HP VXI 75000 C Series, User'S And Scpi Programming Manual

Page: 367 / 438

Generating User Defined Functions 367 Appendix F
Appendix F
Generating User Defined Functions
Introduction
The HP E1415 Algorithmic Closed Loop Control Card has a limited set of
mathematical operations such as add, subtract, multiply, and divide. Many
control applications require functions such a square root for calculating flow
rate or a trigonometric function to correctly transition motion of moving
object from a start to ending position. In order to represent a sine wave or
other transcendental functions, one could use a power series expansion to
approximate the function using a finite number of algebraic expressions.
Since the above mentioned operations can take from 1.5usec to 4usec for
each floating point calculation, a complex waveform such as sine(x) could
take more than 100usec to get the desired result. A faster solution is
desirable and available.
The HP E1415 provides a solution to approximating such complex
waveforms by using a piece-wise linearization of virtually any complex
waveform. The technique is simple. The DOS disc supplied with your HP
E1415 contains both a ’C’ and Rocky Mountain BASIC program which
calculates 128 Mx+B segments over a specified range of values for the
desired function. You supply the function; the program generates the
segments in a table. The resulting table can be downloaded into the HP
E1415’s RAM with the ALG:FUNC:DEF command where you can select
any desired name of the function(i.e. sin(x), tan(x), etc.). Up to 32 functions
can be created for use in algorithms. At runtime where the function is passed
an ’x’ value, the time to calculate the Mx+B segmented linear approximation
is approximately 17
µ
sec.
The HP E1415 actually uses this technique to convert volts to temperature,
strain, etc. The accuracy of the approximation is really based upon how well
you select the range over which the table is built. For thermocouple
temperature conversion, the HP E1415 fixes the range to the lowest A/D
range(+/-64millivolts) so that small microvolt measurements yield the
proper resolution of the actual temperature for a non-linear transducer. In
addition, the HP E1415 permits you to create Custom Engineering Unit
conversion for your transducer so that when the voltage measurement is
actually made the EU conversion takes place(see SENS:FUNC:CUST ).
Algorithms deal with the resulting floating point numbers generated during
the measurement phase and may require further complex mathematical
operations to achieve the desired result.
With some complex waveforms, you may actually want to break up the
waveform into several functions in order to get the desired accuracy. For
example, suppose you need to generate a square root function for both
voltage and strain calculations. The voltages are only going to range from 0
to +/-16volts, worst case. The strain measurements return numbers in
microstrain which range in the 1000’s. Trying to represent the square root