WO2000063652A1

WO2000063652A1 - A position encoder

Info

Publication number: WO2000063652A1
Application number: PCT/GB2000/001420
Authority: WO
Inventors: Lloyd Francis; Clive Frederickson; Gordon Hoey; Alan Boor; Eric Dean
Original assignee: Vishay Limited
Priority date: 1999-04-16
Filing date: 2000-04-14
Publication date: 2000-10-26
Also published as: JP2002542475A; AU4578900A; GB9908799D0; EP1171757A1

Abstract

In a position encoder having a resistive track (6) forming a closed loop, a wiper arm (7) which makes electrical contact with the closed loop and which is movable around the loop, and at least three terminals (A,B,C) provided around the loop and in electrical contact with the loop, for each position of the wiper arm (7), a series of voltage or current application patterns are applied, a voltage or current for each application pattern is measured, and one of the measured voltages or currents is selected to determine the position and the wiper arm (7) around the loop. The position encoding output characteristic of the device over the full range of movement of the wiper arm (7) is determined by combining linear portions of the position encoding output characteristics of each of the application patterns.

Description

A POSITION ENCODER

Field of the Invention

The present invention relates to a position encoder and in particular to a potentiometric position encoder (PPE).

Background to the Invention

PPEs may be used to provide information about the angular position of a rotating body and control the rotation of that body. Generally, they provide an output voltage corresponding to the angular position of an associated piece of hardware. For example, they may be used within a servo-control system associated with a closed circuit television (CCTV) camera.

Figure 1 shows an example of a conventional PPE. The PPE has a resistive track 1 connected between power supply voltages V+ and V-. A conducting wiper arm 2 is arranged to rotate about a point at the centre of the resistive track 1 having an end 3 in electrical contact with the track 1. As the wiper arm 2 rotates, the relative resistances Rl and R2 vary in proportion to the lengths LI and L2 and the voltage at point 5 on the resistive track 1 and hence an output voltage Vout detected by the wiper arm 2 varies accordingly. The variation of the output voltage Vout is used to determine the angular position of the wiper arm 2 and also any apparatus eg. CCTV camera, mounted on it. However, this PPE design has a "dead band" 4 in which no output voltage Vout is generated. Furthermore, reducing the size of the dead band is not an effective solution since the build up of conductive debris in the dead band may cause a short circuit and a complete breakdown of the device.

One type of device capable of producing a continuous voltage output over a full 360 degree range is the PPE disclosed in United States Patent No. 5,399,981. This device has a closed-loop 360 degree resistive track and a rotating wiper arm in electrical contact with the track. However, the technique used to resolve the angular position of the wiper arm only offers a resolution of ±1°. In addition, since the technique relies on exact algebraic relationships between measured voltages and angular position the device has a rather tight linearity tolerance of around 0.2% (± one half bit error window for measured voltages). This is particularly applicable at the maxima and minima of the output characteristic of the device where linearity worsens and measurements could cause an undefined output to be generated by the

PPE. The stringent linearity tolerance suggests that production yields would be low.

Summary of the Invention

According to a first aspect of the present invention, a potentiometric position encoder

comprises: a resistive track forming a closed loop; a wiper comprising a contact portion which makes electrical contact with the closed loop and which is moveable around the loop; at least three terminals provided around the loop and in electrical contact with the loop; a first control means for applying a voltage or current to the contact portion of the wiper or for measuring a voltage or current at the contact portion of the wiper; and, a second control means for applying voltages or currents to the terminals or for measuring voltages or currents at the terminals, wherein one of the first and second control means is controlled to supply a series of voltage or current application patterns and the other of the first and second control means is controlled to measure a voltage or current for each application pattern, and wherein a selected one of the voltage or current measurements is used to determine the position of the wiper.

The PPE of the present invention provides a defined voltage or current output over a full 360° range allowing the wiper arm position and the position of any associated hardware to be determined in this range. In particular, each voltage or current application pattern has an associated position encoding output characteristic and the position encoding output characteristic for the PPE over the range of movement of the wiper is obtained by combining the linear portions of the output characteristics of each application pattern.

Preferably, the second control means is arranged to apply voltages or currents sequentially between selected sets of terminals and the first control means is arranged to measure a voltage or current at the contact portion in response to each of the sequential voltage or current applications.

Preferably, the PPE comprises an analogue-to-digital converter for converting the voltages or currents received in response to each of the sequential applications of the voltages or currents applied between selected pairs of the terminals into digital signals and a memory for storing the digital signals.

Preferably, the PPE further comprises a memory having a stored algorithm used to select one of the voltage or current values measured by the first control means, the selected value being used to determine a position encoding voltage or current.

Preferably, the algorithm is defined by the following steps:

(a) If V3 is greater than (V2 - y), and V3 is greater than (VI + y), then read VI ; (b) If VI is greater than (V3 - y), and VI is greater than (V2 + y), then

read V2; and,

(c) If V2 is greater than (VI - y), and V2 is greater than (V3 -I- y), then

read V3; in which,

VI is the measured voltage or current from the wiper in response to the first voltage or current application;

V2 is the measured voltage or current from the wiper in response to the second voltage or current application; V3 is the measured voltage or current from the wiper in response to the third voltage or current application; and, y is an offset used in a calculation to enable the processor to select which of the three measured values for the voltage or current is used to calculate the position encoding voltage or current of the PPE.

Since each of the values VI, V2 and V3 are used to obtain the position encoding voltage or current over a respective third (segment) of the entire 360° range, a high resolution is obtainable. This is due to the capacity of the analogue-to-digital (A/D) converter. A standard 8-bit A/D converter may be used and so each segment can use the 256 available bits of the converter. This means a resolution of 0.5° will be possible. In another example of the present invention, the first control means is arranged to apply a voltage or current to the loop via the contact portion of the wiper and the second control means is arranged to measure the voltage or current at each of the terminals in response to the application of the voltage or current applied to the loop, the measured voltages or currents being used to determine the position of the wiper.

Again, the three stage voltage/current application or measurement cycle enables accurate determination of the wiper position to be made. In addition, a simple yet mechanically reliable structure of the PPE is to be achieved.

Preferably, the PPE further comprises a memory having a stored algorithm to select one of the voltage or current values measured by the second control means, the selected value being used to determine a position encoding voltage or current.

Preferably, the stored algorithm is defined by the following steps:

(a) If V3 is greater than (V2 - y), and V3 is greater than (VI + y), then read VI;

(b) If VI is greater than (V3 - y), and VI is greater than (V2 + y), then read V2; and, (c) If V2 is greater than (VI - y), and V2 is greater than (V3 + y), then read V3; in which, VI is an output voltage or current from a first one of the terminals;

V2 is an output voltage or current from a second one of the terminals; V3 is an output voltage or current from the third one of the terminals; and, y is an offset used in a calculation to enable the processor to select which of the three values for the output voltage or current is used to calculate the position encoding voltage or current of the PPE.

Preferably, the PPE further comprises a respective impedance coupled between each of the terminals and a reference wherein the voltage or current at each of the terminals is measured at a node connecting the terminal to the respective impedance.

Preferably, the resistive track is circular and the terminals are positioned equidistantly from each other on the resistive track.

According to a second aspect of the present invention, a servo-control system comprises a rotatable apparatus coupled to a potentiometric position encoder according to the first aspect of the present invention, in which the apparatus is coupled to the wiper such that any rotation of the apparatus causes a corresponding rotation of the wiper and vice- versa.

Preferably, the apparatus is a closed circuit television camera. Such a system allows rotation of the CCTV camera over a complete 360° range enabling the camera to be arranged in any selected position in this range. This allows a user (eg security guard) unconstrained viewing of a site having such a CCTV system such as, for example, a car park or an entrance area to a bank.

According to a third aspect of the present invention, a potentiometric position encoding method for a position encoder having a resistive track forming a closed loop, a wiper which makes electrical contact with the closed loop and which is movable around the loop, and at least three terminals provided around the loop and in electrical contact with the loop, comprises the steps of, for each position of the wiper arm, applying a series of voltage or current application patterns, measuring a voltage or current for each application pattern, selecting one of the measured voltages or currents, and determining the position of the wiper around the loop in dependance on the selected one of the measured voltages or currents.

Preferably, the measured voltage or current used to determine the position of the wiper is selected in dependance on the relative values of the measured voltages or currents.

Preferably, the position encoding output characteristic of the device over the full range of movement of the wiper arm is determined by combining linear portions of position encoding output chracteristics of each of the application patterns. Brief Description of the Drawings

Examples of the present invention will now be described in detail with reference to the accompanying drawings, in which: Figure 1 shows a schematic representation of a conventional PPE;

Figure 2 shows a schematic representation of a first example of a PPE according to a first aspect of the present invention based on a three terminal construction;

Figure 3 shows graphs of a possible variation of input voltage with time applied to the terminals of the PPE shown in Figure 2; Figure 4 shows a set of graphs of output voltage against wiper arm position for each of the three different graphs of input voltage shown in Figure 3;

Figure 5 shows one example of a graph of output voltage against angular displacement of the wiper arm over a continuous 360 degree range for the PPE of

Figure 1; Figure 6 shows another example of a graph of PPE output voltage against angular displacement of wiper arm available from the PPE of Figure 1 ;

Figure 7 shows a second example of a PPE according to the present invention; and,

Figure 8 shows a schematic representation of a CCTV system according to a second aspect of the present invention.

Detailed Description

Figure 2 shows a schematic representation of an example of a PPE based on a three terminal construction according to the present invention. The PPE has a circular resistive track 6 with three equidistantly spaced terminals A, B and C. In this example, a rotatable wiper arm 7 which pivots about the centre 8 of the circle defined by the resistive track 6 has an end 9 in electrical contact with the resistive track 6. Any contacting wiper could be used. As will be explained in detail below, in this case predetermined voltages are applied sequentially in a cyclical manner between selected pairs of the terminals A, B and C on the resistive track 6, although currents could be used as inputs instead of voltages. The voltage application cycle consists of three voltage application patterns as is described below, and for each case an output voltage is derived from the wiper arm 7.

In this example, the input voltages applied to the terminals A, B and C are applied by a processor 10 which also serves to receive the output voltages from the wiper arm 7. The processor may be an analog processor, a digital microprocessor or an application specific integrated circuit (ASIC). As will be explained below, the input voltages are applied in a cyclical manner respectively between selected pairs of terminals A, B and C. In response to a complete voltage application cycle, the processor 10 determines a monotonic output voltage for the PPE which serves as a position encoding voltage. The processor 10 receives three output voltages from the wiper arm in each cycle and uses preprogrammed logic algorithms to determine the position encoding voltage for the PPE, which subsequently enables the angular position of the wiper arm 7 at that instant to be determined. The operation of the PPE will now be described with reference to Figures 2 to 4 of the accompanying drawings. Figure 3 shows graphs of the variation of input voltage

VA, VB, and VC with time applied respectively to the terminals A, B and C of the

PPE shown in Figure 2, defining input voltage application patterns. In this example, square wave pulse signals are applied sequentially to the terminals A, B and C such that the falling edge of the voltage VA applied to terminal A precedes the rising edge of the voltage VB applied to terminal B. Likewise, the falling edge of voltage VB precedes the rising edge of voltage VC.

An input voltage to suit the processor 10 is applied between terminals A and C.

Terminal B at this stage is left open circuit. In this case, the longer arc of the resistive track 6 between terminal A and terminal C acts in the same manner as a single variable resistor would in a conventional voltage divider so that the angular position of the wiper arm 7 determines the magnitude of the detected voltage. The value of the output voltage is transferred to the processor 10 where it is stored in a memory 11. The memory 11 may be on board the processor 10 or it may be a separate component coupled to the processor 10.

The next step in the voltage application cycle is that the input voltage is applied between terminals B and A and terminal C is left open circuit. At this time, the longer arc of the resistive track between terminal B and terminal A now functions as the single variable resistor referred to above. As such, the output voltage from the wiper arm 7 changes accordingly and this second value of the output voltage is transferred to the processor 10 where it is stored in the associated memory 11.

During the third and final step of the voltage application cycle terminal A is left open circuit, and the input voltage is applied between terminals B and C. The same transition of the effective position of the single variable resistor occurs and a third value of the output voltage is stored in the memory 11. Since the frequency of the voltage application cycle is high in relation to any wiper arm movement for each position of the wiper arm 7, or in each sampling window, three values of output voltage are determined and stored in the memory 11 for use by the processor 10.

Figure 4 shows a set of graphs of output voltages against wiper arm position for each of the three different voltage application patterns. In this case a linear section 12, 13 and 14 of each graph is selected which corresponds to the wiper arm 7 being in a particular sector of the resistive track 6. The graphs generated will not be perfectly linear throughout and in particular as the wiper arm passes each of the terminals a flattening out of the graphs (and detected output voltages) occurs. However, this does not effect the linearity of the relationship between the position encoding voltage and the wiper arm angular position since the sections 12, 13 and 14 are selected from linear portions of the graphs shown in Figure 4.

After each sampling window, the processor 10 must determine which of the three stored values of the output voltage it will use to generate the position encoding voltage of the PPE. Each of the linear sections 12, 13 and 14 of the graphs shown in Figure 4 correspond to the contact portion of the wiper arm 7 being in one of three sectors of the resistive track 6. By combining the sections of these graphs a single linear voltage output over a full 360 degree range of wiper arm position can be generated. As will be explained below, the processor 10 executes a stored program to determine a position encoding voltage which can be used to determine the wiper arm position.

One possible algorithm implemented by the stored program is as follows:

1. If V3 is greater than (V2 - y), and V3 is greater than (VI + y), then read VI;

2. If VI is greater than (V3 - y), and VI is greater than (V2 + y), then read V2; and, 3. If V2 is greater than (VI - y), and V2 is greater than (V3 + y), then read V3; in which,

VI is the output voltage from the wiper arm 7 in response to the first voltage application pattern; V2 is the output voltage from the wiper arm 7 in response to the second voltage application pattern;

V3 is the output voltage from the wiper arm 7 in response to the third voltage application pattern; and, y is a constant offset used in the calculation to enable the microprocessor 10 to determine which of the three stored values for the output voltage should be used to generate the position encoding voltage of the PPE.

Once the value of the output voltage has been selected from the three stored values of the output voltage, a weighting may be added by the processor 10 dependent on which value (VI , V2 or V3) was selected, to generate the position encoding voltage of the PPE. The linear relationship is generated by the superposition of sections 12, 13 and 14 from the graphs of Figure 4 and by adding an appropriate weighting to each of these sections, as discussed above. The processor 10 may be configured to provide linearisation using, for example a stored look-up table.

In the present invention three separate measurements of voltage or current are made for each wiper position. Therefore the output characteristic of the device is determined using only the linear sections of the individual graphs. In other words, it is not necessary to use any portion of the graphs shown in Figure 4 close to the extreme maximum or minimum values. This improves the overall linearity of the output of the PPE.

In operation, the PPE can be used in a static mode or in a rotating mode. In a static mode, a selected piece of hardware eg a closed circuit television camera, is fixed on a shaft (not shown) connected to the PPE. The wiper arm will be at some predetermined angular position and so the output voltage from the PPE will be constant which will imply that the wiper arm 7 is stationary. In a rotating mode, the position encoding voltage will be changing. By monitoring the change in the voltage, the movement of the wiper arm and associated hardware can be determined.

The output from the PPE is a position encoding voltage which a user must use to determine the wiper arm position and consequently the position of any associated hardware (eg CCTV camera). The position encoding voltage will vary in dependence on the wiper arm position, for example, between zero volts and the maximum voltage. The user must initially orientate the wiper arm 7 of the PPE in a selected position such that a reference voltage output corresponds to a known angular position. Any change in the output voltage will correspond to a proportionate angular movement of the wiper arm 7 and the associated hardware from the selected reference position. Alternatively, the PPE may be manufactured with a mechanical stop at a predefined position.

Figure 6 shows a graph of an alternative output from the PPE according to the present invention. In this case a linear ramp over a full 360 degree revolution is not required and the processor has been configured such that a linear voltage output is provided between wiper arm 7 angular positions of 0 degrees and 90 degrees, but a zero output voltage is given at all other times. Any other output voltage may be provided dependent on the programming of the processor 10.

The output from the PPE may be a digital signal or an analogue voltage depending on the user's requirements. The output from the wiper arm 7 will be an analogue voltage which may be converted to a digital signal for processing by an analogue-to- digital converter (not shown). The analogue-to-digital converter may be on board the processor 10 or it may be a separate component coupled to the processor 10. If desired, the processed signal may then be converted back to an analogue voltage in accordance with the user's requirements.

In this case, the PPE provides a linear output over a full 360 degree range allowing the wiper arm position and the position of any associated hardware to be determined in this range. Furthermore, since the device is easily manufactured and has no 'dead band' gap, the service life of the PPE is longer than that of conventional position encoders.

Figure 7 shows a second example of a PPE according to the present invention also using a three terminal arrangement. In this case, an input voltage or current is applied via a rotating wiper arm 15 to a 360 degree closed loop resistive track. Three terminals 16, 17 and 18 act as output terminals on the resistive track, coupling respective detected outputs to a processor 19 via nodes 20, 21 and 22. In this case there are three load resistors 23, 24 and 25 coupled between the output terminals and a supply voltage. As the wiper arm 15 rotates, the length of the arc of the resistive track between the point of wiper arm contact with the track and the next terminal in sequence (16 in this case) reduces. As such, the voltage detected at the terminal increases since the ratio between the resistance of the arc of track and the corresponding load resistor (24 in this case) decreases. Thus each terminal effectively acts as the take off point for a potential divider.

Again, the processor 19 executes a stored program to generate a single position encoding voltage output since a different voltage output will be provided by each of the terminals at any one time, thereby allowing the position of the wiper arm 15 to be determined at any angular position over a full 360 degree range.

In both examples of the PPEs described above, the position encoding voltage can also be used to determine the speed of rotation or the angular acceleration of the wiper arm. For example, by determining the position of the wiper arm at the start and end of a predetermined interval the average velocity of the wiper arm over that interval can also be determined. Alternatively, the time interval it takes for the wiper arm to move from one predetermined position to another can be measured and this time can be used to determine the average velocity of the wiper arm over that interval.

Figure 8 shows a schematic representation of a CCTV surveillance system including a PPE as described above. The system has a camera 26 coupled to a shaft 27 which in turn is coupled to the wiper arm of a PPE (not shown). In this case the position encoding voltage is coupled to a control interface unit 28 having a processor (not shown) which is programmed to inform a user of the angular position of the shaft and

CCTV camera at all times. The control interface unit 28 may be a joystick to enable a user to adjust the direction in which the camera 26 points.

Claims

1. A potentiometric position encoder comprising: a resistive track forming a closed loop; a wiper comprising a contact portion which makes electrical contact with the closed loop and which is moveable around the loop; at least three terminals provided around the loop and in electrical contact with the loop; a first control means for applying a voltage or current to the contact portion of the wiper or for measuring a voltage or current at the contact portion of the wiper; and, a second control means for applying voltages or currents to the terminals or for measuring voltages or currents at the terminals, wherein one of the first and second control means is controlled to supply a series of voltage or current application patterns and the other of the first and second control means is controlled to measure a voltage or current for each application pattern, and wherein a selected one of the voltage or current measurements is used to determine the position of the wiper

2. A potentiometric position encoder according to claim 1, in which the second control means is arranged to apply voltages or currents sequentially between selected sets of terminals and the first control means is arranged to measure a voltage or current at the contact portion in response to each of the sequential voltage or current

applications.

3. A potentiometric position encoder according to claim 1 or 2, in which the number of terminals is three.

4. A potentiometric position encoder according to any preceding claim, in which the first control means comprises a processor arranged to receive a respective voltage or current in response to each of the sequential applications of the voltages or currents applied between selected sets of terminals and is arranged to determine a position encoding voltage or current of the potentiometric position encoder in dependence on the received voltages or currents, the position encoding voltage or current being used to determine the position of the wiper.

5. A potentiometric position encoder according to claim 4, further comprising an analogue-to-digital converter for converting the voltages or currents received in response to each of the sequential applications of the voltages or currents applied between selected pairs of the terminals into digital signals and a memory for storing the digital signals.

6. A potentiometric position encoder according to claim 5, in which said analogue-to-digital converter and said memory are provided on board the processor.

7. A potentiometric position encoder according to any of claims 2 to 6, in which the voltages applied between selected sets of terminals comprise a square wave pulse.

8. A potentiometric position encoder according to any of claims 2 to 7, comprising a memory having a stored algorithm used to select one of the voltage or current values measured by the first control means, the selected value being used to determine a position encoding voltage or current.

9. A potentiometric position encoder according to claim 8, in which the stored algorithm is defined by the following steps:

(b) If VI is greater than (V3 - y), and VI is greater than (V2 + y), then read V2; and, (c) If V2 is greater than (VI - y), and V2 is greater than (V3 + y), then read V3; in which,

VI is the measured voltage or current from the wiper in response to the first voltage or current application; V2 is the measured voltage or current from the wiper in response to the second voltage or current application;

V3 is the measured voltage or current from the wiper in response to the third voltage or current application; and, y is an offset used in a calculation to enable the processor to select which of the three measured values for the voltage or current is used to calculate the position encoding

voltage or current of the PPE.

10. A potentiometric position encoder according to claim 8 or 9, in which the stored algorithm further comprises the step of adding a weighting value to the measured voltage or current from the wiper wherein the weighting value is dependent on which voltage or current from the wiper was selected to generate the position encoding voltage or current of the potentiometric position encoder.

11. A potentiometric position encoder according to claim 1 , in which the first control means is arranged to apply a voltage or current to the loop via the contact portion of the wiper and the second control means is arranged to measure the voltage or current at each of the terminals in response to the application of the voltage or current applied to the loop, the measured voltages or currents being used to determine the position of the wiper.

12. A potentiometric position encoder according to claim 11, comprising a memory having a stored algorithm to select one of the voltage or current values measured by the second control means, the selected value being used to determine a position encoding voltage or current.

13. A potentiometric position encoder according to claim 12, in which the stored algorithm is defined by the following steps:

(a) If V3 is greater than (V2 - y), and V3 is greater than (VI 4- y), then read VI; (b) If VI is greater than (V3 - y), and VI is greater than (V2 -I- y), then read V2; and,

(c) If V2 is greater than (VI - y), and V2 is greater than (V3 + y), then read V3; in which, VI is an output voltage or current from a first one of said terminals;

V2 is an output voltage or current from a second one of said terminals;

V3 is an output voltage or current from the third one of said terminals; and, y is an offset used in a calculation to enable the processor to select which of the three values for the output voltage or current is used to calculate the position encoding voltage or current of the PPE.

14. A potentiometric position encoder according to any of claims 11 to 13, further comprising a respective impedance coupled between each of the terminals and a reference wherein the voltage or current at each of the terminals is measured at a node connecting the terminal to the respective impedance.

15. A potentiometric position encoder according to any of claims 11 to 14, in which the second control means comprises a processor arranged to receive a respective voltage or current from each of the terminals and arranged to determine a position encoding voltage or current of the potentiometric position encoder in dependence on the received voltages or currents.

16. A potentiometric position encoder according to claim 15, further comprising an analogue-to-digital converter arranged to convert the respective received voltages or currents from each of the terminals into digital signals to enable the signals to be processed by the processor.

17. A potentiometric position encoder according to claim 15, in which said analogue-to-digital converter is provided on board the processor.

18. A potentiometric position encoder according to any preceding claim, in which the resistive track is circular.

19. A potentiometric position encoder according to any preceding claim, in which the terminals are positioned equidistantly from each other on the resistive track.

20. A potentiometric position encoder according to any preceding claim, in which the wiper comprises a wiper arm pivoted at the centre of the resistive track and an end in electrical contact at all times with the resistive track.

21. A potentiometric position encoder according to any preceding claim, in which the first and second control means comprise a microprocessor control unit.

22. A servo-control system comprising a rotatable apparatus coupled to a potentiometric position encoder according to any preceding claim, in which the apparatus is coupled to the wiper such that any rotation of the apparatus causes a corresponding rotation of the wiper.

23. A system according to claim 22, in which the apparatus is a closed circuit television camera.

24. A system according to claim 22, in which the apparatus is a section of a digging arm of an industrial digger.

25. A system according to claim 22, in which the apparatus is a wind direction indicator.

26. A potentiometric position encoding method for a position encoder having a resistive track forming a closed loop, a wiper which makes electrical contact with the closed loop and which is movable around the loop, and at least three terminals provided around the loop and in electrical contact with the loop, the method comprising the steps of, for each position of the wiper, applying a series of voltage or current application patterns, measuring a voltage or current for each application pattern, selecting one of the measured voltages or currents, and determining the position of the wiper around the loop in dependance on the selected one of the measured voltages or currents.

27. A method according to claim 26, in which the measured voltage or current used to determine the position of the wiper is selected in dependance on the relative values of the measured voltages or currents.

28. A method according to claim 26, in which the position encoding output characteristic of the device over the full range of movement of the wiper arm is determined by combining linear portions of the position encoding output characteristics of each of the application patterns.