is blocked, and the transistor 17 becomes conductive, which causes the passage of the current i in the opposite direction to that which it had in the previous case.

FIG. 14 illustrates another example of a circuit realizing the function of the calculation circuit 13 of FIG. 4.

This circuit comprises a flip-flop 91, of type D, the clock input Ck of which receives the signal S8 from the output of circuit 8 in FIG. 4. The input D of this flip-flop 91 is permanently at l 'logical state "1". Its output Q is connected to the U / D input for determining the counting direction of a reversible counter 92. This counter 92 is also preselectable, which means that, in response to a pulse on a control input C, its content takes a value determined by the logic states "0" or "1" which are applied to preselection inputs designated together by P.

The control input C of the counter 92 is also connected to the output S8 of the circuit 8, and its inputs P are connected, in a fixed or modifiable manner which will be described below, to the potentials representing the logic states "0" and "1".

The counter 92 also includes a clock input Ck which is connected to the output of an OR gate 93 whose inputs are respectively connected to the outputs of two AND gates 94 and 95.

The inputs of gate 94 are respectively connected to the output Q of the flip-flop 45 of FIG. 12, not shown in this FIG. 14, to the output Q of the flip-flop 91, and to a circuit, also not shown, which delivers a periodic signal having a frequency fl. This circuit can be circuit 8 in FIG. 4 and the frequency f1 is chosen in a manner which will be described later.

The inputs of gate 95 are respectively connected to the output Q of the flip-flop 45, to the output Q * of the flip-flop 91 and to a circuit, which can also be circuit 8 of FIG. 4, and which delivers a periodic signal having a frequency f2, the choice of which will also be described below.

The outputs of counter 92, designated together by S, are connected to a detection circuit 96, the output of which takes the state "1" when the content of counter 92 is equal to zero. This detection circuit 96 can simply consist of a reverse OR gate, each input of which is connected to an output of the counter 92.

The output of this detection circuit 96 is connected to an input of an AND gate 97, the other input of which is connected to the output of the flip-flop 91.

Finally, the output of gate 97 is connected to the reset input R of flip-flop 45 of FIG. 12, not shown in FIG. 14.

• Lorsque le signal S8 passe à l'état "1", le contenu N du compteur 92 prend l'état Ni qui lui est imposé par l'état de ses entrées P. En même temps, la sortie Q du flip-flop 91 passe à l'état "1".

The operation of this circuit, which is illustrated in FIG. 15, is as follows:

• When the signal S8 changes to state "1", the content N of the counter 92 takes the state Ni which is imposed on it by the state of its inputs P. At the same time, the output Q of the flip-flop 91 changes to state "1".

When, at the end of the pulse S8, the output Q of the flip-flop 45 goes to state "1", the frequency pulses fl pass through the gates 94 and 93 and begin to increment the content of the counter 92, at from the value Ni that this content has taken in response to the signal S8.

At the end of time T2 ', the induced voltage measured by circuit 12 reaches the value of the reference voltage, and the output S12 goes to state "1". The output Q of the flip-flop 91 therefore passes to the state "0" and its output Q ^k to the state "1".

The value Nd of the content of the counter 92 at this instant depends on the time T2 'taken by the induced voltage U to reach the threshold voltage U, of the initial value Ni taken by the content of this counter 92 in response to the signal S8, and of the frequency fl.

The output Q * of the flip-flop 91 now being in state "1", the frequency pulses f2 pass through the gates 95 and 93, and begin to decrement the content of the counter 92, from this state Nd.

When the content of the counter 92 reaches the value zero, the output of the detection circuit 96 and the output of the gate 97 pass to the state "1", which sets the output Q of the flip-flop 45 to "0". The driving pulse which had started at the end of signal S8 is thus interrupted.

The time T3 'taken by the counter 92 to reach the zero state depends on the value Nd reached by its content at the time when the output S12 of the circuit 12 changes to the state "1" and on the frequency f2.

In a similar manner to the case of FIG. 13, the duration Tl 'of the driving pulse is equal to the sum of the durations T2' and T3 '. As the duration T3 'depends on the value Nd, and since this value Nd itself depends on the duration T2', the duration Tl 'of the driving pulse depends directly on the time T2' put by the voltage U induced in the coil of the motor by the rotation of the rotor to reach the predetermined value U.

In this case, the frequencies fl and f2 play the role of the cons time aunts τ1 and τ2 in the case of FIG. 12, and the initial value Ni plays that of the voltage Ub.

These frequencies f 1 and f 2 ′ and this initial value Ni must therefore be determined by the same tests as those which are necessary for the determination of the time constants τ1 and 12 and of the voltage Ub in the case of FIG. 9, so that the relation (1) mentioned above is verified. It is in the form of these frequencies fl and f2 and of this initial value Ni that the constants k and K of this relation (1) are introduced in this example of calculation circuit 13.

If necessary, according to the sign of the constant K, a negative initial value Ni must be introduced into the counter 92. As the value of the content of a counter is always a positive number, in this case it is necessary to enter into the counter 92 an initial value Ni 'equal to the difference between the counting capacity of the counter 92 and the absolute value of Ni.

In this case, the content of the counter 92 goes through zero after Ni frequency pulses f1 have been received by its input Ck. But as at this moment the output Q * of the flip-flop 91 is still in the state "O", the signal "1" delivered by the output of the circuit 96 is blocked by the gate 97. The driving pulse is not therefore not interrupted at this time.

It is obvious that the circuits described above only constitute examples allowing the implementation of the invention. Other circuits for measuring the voltage U r could be produced. Similarly, the information provided by this measure could be used differently. Finally, even in the case where this information is provided by the time taken by this voltage U to exceed a determined threshold U, the calculation circuit 13 could be produced differently.

However, these differences in the implementation of the invention would not go beyond the scope of the latter.

It should also be noted that the relation (1) between the optimum duration of the driving pulse and the time T2 set by the voltage U _r to exceed the threshold voltage U might not be linear. But even then it could be defined by a few tries. The computing circuit 13 should then simply be designed to perform the desired function.

Claims (5)

1. Method for measuring the voltage induced in the coil of a stepping motor by the rotation of its rotor in response to the application to the coil of a supply voltage, said coil having an equal time constant at the quotient of its resistance and its inductivity, characterized in that it consists in producing a representation of the difference between the current which would circulate in the coil at a second instant if the induced voltage was zero since a first instant, prior to second instant and separated from it by a determined duration, and the current which actually flows in the coil at this second instant, said difference being proportional to said induced voltage. 2. Method according to claim 1, characterized in that it consists in periodically producing said representation with a period greater than or equal to said determined duration. 3. Method according to claim 1 or 2, characterized in that the production of said image consists in producing a first voltage proportional to the current flowing in the coil, in producing a second voltage which increases exponentially from the first instant from the value of the first voltage at the first instant with a time constant equal to the time constant of the coil, and in producing a third voltage equal to the difference between the values of the second and of the first voltage at the second instant, said image being constituted by said third voltage. 4. Method according to claim 1 or 2, characterized in that the production of said image consists in producing a first voltage proportional to the current flowing in the coil, in memorizing the value of the first voltage at the first instant, in producing a second voltage equal to the difference between said stored value and the value of the first voltage at the second instant, to produce a third voltage equal to the difference between said supply voltage and said stored value, and to produce a fourth voltage equal to the sum of the second voltage and the product of the third voltage by the quotient of said duration and said time constant, said image being constituted by said fourth voltage. 5. Method according to claim 2, characterized in that the production of said image consists in producing a first voltage proportional to the current flowing in the coil, in storing, at each first instant, a second voltage equal to the first voltage, to produce, at each second instant, a third voltage equal to the difference between the second voltage and the first voltage, to memorize, at a second determined instant situated before the start of the rotation of the rotor, a fourth voltage equal to the difference between the third voltage and the product of the second voltage by a constant factor equal to the quotient of said duration and of said time constant, and in producing a fifth voltage equal to the difference between, on the one hand, the difference between the third voltage and the product of the second voltage by said constant factor and, on the other hand, the fourth voltage, said image being constituted by said fifth voltage.

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