EP0345120B1 - Washing machine or dryer with means for automatically determining the weight of the laundry - Google Patents

Description

The invention relates to a washing machine or dryer type laundry rotating drum which comprises means for automatically detecting the load of laundry introduced into the drum.

A household washing machine usually has a rotating drum in which the laundry is placed. This drum is perforated and is placed in a tank receiving the water or the mixture of water and detergent. The mixing of the linen is obtained for example by means of projections inside the drum.

It is generally preferable that the volume of water introduced into the machine, the quantity of detergent and other parameters, such as the durations of the various phases of operation of the washing machine: prewash, wash, rinse, spin, depending of the load of laundry introduced into the machine.

In European patent n ° 84 402090 in the name of the company ESSWEIN, a washing machine has been proposed in which the load of laundry is measured by the moment of inertia L of the laundry around the axis of rotation of the drum. This moment of inertia is determined by the drive torque. drum with non-zero determined acceleration, preferably constant. When the drum is driven by an electric motor of the universal type the torque is measured by the intensity of the electric current passing through the motor. However, this determination involves an estimate of the resistant torque (C _R ) opposed by the drum. This estimate gives an inaccuracy to the measurement of the load of linen.

In British patent application GB-A-2 202 332 published after the priority dates of this application, it was describes a system for detecting the weight of the laundry in the machine in order to monitor the amount of rinse water. The system described uses a microprocessor.

In fact, the invention relates to an improvement in the washing machine described in this European patent 84 402090. It allows a more precise measurement. It also makes it possible, in one embodiment, to simplify the manufacture of the washing machine, in particular by doing without means for measuring the intensity of the electric current passing through the drive motor of the drum.

The washing machine or dryer according to the invention comprises, for determining the load of laundry in the drum, a means of measuring the moment of inertia of the laundry relative to the axis of rotation of this drum, this measurement being obtained by rotating the drum at constant acceleration. It is characterized in that it comprises a processor, in particular a microprocessor, controlling the rotation of the drum successively according to two different values of acceleration, this processor determining the moment of inertia of the laundry from a difference between, of on the one hand, a measurement of a parameter as a function of the acceleration which is carried out during the first acceleration, and on the other hand, a measurement of the same parameter carried out during the second acceleration.

In this way we eliminate the parameter C _R from the calculation.

In a first embodiment of the invention, the value ϑ of the phase angle of a control with phase control of the speed of the drum is used, without involving the intensity of the electric current passing through the motor.

In a second embodiment, the moment of inertia is determined from a difference between a measurement of the intensity of the electric current passing through the motor produced during the first acceleration and a measurement of this intensity passing through the motor during the second acceleration .

According to another aspect, the invention relates to a washing machine or dryer, characterized in that the universal drum drive motor being supplied with alternating current and its speed being determined by a phase control command by means of to a processor, in particular a microprocessor, this processor determines the moment of inertia from the value of the phase angle.

We see that this is how the processor determines the moment of inertia without the need to provide a particular means of measuring the intensity of the electric current. going through the engine.

• la figure 1 est un schéma montrant un moteur d'entraînement de tambour de lave-linge avec son circuit de commande,
• les figures 2 et 3 sont des diagrammes illustrant une commande de lave-linge selon l'invention, et
• les figures 4 et 5 sont d'autres diagrammes illustrant le fonctionnement d'un lave-linge pour une variante.

Other characteristics and advantages of the invention will appear with the description of some of its embodiments, this being carried out with reference to the attached drawings in which:

• FIG. 1 is a diagram showing a washing machine drum drive motor with its control circuit,
• FIGS. 2 and 3 are diagrams illustrating a washing machine control according to the invention, and
• Figures 4 and 5 are other diagrams illustrating the operation of a washing machine for a variant.

In the example the washing machine (not shown as a whole) is of the domestic type with a washing drum with a perforated cylindrical wall rotating around a horizontal axis inside a tank.

The electric motor 10 (FIG. 1) for driving the drum is of the universal type. It is supplied with alternating current 11, for example at the frequency of 50 Hz from the network, by means of a controlled switch 12 such as a triac.

For the control of the switch 12 and therefore of the motor 10, a microprocessor 13 is provided, connected to the triac control electrode 12 by means of an interface circuit 14.

The microprocessor 13 imposes on the motor 10 a set speed dependent on a program prerecorded in its memory. This microprocessor also constitutes the comparator for speed regulation. To this end, it has an input 13 to which the output signal of a tachometer generator 15 driven by the motor 10 is applied.

The microprocessor 13 controls the angle ϑ (FIG. 2) of opening of the triac 12 at each alternation of the alternating signal 11, that is to say the duration during which this switch 12 is conductive during each period of this signal 11.

In the diagram of FIG. 2, we have represented in abscissa the opening angle ϑ and on the ordinate the alternating signal 11. During a alternation of the signal 11, that is to say for phase angles ϑ between 0 and π radians, the triac is open , that is to say non-conductive, between angles 0 and ϑ and conductive between angles ϑ and π. It is the microprocessor 13 which provides the closing control pulse for the triac 12.

According to one aspect of the invention, this phase angle ϑ, which is determined by the microprocessor 13, is used for measuring the moment of inertia L of the laundry in the drum, that is to say for measuring the load of laundry.

Indeed we start from the following formula: $$\text{C = (L + J)}\frac{{\text{d}}_{\text{ω}}}{{\text{d}}_{\text{t}}}{\text{+ C}}_{\text{R}}$$

In this formula C is the engine torque, L the moment of inertia of the laundry with respect to the axis of the drum, J the moment of inertia of the drum with respect to its axis of rotation, d _ω / d _t the acceleration (or decelaration) of the rotation of the drum and C _R the resistant torque that opposes the drum.

For a universal motor, the motor torque is proportional to the intensity of the electric current flowing through it, that is to say: $$\text{C = KI}$$

In this formula K is a constant specific to the motor and I the intensity of the electric current which crosses it.

In addition, we know that the counter-electromotive force E of the universal motor is proportional to its speed of rotation; we can therefore write: $${\text{E = K ′}}_{\text{ω}}$$

In this formula K ′ is a constant.

We also know that the voltage U across the motor is related to the counter-electromotive force E, the electrical resistance R presented by this motor and the intensity I by the following relationship: $$\text{U = E + RI}$$

From this formula we deduce: $$\text{U = E + RI = K′ω + RI = K′ω +}\frac{\text{RC}}{\text{K}}$$

However, the voltage U supplied to the motor is (FIG. 2) a function of the angle ϑ, that is to say: $$\text{U = V f (ϑ)}$$

In this formula V _S is the maximum amplitude of the voltage 11.

From formulas (5) and (6) above we deduce: $${\text{V}}_{\text{S}}\text{f (ϑ) - K′ω =}\frac{\text{RC}}{\text{K}}\text{=}\frac{\text{R}}{\text{K}}\text{(L + J)}\frac{{\text{d}}_{\text{ω}}}{{\text{d}}_{\text{t}}}\text{+}\frac{\text{R}}{\text{K}}{\text{VS}}_{\text{R}}$$

According to one aspect of the invention for the calculation of L (the moment of inertia of the laundry) we make the following approximation: we consider that f (ϑ) is proportional to ϑ, that is to say that can write: $$\text{f (ϑ) = K₁ϑ,}$$

K₁ being a constant.

So : $${\text{V}}_{\text{S}}\text{K₁ϑ - K′ω =}\frac{\text{R}}{\text{K}}\text{(L + J)}\frac{{\text{d}}_{\text{ω}}}{{\text{d}}_{\text{t}}}\text{+}\frac{\text{R}}{\text{K}}{\text{VS}}_{\text{R}}$$

In relation (9) above V _S , K₁, K ′, R, K, J and C _R are constants, ω is a datum introduced (thanks to the tachometric generator 15) at the input 13 of the microprocessor 13 and the data ϑ and d ω / d _t are calculated by the microprocessor. As a result, the microprocessor 13 can be programmed to calculate the moment of inertia L from the formula (9) above.

However, to simplify the calculation, and so that this calculation does not depend on the value of the resistive torque C _R which can vary with speed, we prefer to proceed as follows:
The microprocessor is programmed in such a way that before introducing water into the machine, the motor 10 is made to rotate at a speed V corresponding for example to 200 revolutions / minute for the drum, then from time t₁ (Figure 3) increasing this speed at constant acceleration to a speed V₂, for example corresponding to a rotation speed of 400 revolutions / minute for the drum. The duration of this ramp up is Δt₁, that is to say approximately 4 seconds in the example.

Then the motor speed is reduced to the value V₁ and then the acceleration of the drum is started again with a different acceleration, four times smaller in the example. This second acceleration is stopped when the motor speed reaches the value V₂. The duration of this ramp is Δt₂. Since the acceleration is four times lower we can write: $$\text{Δt₁ =}\frac{\text{Δt₂}}{\text{4}}$$

During the first period of duration Δt₁ the microprocessor periodically determines, every twenty milliseconds (that is to say at the frequency of 50 Hz) in the example, the value of the angle ϑ₁ of control of the triac 12 and this angle is stored; the microprocessor also determines the sum, noted Σϑ₁, of all these angles ϑ₁.

During the second ramp of duration t₂, the value of the phase control angle ϑ₂ of the triac 12 is determined every 80 milliseconds (four times twenty milliseconds) and, as for the first ramp, the sum Σϑ₂ of all is carried out. these angles that we put in memory.

Then we make the difference between these two sums either: $$\text{D = Σϑ₁ -Σϑ₂}$$

This difference D is proportional to L + J, that is to say represents the load of laundry in the drum. Indeed :

When the engine speed has the value V _i during the first ramp, the above relation (9) is written: $${\text{V}}_{\text{S}}{\text{K₁ϑ₁ - K′V}}_{\text{i}}\text{=}\frac{\text{R}}{\text{K}}\text{(L + J)}\frac{{\text{d}}_{\text{w}}}{{\text{d}}_{\text{t}}}\text{1 +}\frac{\text{R}}{\text{K}}{\text{VS}}_{\text{R}}$$

In this formula: $$\frac{{\text{d}}_{\text{ω}}}{{\text{d}}_{\text{t}}}\text{1 =}\frac{\text{V₂ - V₁}}{\text{Δt₁}}$$

When the engine speed has the same value V _i during the second ramp, the relation (9) is still written: $${\text{V}}_{\text{S}}{\text{K₁ϑ₂ - K′V}}_{\text{i}}\text{=}\frac{\text{R}}{\text{K}}\text{(L + J)}\frac{\text{d}{}_{{\text{w}}_{\text{2}}}}{{\text{d}}_{\text{t}}}\text{+}\frac{\text{R}}{\text{K}}{\text{VS}}_{\text{R}}$$

In this formula: $$\frac{\text{from}}{{\text{d}}_{\text{t}}}\text{=}\frac{\text{V₂ - V₁}}{\text{Δt₂}}\text{=}\frac{\text{1}}{\text{4}}\frac{{\text{d}}_{\text{ω1}}}{{\text{d}}_{\text{t}}}$$

If we make the member-to-member difference between relations (12) and (14) above we obtain:

C_R s'éliminent en toute rigueur car ces formules correspondent aux mêmes vitesses de rotation, donc aux mêmes valeurs de couple résistant C_R.It will be observed that in the formulas (12) and (14) the terms $\frac{\text{R}}{\text{K}}$

C _{R are} eliminated in all rigor because these formulas correspond to the same rotational speeds, therefore to the same values of resistant torque C _R.

The number n of measurements of the angle ϑ or number n of samples, being the same for the two acceleration ramps, we can write:

We therefore see that the difference D = Σϑ₁ -Σϑ₂ is indeed proportional to L + J.

As a variant, the sampling period is the same during the second ramp, that is to say that in the example the number of samples is four times greater for the second ramp than for the first. In this case it is necessary to divide the sum of the values of ϑ₂ by four to obtain the quantity D proportional to L + J, that is to say that the microprocessor calculates the quantity D such that: $$\text{D = Σϑ₁ -}\frac{\text{1}}{\text{4}}\text{Σϑ₂}$$

Generally if the same number n of samples is desired during the two ramps, the sampling period during the second ramp must be λ times greater than during the first ramp, λ being the ratio between the first and second acceleration. If the sampling period is the same for the two ramps, it will then be necessary to assign to the sum of the angles ϑ for the second ramp a division factor equal to this same ratio λ between the first and the second acceleration.

Whatever the embodiment, the washing machine according to the invention is of a particularly simple embodiment since it does not require any particular means of measuring the intensity of the electric current passing through the motor 10. In addition, the indication of load of linen is more precise than with the provisions described in said European patent mentioned above because the calculation carried out makes it possible to eliminate the factor C _R in all rigor.

It is of course not essential that the second ramp 21 immediately follow the first ramp 20 as shown in Figure 3; it is possible to separate the end of the first ramp from the start of the second ramp.

We will now describe in relation to FIGS. 4 and 5 another embodiment of the invention which also allows a more precise measurement of the laundry load thanks to the elimination of the factor C _R. It differs from the embodiment previously described by the fact that the measurement involves the intensity of the electric current passing through the motor instead of the phase angle.

Formulas (1) and (2) above deduced: $$\text{I =}\frac{\text{L + J}}{\text{K}}\frac{{\text{d}}_{\text{ω}}}{{\text{d}}_{\text{t}}}\text{+}\frac{\text{VS}}{\text{K}}\text{R}$$

est calculé à partir de ω . Le calcul s'effectue dans l'exemple à l'aide d'un microprocesseur.In this relation (20) above I is measurable, for example by placing a resistor in series with the motor and by determining the voltage across this resistor, J and K are constants, ω is measurable, for example, using a tachometer generator and $$\frac{{\text{d}}_{\text{ω}}}{{\text{d}}_{\text{t}}}$$

is calculated from ω. The calculation is carried out in the example using a microprocessor.

On the other hand, as already indicated, the resisting torque C _R cannot be easily measured directly. This is why, according to the invention, provision is made for a command which makes it possible to eliminate this parameter C _R. To this end:
Before introducing water into the machine, the drum drive motor is rotated at a speed V corresponding for example to 200 revolutions / minute for the drum, then from the instant t₁ (FIG. 4) we increases this speed at constant acceleration to a speed V₂, for example corresponding to a rotation speed of about 400 revolutions / minute for the drum. The duration of this ramp up is Δ t₁, between the instants t₁ and t₂, that is to say approximately 4 seconds in the example.

Then the motor speed is reduced to the value V₁ and then the acceleration of the drum is started again at time t avec with a different acceleration, four times smaller in the example. This second acceleration is stopped at time t₄ when the engine speed reaches the value V₂. The duration of this ramp is Δ t₂. Since the acceleration is four times lower we can write: $$\text{Δt₁ =}\frac{\text{Δt₂}}{\text{4}}$$

The variation of the intensity I of the current passing through the universal motor, driving the drum is shown in FIG. 5.

During the first period of duration Δ t₁, using said microprocessor, periodically, every twenty milliseconds (that is to say at the frequency of 50 Hz) is determined in the example, the intensity I of the current passing through the motor and these intensities are stored in memory. The microprocessor also determines the sum, notedΣ I₁, of all these intensities I₁.

During the second ramp of duration Δ t₂, the intensity I₂ of the current passing through the motor is determined every 80 milliseconds (four times twenty milliseconds) and, as for the first ramp, the sum Σ I₂ of all these intensities is taken we put in memory.

Then we make the difference between these two sums either: $$\text{D = ΣI₁ - ΣI₂}$$

This difference D is proportional to L + J, that is to say represents the load of laundry in the drum. Indeed :
When the speed of rotation of the motor has the value V _i during the first ramp, the relation (20) above is written: $${\text{I}}_{\text{1i}}\text{=}\frac{\text{L + J}}{\text{K}}\frac{\text{d}{}_{{\text{ω}}_{\text{1}}}}{{\text{d}}_{\text{t}}}\text{+}\frac{\text{VS}}{\text{K}}\text{Ri}$$

In this formula: $$\frac{\text{d}{}_{{\text{ω}}_{\text{1}}}}{{\text{d}}_{\text{t}}}\text{=}\frac{\text{V₂ - V₁}}{\text{Δt₁}}$$

When the engine speed has the same value V _i during the second ramp, the relation (20) is still written: $${\text{I}}_{\text{2i}}\text{=}\frac{\text{L + J}}{\text{K}}\frac{\text{d}{}_{{\text{ω}}_{\text{2}}}}{{\text{d}}_{\text{t}}}\text{+}\frac{\text{VS}}{\text{K}}\text{Ri}$$

In this formula: $$\frac{\text{d}{}_{{\text{ω}}_{\text{2}}}}{{\text{d}}_{\text{t}}}\text{=}\frac{\text{V₂ - V₁}}{\text{Δt₂}}\text{=}\frac{\text{1}}{\text{4}}\frac{\text{d}{}_{{\text{ω}}_{\text{1}}}}{{\text{d}}_{\text{t}}}$$

If we make the member-to-member difference between relations (23) and (25) above we obtain:

Ri s'éliminent en toute rigueur car ces formules correspondent aux mêmes vitesses de rotation, donc aux mêmes valeurs C_Ri de couple résistant.It will be observed that in the formulas (23) and (25) the terms $\frac{\text{VS}}{\text{K}}$

Ri are eliminated in all rigor because these formulas correspond to the same rotational speeds, therefore to the same values C _Ri of resisting torque.

The number n of measurements of intensity I, or number n of samplings, being the same for the two acceleration ramps, we can write:

We therefore see that the difference D = ΣI₁ - Σ I₂ is indeed proportional to L + J.

As a variant, the sampling period is the same during the second ramp, that is to say that in the example the number of samples is four times higher for the second ramp than for the first. In this case it is necessary to divide the sum of the values of I₂ by four to obtain the quantity D proportional to L + J, that is to say that the microprocessor calculates the quantity D such that: $$\text{D = Σ I₁ -}\frac{\text{1}}{\text{4}}\text{Σ I₂}$$

Generally, if the same number n of samples is desired during the two ramps, the sampling period during the second ramp must be λ times greater than during the first ramp, λ being the ratio between the first and second acceleration. If the sampling period is the same for the two ramps, then it will be necessary to assign to the sum of the intensities I for the second ramp a division factor equal to this same ratio between the first and the second acceleration.

The formula (27) above shows that it is not essential to carry out a sum of samples during each ramp. It suffices to measure the intensity of the current for a speed V _i determined during the first ramp, to measure the intensity of the current during the second ramp for the same speed V _i and to make the difference between these two intensities to obtain a quantity proportional to L + J.

The laundry load can be determined not only before any water is introduced into the washing machine, but also at other times during machine operation.

The invention also applies to a dryer.

Claims (17)

1. A washing machine or dryer comprising, in order to determine the load of washing in the drum, a means for determining the moment of inertia (L) of the washing as related to the axis of rotation of the drum, said measurement being obtained by causing rotation of the drum at a preferably constant acceleration, characterized in that it comprises a processor, more particularly a microprocessor (13) controlling the rotation of the drum in order to make it turn successively (20, 21) at two different acceleration values, said processor determining the moment of inertia of the washing on the basis of a difference between, on the one hand, a measurement of a parameter (C, I, Θ) which is a function of the acceleration which is performed during the first acceleration and, on the other hand, a measurement of the same parameter (C, I, Θ) performed during the second acceleration.
2. The washing machine or dryer as claimed in claim 1, characterized in that, the motor (10) for driving the drum being of the universal type supplied with AC (11), its speed is determined by a phase control command from the processor (13) and in that the said parameter is the value (Θ) of the phase angle.
3. The washing machine or dryer as claimed in claim 2, characterized in that the processor (13) causes the rotation of the drive motor (10) for driving the drum from a first speed (V₁) up to a second speed (V₂) with a first acceleration, determines periodically, during this first acceleration, the values (Θ₁) of the phase angle and produces the sum (ΣΘ₁) thereof, then causes a second acceleration ramp of the speed of the motor (10) between the first and second speeds, with a different acceleration, the phase angle (Θ₂) also being determined periodically and summated (ΣΘ₂), the microprocessor then determining the difference between the two sums which represents the moment of inertia of the washing in the drum.
4. The washing machine or dryer as claimed in claim 3, characterized in that the period for the determination of the phase angles (Θ₂) during the course of the second acceleration is equal to the product of the period of determination of the phase angles (Θ₁) during the course of the first acceleration times the ratio (Δt₂/Δt₁) between the first and the second accelerations.
5. The washing machine or dryer as claimed in claim 3, characterized in that the periods of determination of the phase angles (Θ₁, Θ₂) are the same during the course of the first and the second accelerations, and in that the load of washing is represented by the following magnitude: $$\text{D = ΣΘ₁ -}\frac{\text{ΣΘ₂}}{\text{λ}}$$

   

   λ being the ratio between the first and the second acceleration.
6. The washing machine or dryer as claimed in any one of the claims 3 through 5, characterized in that the first speed (V₁) corresponds to a speed of rotation of the drum of the order of 200 rpm and the second speed (V₂) of rotation corresponds to a speed of rotation of the drum of the order of 400 rpm.
7. The washing machine or dryer as claimed in any one of the claims 2 through 6, characterized in that it comprises a tachometer generator (15) driven by the universal motor (10), said tachometer generator being connected with one input (13₁) of the processor (13) in order to regulate the speed of the motor (10) as a function of the program in the memory of the processor.
8. The washing machine or dryer as claimed in claim 7, characterized in that the processor (13) determines the moment of inertia (L) on the basis of the angle (Θ) in accordance with the following relationship: $${\text{V}}_{\text{S}}\text{K₁Θ - K′ω =}\frac{\text{R}}{\text{K}}\text{(L+J)}\frac{\text{dω}}{\text{dt}}\text{+}\frac{\text{R}}{\text{K}}{\text{C}}_{\text{R}}$$

   

   V_S being the maximum amplitude of the alternating feed signal of the motor (10), K, K₁ and K′ being constants, R being the electrical resistance of the motor, C_R being the resistant couple opposed by the drum, dΩ/dt being the acceleration of the drum and J being the moment of inertia of the drum in the strict sense.
9. The washing machine or dryer as claimed in claim 1, characterized in that, the drum being driven by an electric universal motor, the drum is caused to rotate successively in accordance with two different acceleration values (dω₁/dt, dω₂/dt), preferably constant ones, and in that the moment of inertia is determined on the basis of a difference between, on the one hand, a measurement of the intensity of the current flowing through the motor perfomed at the time of the first acceleration, and on the other hand, a measurement of the intensity of the current flowing through the motor at the time of the second acceleration.
10. The washing machine or dryer as claimed in claim 9, characterized in that the measurements made during the two accelerations are made at the same speed V₁ of rotation of the drum.
11. The washing machine or dryer as claimed in claim 9 or in claim 10, characterized in that a processor periodically determines the intensity I₁ of the current flowing through the motor during the first acceleration and produces the sum thereof and in that during the second acceleration the intensity of the current I₂ flowing through the motor is also determined periodically, the said difference being the difference between the two sums.
12. The washing machine or dryer as claimed in claim 11, characterized in that the period of determination of the current levels I₂ in the course of the second acceleration is equal to the product of the period of determination of the current levels I₁ in the course of the first acceleration multiplied by the ratio (Δt₂/Δt₁) between the first and the second acceleration.
13. The washing machine or dryer as claimed in claim 11, characterized in that the periods of determination of the current levels (I₁, I₂) are the same in the course of the first and the second accelerations and in that the load of washing is represented by the following magnitude: $$\text{D = ΣI₁ - Σ}\frac{\text{I₂}}{\text{λ}}$$

    

    λ being the ratio between the first and the second acceleration.
14. The washing machine or dryer as claimed in any one of the claims 9 through 13, characterized in that the first speed (V₁) is equal to a speed of rotation of the drum of the order of 200 rpm and the second speed (V₂) of rotation corresponds to a speed of rotation of the drum of the order of 400 rpm.
15. A washing machine or dryer comprising, in order to determine the weight of the load of washing in the drum, a means for determining the moment of inertia (L) of the washing as related to the axis of rotation of the drum, the motor (10) for driving the drum being of the universal type, characterized in that, the universal motor (10) being supplied with alternating current (11) and its speed being determined using a processor, more particularly a microprocessor (13), said processor determines the said moment of inertia on the basis of the value (Θ) of the phase angle.
16. The washing machine or dryer as claimed in claim 15, characterized in that it comprises a tachometer generator (15) driven by the universal motor (10), said tachometer generator being connected with an input (13₁) of the processor (13) in order to regulate the speed of the motor (10) as a function of the program in the memory of the processor.
17. A washing machine or dryer as claimed in claim 16, characterized in that the processor (13) determines the moment of inertia (L) on the basis of the angle (Θ) in accordance with the following relationship: $${\text{V}}_{\text{S}}\text{K₁Θ - K′ω =}\frac{\text{R}}{\text{K}}\text{(L+J)}\frac{\text{dω}}{\text{dt}}\text{+}\frac{\text{R}}{\text{K}}{\text{C}}_{\text{R}}$$

    

    V_S being the maximum amplitude of the alternating feed signal of the motor (10), K, K₁ and K′ being constants, R being the electrical resistance of the motor, C_R being the resistant couple opposed by the drum, dω/dt being the acceleration of the drum and J being the moment of inertia of the drum in the strict sense.

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