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Title:
PROCEDURE FOR REGULATING THE VELOCITY OF AN ELEVATOR, AND AN ELEVATOR SYSTEM
Document Type and Number:
WIPO Patent Application WO/1998/057878
Kind Code:
A2
Abstract:
The invention relates to a procedure for regulating the velocity of an elevator. In the procedure, the regulation of velocity employs feedback and is digitally implemented. The feedback for velocity regulation is effected using a feedback signal (V¿est?) which is generated from a reference (T¿ohje?) controlling the elevator drive (4) and based on the result (V¿olo?) of a measurement of the velocity of the elevator. The invention also relates to an elevator system in which the velocity data (V¿olo?) produced by a velocity measuring device is used to generate a feedback signal (V¿est?) by using the parameters ($g(b)) of a model describing the operation of the elevator.

Inventors:
LAAKSONHEIMO JYRKI (FI)
Application Number:
PCT/FI1998/000484
Publication Date:
December 23, 1998
Filing Date:
June 05, 1998
Export Citation:
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Assignee:
KONE CORP (FI)
LAAKSONHEIMO JYRKI (FI)
International Classes:
G05D17/00; H02P23/16; (IPC1-7): B66B1/28
Domestic Patent References:
WO1996004708A11996-02-15
Foreign References:
US5006770A1991-04-09
US4940117A1990-07-10
Attorney, Agent or Firm:
KONE CORPORATION (P.O. Box 677, Hyvinkää, FI)
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Claims:
CLAIMS
1. Procedure for regulating the velocity of an elevator, in which procedure feedback is applied in the regulation of velocity, characterised in that the feedback for veloc ity regulation is implemented using a feedback signal (vest) which is generated using a reference (Tohje) control ling the elevator drive (4) or some other reference sub stantially proportional to it and the result (volt) of a measurement of the velocity of the elevator.
2. Procedure as defined in claim 1, characterised in that the reference (Tohje) controlling the elevator drive (4) is one of the following: voltage and frequency reference, current and frequency reference, torque reference, accel eration reference.
3. Procedure as defined in one or more of the preceding claims, characterised in that a model describing the ele vator is defined and the model is used to generate the feedback signal (vest) on the basis of the reference (The) and the result (volt) of the velocity measurement.
4. Procedure as defined in claim 3, characterised in that the model describing the elevator is defined as an un changeable part of the velocity regulation of the eleva tor.
5. Procedure as defined in claim 3, characterised in that a model describing the elevator is defined and that the model is repeatedly updated.
6. Procedure as defined in claim 5, characterised in that the model is updated on the basis of a preset schedule.
7. Procedure as defined in claim 5, characterised in that the velocity regulation employs a control loop time inter val and that the updating of the model employs a control loop time interval, and that the control loop time inter val used in updating the model is longer than the control loop time interval used in velocity regulation.
8. Elevator system comprising a motor drive and a motor, an elevator and its mechanisms, a velocity measuring de vice and a control system producing a reference (Tohje) for the motor drive, said control system comprising a digital controller in which at least the velocity data (vOlO) pro duced by the velocity measuring device is available, char acterised in that, in the controller, the reference (Tohje) is generated using a feedback signal (vest) formed from the reference and the velocity data by using the parameters ( ) of a model describing the operation of the elevator.
9. Elevator system as defined in claim 8, characterised in that the parameters ( ) of the model are updateable.
10. Elevator system as defined in claim 9, characterised in that the time interval between successive updates of the model parameters ( ) is longer than the time interval between successive generations of the feedback signal.
Description:
PROCEDURE FOR REGULATING THE VELOCITY OF AN ELEVATOR, AND AN ELEVATOR SYSTEM The present invention relates to a procedure as defined in the preamble of claim 1 for regulating the velocity of an elevator and to an elevator system as defined in the pre- amble of claim 8.

In the regulation of elevator speed, problems frequently arise due to various disturbances in the feedback loop used for speed control. The disturbances have an adverse effect on the quality of the response at the output of the drive motor of the elevator, thereby reducing the travel- ling comfort provided by the elevator.

In an elevator application, the source of power to be used can be selected from among different motor types, such as direct-current motor, cage induction motor, alternating- current motor or synchronous motor. In these motor types, regulation of the speed of rotation is implemented in dif- ferent ways. In a direct-current motor, speed regulation is accomplished by regulating the voltage and current sup- plied to the motor, e.g. by wasting any extra energy into a resistance. A problem in this case is a high power dis- sipation. In alternating-current motors, speed regulation is traditionally accomplished by controlling the slip.

This is equivalent to increasing power dissipation and therefore uneconomical. Nevertheless, a.c. motors are con- siderably better than d.c. motors in respect of effi- ciency, but the traditional speed regulation system used with them leads to a high power dissipation. The economic advantages of an alternating-current motor are lost when traditional slip control is used. By using a frequency converter drive, a fairly low level of power dissipation

can be achieved.

'Frequency converter drive' of an elevator means control- ling an alternating-current motor by using a variable fre- quency and a variable voltage. The voltage taken from the network is e.g. a 50-MHz sinusoidal alternating voltage, which is rectified in the frequency converter. After this, the frequency converter produces a new sinusoidal alter- nating current, whose frequency and amplitude are varied in accordance with the control of the frequency converter.

The new alternating current is supplied to the a.c. motor.

In the measurement of elevator speed, a commonly used ex- pedient is to use an analogue tachometer which outputs a voltage proportional to the speed of rotation of the trac- tion sheave. The voltage signal is filtered and scaled by means of analogue components, whereupon the signal is fed into an analogue/digital converter. The converter produces a digital speed signal, which is used for speed regula- tion.

A problem with speed measurement using an analogue ta- chometer is that the speed signal obtained from the volt- age is always subject to disturbances due to the rotation of the tachometer, electrical interference from the ma- chine room equipment and to the resolution of the ana- logue-to-digital conversion (of the voltage into velocity data). In an attempt to eliminate the problem, the voltage signal has been filtered using analogue components before the A/D conversion. The filtering produces a delay that leads to new disturbances when it becomes too long.

At low speeds, an analogue tachometer produces a very low voltage, and this means that the analogue components must

meet accuracy requirements in the per mill category. The offset in an A/D converter easily amounts to tens of mil- livolts, which is a level rather more appropriately ex- pressed as a percentage of the 4.5 V signal for the nomi- nal elevator speed.

The speed detector used may be a resolver which sends sine and cosine signals proportional to position. From these signals, a resolver/digital converter (RD converter) out- puts a pulse when the angle changes. The speed is measured by a method in which the number of pulses received from the RD converter in a given period of time is counted (so- called MT method). The speed can be computed from the pulse count. When a resolver is used, disturbances appear at the rotational frequency of the resolver and at multi- ples of that frequency. At low speeds, problems arise be- cause the number of pulses available is very small. The measured speed value is apt to change and typically re- mains oscillating between certain values. Since the re- solver is a position detector and it is used for speed measurement, the conversion produces a certain noise in the digital signal. Filtering is used to eliminate spuri- ous effects, but filtering leads to the same problems as when a tachometer signal is used.

Sometimes speed feedback is implemented using an encoder giving the absolute position of the traction sheave. The position data can be converted to a speed value by the MT method. Encoders can output a digital signal, which is less susceptible to electrical interference. At low speeds, however, resolution is a problem. In other re- spects, too, the use of an encoder leads to problems simi- lar to those associated with a resolver, although the po- sition data is obtained directly in digital form.

The object of the present invention is to eliminate the drawbacks of prior art and, in particular, to create a new speed regulation system for an elevator that is less sus- ceptible to disturbances than earlier systems. The basic idea of the invention is to generate a feedback signal to be used in speed regulation, said signal being generated using measured elevator speed data and a reference con- trolling the elevator drive. The details of the features characteristic of the invention are presented in the claims.

By applying the invention, it is possible to considerably reduce disturbances appearing in the measured speed and therefore also in the motor output (torque). More particu- larly, the so-called random disturbances, or rather their adverse effects on speed regulation can be eliminated from the feedback signal. Thus, more accurate and stable regu- lation is achieved. The invention is readily applicable for use with various discrete speed regulation systems in an elevator. The invention can also be used with different types of elevator drive.

The invention makes it possible to achieve a significant improvement in the quality of elevator operation and an increased robustness of regulation at a relatively low cost. Due to the robustness, the need for fine adjustment of speed regulation in conjunction with installation and maintenance is reduced, which means less work and lower costs. Moreover, the speed regulation is adaptable to changes in the operating conditions of the elevator, e.g. to the effects of a temperature change on the friction be- tween the guides and guide rails of the elevator. Simi- larly, long-time changes appearing with the ageing of the

elevator system can be compensated. This adaptability is accomplished by implementing the regulation using an up- dateable model describing the elevator. The updating can be performed in different ways. It is preferable to define an updating schedule that will keep the model sufficiently up-to-date without imposing an excessive load on the com- puting capacity available.

In a simplified form, the speed regulation system of an elevator can be said to consist of four components: the control system, the motor drive and motor, the elevator and its mechanisms, and a speed measurement system.

'Elevator and its mechanisms' in this context refers to the assembly comprising the elevator car, the equipment for mechanical guidance of the movement of the elevator car along a track in the elevator shaft, the means for transmitting the motional effect generated by the motor into movement of the elevator car, e.g. hoisting ropes and counterweight and other equipment that may be needed. The motor drive transmits the elevator control instructions from the control system to the elevator. The control sys- tem obtains speed feedback data from the elevator via speed measurement.

The boundary between the speed measurement system and the control system can be drawn at the point where the veloc- ity obtained from the speed detector is in digital form.

Changes and scaling of the speed feedback are preferably carried out on the same circuit card as the speed regula- tion, so that a short signal path between these functions is achieved. In speed measurement, it is usually necessary to use filtering in order to eliminate disturbances. The filtering causes a delay in the speed feedback, which in turn leads to oscillation in the speed feedback loop.

The control of the velocity and position of the elevator is effected by the control system, and so is the control of acceleration and changes of acceleration if needed. Via speed feedback measured from the elevator, the control system monitors the elevator speed to determine whether it follows the speed reference, and if necessary, corrects the control of the servo system and motor. The motor drive comprises the frequency converter and the motor. These process the speed reference obtained from the control sys- tem to produce a torque which is to be transmitted from the motor shaft to the traction sheave, via a gear if nec- essary. In the frequency converter, the digital reference is converted into analogue supply voltages for the motor phases. The conversion generates disturbances, which mani- fest themselves on the traction sheave. The invention al- lows these disturbances to be substantially reduced.

In the following, the invention will be described by the aid of an embodiment example, which is not to be regarded as a restriction of the invention, and by referring to the attached drawings, in which Fig. 1 is a diagram representing a prior-art speed con- trol loop in an elevator system, Fig. 2 is a diagram representing another prior-art speed control loop in an elevator system, Fig. 3 is a diagram representing an elevator speed con- trol loop according to the invention, Fig. 4 is a diagram representing another elevator speed control loop according to the invention, Fig. 5 represents the identification of a model, Fig. 6 presents the results of elevator speed measure- ment and a corresponding simulated speed,

Fig. 7 presents measured curves of the torque refer- ence, and Fig. 8 presents measured curves of the speed signal.

The diagram in Fig. 1 represents a prior-art speed control loop for the regulation of elevator speed. In Fig. 1, the speed control loop is divided into four blocks, which are speed regulation 101, elevator drive 104 comprising a fre- quency converter 102 and a motor 103, the elevator 106 as a process component and, fourth, speed measurement 107, which produces the actual velocity value v010 as a feedback signal. In the speed measurement, a controller 110 gener- ates a reference, in this case a voltage and frequency reference Uohje, fohje, for the elevator drive to enable the elevator to be driven at a speed consistent with the ve- locity reference Vref. Conventionally, one of the following references is generated for the elevator drive: voltage and frequency reference, current and frequency reference, torque reference, acceleration reference. The basic data used for the generation of these signals typically in- cludes the position, speed or acceleration reference.

In the speed measurement 107, the velocity of the elevator 106 is measured e.g. directly from the traction sheave of the elevator 106 using an analogue tachometer 108, which produces a voltage proportional to the speed of rotation of the traction sheave. If necessary, the signal obtained from the tachometer is filtered and scaled by means of analogue components, whereupon the signal is taken to an A/D converter 109. The A/D converter 109 gives a digital speed signal volt, to be used as a feedback signal in speed regulation 101.

Fig. 2 shows a diagram representing another prior-art

speed control loop for the regulation of elevator speed.

In Fig. 2, the speed control loop is divided into four blocks, which are speed regulation 121 with a controller 130, elevator drive 124 comprising a servo system 122 and the motor 123, the elevator 126 as a process component 125 and, fourth, speed measurement 127, which produces the ac- tual velocity value v010 as a feedback signal.

In the speed measurement 127, the velocity of the elevator 126 is measured e.g. from the traction sheave of the ele- vator 126 by using a resolver 128, which produces sine and cosine signals proportional to position. From these sig- nals, a resolver/digital converter 129 produces a pulse when the angle changes. The actual speed value v010 for speed feedback is generated by the M/T method, in which the number of pulses produced by the RD converter in a given period of time is counted. The velocity can be com- puted from the pulse count. The digital speed signal thus obtained shows disturbances e.g. at the rotational fre- quency of the resolver and at multiples of that frequency.

Low speeds cause problems because the number of pulses is very small. The measured speed changes and typically re- mains oscillating between certain values. As the resolver is a position detector and it is used for speed measure- ment, this creates a certain noise in the digital signal.

Fig. 3 shows a diagram representing a speed control loop according to the invention. The speed control loop in Fig.

3 is divided into five blocks, which are speed regulation 1, elevator drive 4 comprising a servo system 2 and a mo- tor 3, and the elevator 6 as a process component 5, speed measurement 7 producing the actual velocity value v010 as a feedback signal and, fifth, a signal processing block, in which the element 11 performing the signal processing

preferably is an estimator. The feedback signal vest is taken to a controller 12 in the speed regulation block 1 in the conventional manner.

In the speed measurement block 7, the velocity of the ele- vator is measured by means of a resolver 8. The resolver produces sine and cosine signals proportional to position.

From these signals, a resolver/digital converter 9 pro- duces a pulse when the angle changes. The actual speed value v010 for speed feedback is generated by the M/T method, in which the number of pulses produced by the RD converter in a given period of time is counted. The veloc- ity can be computed from the pulse count. The digital speed signal v010 thus obtained contains various distur- bances, noise and possibly measuring errors. The speed signal vOlO is fed into an estimator in the signal process- ing block. The inputs fed into the estimator are the torque reference Tchje, supplied from the speed regulation block 1 to the elevator drive, and the actual velocity value signal v010 obtained from the speed measurement block. Making use of a model of elevator dynamics and tak- ing the typical system noise and other sources of error into account, the estimator eliminates quantum noise and other disturbances generated in the speed measurement 7.

Fig. 4 presents an alternative speed control loop in which one of the inputs to the signal processing block 10 is an acceleration reference aref instead of the torque reference Tohje supplied to the motor drive. In this case, the pa- rameters have to be selected differently, but otherwise the regulation works in substantially the same way as in the case illustrated by Fig. 3. From the point of view of the invention, the use of the acceleration reference in- stead of the reference applied to the motor can be re-

garded as a special case that simplifies the computing work involved.

In practice, in the computation of a status estimate, the estimator in Fig. 3 and 4 could be replaced with a monitor which only works by a different algorithm, aiming at ex- actly the same effect, i.e. at compensating the speed feedback. Instead of an estimator, it would be possible to use a monitor. A monitor cannot make use of a dynamic ele- vator model in the way an estimator does. In other re- spects, the operating principle of a monitor closely cor- responds to that of an estimator. For both an estimator and a monitor, it is necessary that a model of the eleva- tor exists. The parameters of the elevator model can be advantageously estimated by using a Kalman filter as the element 11 processing the feedback signal, in which the filter status also comprises the required parameters. The elevator speed regulation system has only a limited com- puting capacity, so the estimation and the identification of the parameters of the elevator model cannot be accom- plished without increasing the computing capacity from the conventional level if the same control loop time interval is used. In this case the identification algorithm can be divided into sections, which are computed one at a time.

In this way, the identification algorithm will not update the estimator parameters during each control loop time in- terval.

Fig. 5 represents the identification of the model as part of the generation of the feedback signal vest. From the reference u fed to the motor drive and from the velocity data v, the estimation block 20 produces a velocity esti- mate Vest, which is used as a feedback signal to the con- troller 22. Using the velocity estimate vest and the refer-

ence u, the identification block identifies the parameters of the model describing the elevator, and this model is fed as basic estimation data into the estimation block.

Thus, the estimation has an effect on the model, and the model has an effect on the estimation. To save computing capacity, it is preferable to update the model identifica- tion and recalculate the parameters at longer intervals than those at which the feedback signal is updated.

Based on the reference Tobje given by the speed controller or some other reference substantially proportional to it and the result V010 of the velocity measurement, a velocity estimate Vest is generated by means of the estimator and used as a feedback signal in speed regulation 4.

The computing algorithm constituting the velocity estimate can be solved by using the following estimator status model: Xk+l = Ae Xk + BeUek #k+1 = Ce#k+1 + Deuek+1, where Ae is the system matrix of the estimator status equa- tion, Be is the matrix of amplification of the inputs of the estimator status equation, Ce is the measuring matrix of the measuring equation of the estimator, De is the matrix of amplification of the inputs of the measuring equation of the estimator, xk is the estimator status vector at instant k, Yk is the velocity estimate at instant k,-

Uek is the estimator control vector at instant k, U,k = Tohjek V,lokI where Tohjek is the torque reference at instant k, and Volok is the velocity measurement at instant k.

When an estimator is used, a model of the elevator is needed. The model properties are identified on the basis of process tests.

For an elevator with rope suspension, it is possible to create a simplified model based on inertia mass. Such a model is sufficient for most practical elevators.

The model is described by the equation wnere co is the angular acceleration of the traction sheave, o is the angular velocity of the traction sheave, Jm is the total flywheel action of the elevator system Bm is the total friction of the elevator system, and Tm is the controlling torque.

As the feedback consists of velocity data, the angular ve- locity CO is converted into velocity v. This does not cause any problems because the angular velocity only needs to be multiplied by a scalar (radius of the traction sheave). This system can be described by a continuous status equation and a measuring equation:

x=Ax+Bu+v y = Cx+Du+w, where A is the system matrix of a general continuous status equation, B is the coefficient matrix of control of a gen- eral continuous status equation C is the measuring matrix of a general continuous measuring equation D is the coefficient matrix of control of a gen- eral continuous measuring equation u is the controlling torque Tm, x is the velocity v of the traction sheave, v is stochastic disturbance (noise) in the proc- ess, and w is stochastic disturbance (noise) in the meas- urement.

Turning the system into a discrete one, we obtain Xk+i = Akxk + B*uk + Vk Yk = CkXk + DkUk + Wk, where Ak is the system matrix of a general discrete status equation, Bk . is the coefficient matrix of control of a gen- eral discrete status equation, Ck is the measuring matrix of a general discrete measuring equation, Dk iS the coefficient matrix of control of a gen- eral discrete measuring equation, uk is the controlling torque Tm at instant k,

xk is the velocity v of the traction sheave at in- stant k, and vk, Wk are stochastic disturbances (noise) in the process and measurement.

NB! The subscript k in Ak, Bk, Ck and Dk here refers to the matrices of the discrete status model. The matrices are constant. In xk, uk and yk, the subscript k refers to in- stant k.

For the identification of the model, data representing the elevator speed Volo and the torque reference Tohje are needed. These are directly available in the speed control loop. In the identification, a certain torque requirement due to friction and the effect of the current load must be taken into account. The effect of the load can be taken into account by using weight data obtained from the load weighing device in the car. Fig. 6 presents the measured 31 and simulated 30 velocities of the elevator. The meas- urement has been carried out during maintenance operation of the elevator. The simulation has been effected by using a second-order status model and driving the elevator in the up direction at maintenance operation speed.

A good practical solution for implementing the estimator is a Kalman filter. The Kalman filter is used to monitor the velocity of the traction sheave or some other velocity proportional to the speed of the elevator car. The equa- tions for the Kalman filter can be written as #k = (Ak - AkLCk)#k + (Bk - Ak LDk)uk #k = (Ck - CkLCk)#k + CkLyk + (Dk - CkLDk)uk, where Ak is the system matrix of a general discrete

status equation, Bk is the coefficient matrix of control of a gen- eral discrete status equation, Ck is the measuring matrix of a general discrete measuring equation, Dk is the coefficient matrix of control of a gen- eral discrete measuring equation, uk is the controlling torque Tm at instant k, #k is the status vector of the Kalman filter at in- stant k, is the output of the estimator (velocity esti- mate Vest) Yk is the measurement (velocity Volo) L is the matrix of amplification of the Kalman filter.

The amplification matrix L can be computed by the digital linear least squares method. The covariance values for measurement noise and process noise are obtained by con- sidering the constant velocity range and using the equa- tion <BR> <BR> <BR> <BR> <BR> Q<q2 <BR> <BR> <BR> <BR> <BR> R < r2 where Q is the covariance of process noise (torque To hje) R is the covariance of measurement noise (velocity measurement Volo) and q, r are the corresponding standard deviation values.

After this, a discrete Kalman filter is generated by solv- ing the equations by a suitable numeric method. If it is assumed that the process noise and measurement noise are

white noise and if their covariance values are known, then a numeric solution can be easily accomplished by using e.g. a commercially available numeric program. When the required data are computed from the measurement data and simulation is carried out, it will be seen that the esti- mated and measured velocity signals are almost coincident.

In practice, the estimator is more or less system depend- ent. When the invention was tested in an elevator provided with a with permanent-magnet synchronous motor operated by a frequency-converter drive and the elevator was driven at a maintenance operation speed of 0.3 m/s using an estima- tor, it was established that speed regulation as provided by the invention had a pronounced effect on the quality of elevator travel. At frequencies above 10 Hz, both the measured ripple in the velocity and the ripple in the torque reference were reduced significantly, i.e. by about 15 dB. Fig. 7 presents the measured curves for downward elevator travel and torque reference without 34 the use of an estimator and with regulation 35 using an estimator, and Fig. 8 shows the velocity signal for torque reference without 34 the use of an estimator and with regulation 35 using an estimator. The estimator used in the operation tests in Fig. 7 and 8 was based on the first-order model.

An operation result like this is absolutely baffling. The substantial reduction of vibrations in the torque has a direct effect on travelling comfort.

The estimator itself can be easily implemented via soft- ware. In practice, only a relatively short routine is needed. It is to be noted that although the above descrip- tion focuses on torque input, the model does not make a difference e.g. between torque and acceleration. The most important point is that the input quantity, i.e. control

signal, is proportional to the torque. The implementation of the model therefore culminates in the identification of the model. For identification, at least the following three alternatives are applicable: Advance calculation and tabulation of parameters, identification setup, and real- time identification algorithm. Thus, the practical model used to implement the invention can be formed in several ways.

In principle, the model need not be accurate according to the stochastic control theory. This may provide the pos- sibility to use a limited number of predetermined sets of parameters which can be computed in advance, i.e. to com- pute and tabulate the parameters beforehand. From the ta- ble of parameters, suitable values e.g. according to the weight of the elevator are then selected. Although this alternative may be sufficient in many practical cases, it should be remembered that such a model is a very imperfect representation of the system and that an improved model generally leads to improved regulation.

Another method, which is better than the previous one and requires but relatively little processing power, is to in- clude data collection e.g. in the shaft setup of the ele- vator to allow identification. A few seconds would be suf- ficient for the regulation system to measure the torque or the voltage reference and the actual velocity. After shaft setup, the required coefficients for the estimator would be computed. After this, the elevator could be run in nor- mal operation with the estimator activated.

A more advanced method is to include in the algorithm for the model and filter an additional function for periodic updating of the model parameters and calculation of new

parameters for the estimator. In this way, the model and the regulation will be adapted to changing shaft and load conditions. However, such a system consumes more computing capacity and therefore requires hardware having somewhat more processing power than is needed for conventional regulation. Especially in fast elevators travelling at speeds of the order of 5 m/s or higher, this may make it necessary to choose a more powerful processor. As the es- timation of the parameters for the mechanical model is a repeated function in the regulation, it can be implemented e.g. by the least squares method. It is to be noted that the estimation of the model parameters can be performed in a clearly slower loop than the actual speed regulation; for example, speed regulation at 4 ms intervals, and iden- tification of coefficients at 100 ms intervals. In this way, the time interval between successive updates of the updateable model describing the elevator is longer than the time interval between successive generations of the feedback signal.

Regarding the selection of some of the quantities to be used in the model, there may be different and more advan- tageous alternatives than in the above description. For instance, using the acceleration reference instead of the actual torque as an input will improve the model in re- spect of initial torque and friction values.

It is obvious to the person skilled in the art that the embodiments of the invention are not restricted to the ex- ample presented above, but that they may be varied within the scope of the following claims.