Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
  • G01D1/00—Measuring arrangements giving results other than momentary value of variable, of general application
  • G01D1/10—Measuring arrangements giving results other than momentary value of variable, of general application giving differentiated values

Definitions

• the invention is based on a method for numerically differentiating a digital sensor signal.
• the differentiated sensor signals are often required in addition to the actual sensor signals. These differentiated sensor signals can be obtained, for example, by numerical differentiation.
• the differentiated size is determined by forming the difference between two samples with a fixed time interval and dividing the difference by this time interval.
• a small discretization error arises in relation to the absolute value of the differentiated size at small rates of change of the size to be differentiated.
• discretization error is meant the error that occurs when digital sensor signals are sampled and either one or an adjacent discrete point of the signal is used.
• a time measurement is customary when there is a predetermined change in the size to be differentiated, for example the time that is required for a fixed path interval with position sensors is measured.
• the differentiated size can be obtained by forming the reciprocal.
• the relative discretization error can be reduced by increasing the predetermined intervals, but this means that the differentiated signal has an increased phase shift compared to the original signal, which cannot be tolerated in a control method.
• the relative error resulting from the discretization of the digital sensor signal should be as low as possible, especially in the case of small rates of change of the differentiated size.
• the differentiation is formed by the first method by forming the difference between two samples, the first requirement is a small time interval between the two samples ten met, while the second requirement requires a large time interval.
• the method according to the invention for the numerical differentiation of a digital sensor signal has the advantage that it fulfills the two requirements for a small phase loss and a small relative discretization error at the same time, since the differentiation interval should be variable and can therefore be adapted to the prevailing conditions.
• the differentiation interval is present as a sliding differentiation interval, the current differentiation interval being formed as a function of at least one preceding one.
• measured values are obtained as shown in FIG. 1.
• a digital sensor for example an incremental scale or an absolute encoder
• measured values are obtained as shown in FIG. 1.
• a series of discrete measurement values 10 ⁇ m apart are obtained. If such systems are scanned, apart from the error caused by the discretization (quantization error) which leads to the so-called discretization noise, no further errors and no further measurement noise occur.
• a differentiated signal can be obtained by subtracting the two successive values X1 and X2 and the difference divided by the sampling time T. To distinguish them, the individual values X1, X2 are designated as and and.
• the differentiated variable V ex thus lies within a range which is referred to below as the confidence range.
• FIG. 2 shows a flow chart which indicates how the differentiation process works. To explain this flowchart, the following definitions should first be given:
• ⁇ N current length of the time interval
• ⁇ End maximum length of the time interval when the section is limited
• ⁇ Max maximum length of the time interval.
• step S1 the differentiated size is determined with a minimal differentiation interval and the confidence interval corresponding to the quantization error.
• step S11 which is a sub-step of step S1
• the upper limit of the confidence range Ogr is read in as the largest positive number that can be represented.
• the lower limit of the confidence interval is read in and the current length of the time interval ⁇ N specifies the maximum value from ( ⁇ Nalt / DiffN, T as well as the maximum length of the time interval in the case of cutout limitation ⁇ End.
• the intermediate result of the differentiation is determined in the next step S12 by subtracting the N- ⁇ Nth sample value of the variable X to be differentiated from the Nth sample value of the variable X to be differentiated and dividing the difference by the current length of the time interval .
• step S13 it is checked whether the intermediate result of the differentiation Xd determined in step S12 lies within the confidence interval.
• [Ugr, Ogr] [Xd-1 / ⁇ N, Xd + 1 / ⁇ N] ⁇ [Ugr, Ogr] is determined.
• step S15 it is checked whether the current length of the time interval ⁇ N is less than the maximum length of the time interval when the cutout is limited. If this is the case, the current length of the time interval ⁇ N is doubled in step S16 and that
• step S13 If it is recognized in step S13 that the intermediate result of the differentiation Xd lies outside the confidence range VB,
• Step S17 halves the current length of the time interval ⁇ N and the intermediate result of the differentiation Xd from the difference between the Nth sample value of the variable X to be differentiated and the N- ⁇ Nth sample value, which divides by the new current length of the time interval is set. That the result of the sliding differentiation is determined at the value determined in the previous iteration section, at which the limits of the confidence interval had not yet been exceeded.
• step S18 the variable .DELTA.N becomes old , which is the length of the
• the completion step S18 is also carried out if it is determined in step S15 that the length of the time interval ⁇ N has reached the predetermined maximum length of the time interval ⁇ End.
• step S11 In the method shown in FIG. 2, which runs as a program in a computer, the boundary conditions are first defined or read in in a step S11 referred to as step S11.
• the differentiated variable Xd is then firstly determined in a first step S2 with a minimal differentiation interval, which corresponds to the sampling time T, and at the same time the confidence interval corresponding to the quantization error is determined. In the next steps, the differentiation interval is increased and the quantization error is reduced accordingly. If the differentiation interval is doubled, the quantization error is halved.
• the phase error is kept as low as possible without the risk that the signal quality will suffer at a constant speed.
• the method specified in FIG. 2 can be implemented particularly easily if the time intervals are doubled in each case. It is then possible to carry out the specified algorithm with the aid of shift operations that can be carried out easily in a microprocessor.
• FIG. 3 shows an example in which the course of the variable X to be differentiated is plotted over the sampling time T in a).
• Steps are given and in FIG. 3d) the calculated speed value X ", the limit of the confidence interval for the current differentiation interval and the limits of the actual confidence range for 4 steps are given.
• the confidence interval for the current differentiation interval is given by the upper limit Ogr, akt and the lower limit Ugr, act limited, Ogr, tat and Ugr, tat apply accordingly to the limits of the actual trust range.
• the method described can be extended to any digital signals that are to be differentiated.
• the method usually runs in a computing device, e.g. a microprocessor that has the necessary registers or memory.

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• Engineering & Computer Science (AREA)
• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Mathematical Physics (AREA)
• Data Mining & Analysis (AREA)
• Theoretical Computer Science (AREA)
• Mathematical Optimization (AREA)
• Mathematical Analysis (AREA)
• Algebra (AREA)
• Pure & Applied Mathematics (AREA)
• Databases & Information Systems (AREA)
• Software Systems (AREA)
• General Engineering & Computer Science (AREA)
• Computational Mathematics (AREA)
• Complex Calculations (AREA)
• Feedback Control In General (AREA)
• Transmission And Conversion Of Sensor Element Output (AREA)
• Compression, Expansion, Code Conversion, And Decoders (AREA)

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• 1992
  • 1992-05-21 DE DE19924216811 patent/DE4216811A1/de not_active Withdrawn
• 1993
  • 1993-05-06 JP JP5519758A patent/JPH06508709A/ja active Pending
  • 1993-05-06 WO PCT/DE1993/000393 patent/WO1993023815A1/de not_active Application Discontinuation
  • 1993-05-06 EP EP93911436A patent/EP0596080A1/de not_active Withdrawn

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