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SPiiPlus Training Class

SPiiPlus Training Class. Mathematical and Signal Processing Functions. Mathematical and Signal Processing Functions.

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SPiiPlus Training Class

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  1. SPiiPlus Training Class Mathematical and Signal Processing Functions

  2. Mathematical and Signal Processing Functions ACSPL+ includes a large command set of built-in mathematical and signal processing functions. These functions allow for powerful algorithms to be written in minimal lines of code, including: • I/O debouncing • Digital controllers and filters • Teach-and-go • Array processing • Error mapping • Kinematic transformations (forward and inverse)

  3. Assignment Command Assignment Command: • Assigning a value to a variable using an expression • ‘=‘ is used to separate the variable from the expression • An assignment command can only assign a value to a scalar variable, a single element of an array, or a specific bit of a scalar variable or single element of an array. Syntax: variable = expression variable.(bit) = expression 1d_array(index) = expression 2d_array(index1)(index2) = expression

  4. Assignment Command Examples: GLOBAL INTtiVar GLOBALREAL trVar GLOBALINTtiArr(5) GLOBALREALtrArr(7) GLOBALINTtiArr2(10)(3) GLOBALREALtrArr2(12)(7) tiVar = 1 trVar = 1 * 2 tiArr(0) = tiVar + trVar trArr(3) = tiArr(0) / 2 tiArr2(9)(0) = tiArr(0) + trArr(3) trArr2(0)(3) = 1 + tiArr2(9)(0) * 0.4

  5. Unary Operators Unary operators are functions that act on one operand • - (unary minus) • Can be used with INT or REAL variables • ~ (inversion) • Can only be used with INT variables • REAL variables are converted to INT • ^ (logical not) • Can only be used with Boolean (0,1) INT variables • REAL variables and non-Boolean INT variables are converted to Boolean INT variables

  6. Unary Operators Examples: GLOBAL INT tiVar GLOBALREALtrVar GLOBALINT tiArr(3) GLOBALREALtrArr(3) tiVar = 1 tiArr(0) = -tiVar tiArr(1) = ~tiVar tiArr(2) = ^tiVar trVar = 2.5 trArr(0) = -trVar trArr(1) = ~trVar trArr(2) = ^trVar

  7. Binary Operators Binary operators are functions that act on two operands • + (addition) • - (subtraction) • * (multiplication) • / (division) • & (and) • | (or) • ~ (xor) • = (equal to) • <> (not equal) • > (greater than) • >= (greater than or equal to) • < (less than) • <= (less than or equal to)

  8. Binary Operators Examples: GLOBAL INT tiArr(5) GLOBALREALtrArr(5) tiArr(0) = 0b00001010 tiArr(1) = 0b11100100 tiArr(2) = tiArr(0) & tiArr(1) tiArr(3) = tiArr(0) | tiArr(1) tiArr(4) = tiArr(0) ~ tiArr(1) trArr(3) = 5 trArr(0) = trArr(3) * 4 trArr(1) = trArr(3) / 0.1 IF ( trArr(0) > trArr(1) ) trArr(2) = 1 ELSE trArr(2) = 0 END

  9. Order of Operations ACSPL+ uses a standard order of operations. The following table shows the operator precedence from highest to lowest. Operators with the same precedence are evaluated from left to right.

  10. Order of Operations Examples: GLOBALREAL trArr(6) trArr(0) = 1 + 2 * 3 trArr(1) = 1 * 2 + 3 trArr(2) = (1 + 2) * 3 trArr(3) = 5 * 6 / 7 trArr(4) = 5 / 6 * 7 IF( trArr(4) > trArr(3) * 1 + 2 - 5 ) trArr(5) = -1 ELSE trArr(5) = 1 END

  11. General Mathematical Functions ACSPL+ supports a set of standard mathematical functions. • abs( in ) = Absolute value • ceil( in ) = Ceiling of a value • floor( in ) = Floor of a value • hypot( x, y ) = • pow( x, y ) = • sqrt( in ) = • sign( in ) = Sign of a value • roll( in, const) = Modulus of a value

  12. Trigonometric Functions ACSPL+ supports the standard list of trigonometric functions. All trigonometric function use radians (not degrees). • sin( angle ) • cos( angle ) • tan( angle ) • asin( x ) • acos( y ) • atan( x / y ) • atan2( x, y )

  13. Exponential and Logarithmic Functions ACSPL+ supports the standard exponential and logarithmic functions. • exp( in ) = • ldexp( x, y ) = • log( in ) = Natural logarithm • log10( in ) = Base 10 logarithm

  14. Array Processing Functions ACSPL+ support some basic array processing functions • avg( ) = average of array elements • copy( ) Copies elements from one array to another • fill( ) Fills in an array with a constant value • max( ) = maximum entry in an array • maxi( ) = index of maximum entry in an array • min( ) = minimum entry in an array • mini( ) = index of minimum entry in an array

  15. Signal Processing Functions ACSPL+ supports some standard signal processing functions. • deadzone( ) = signal with deadzone • dsign( ) = sign of signal with delay and ramp time • edge( ) = edge detection of signal • intgr( ) = integration of signal • lag( ) = state of signal (high or low) with positive and negative edge delays • sat( ) = signal with saturation range

  16. Mapping / Interpolation Functions ACSPL+ supports some standard 1D mapping and interpolation functions. • map( ) 1D linear interpolation with uniformly spaced points • mapb( ) 1D B-spline interpolation with uniformly spaced points • maps( ) 1D Catmull-Rom spline interpolation with uniformly spaced points • mapn( ) 1D linear interpolation with non-uniformly spaced points • mapnb( ) 1D B-spline interpolation with non-uniformly spaced points • mapns( ) 1D Catmull-Rom spline interpolation with non-uniformly spaced points

  17. Mapping / Interpolation Functions ACSPL+ supports some standard 2D mapping and interpolation functions. • map2( ) 2D linear interpolation with uniformly spaced points • map2b( ) 2D B-spline interpolation with uniformly spaced points • map2s( ) 2D Catmull-Rom spline interpolation with uniformly spaced points • map2n( ) 2D linear interpolation with non-uniformly spaced points • map2nb( ) 2D B-spline interpolation with non-uniformly spaced points • map2ns( ) 2D Catmull-Rom spline interpolation with non-uniformly spaced points

  18. ACSPL+ Programming Example: 1 Digital Input Debouncing: A digital input from a mechanical pushbutton is used to tell a rotary stage to advance 2 rotations. In order to remove false triggers when the pushbutton is pressed and released, a debouncing mechanism is required. • Load program “Programming 08 – DIODebouncing.prg” to the controller. • Should populate buffer 11 • Open communication terminal and set it up to show DISP messages • Plot the variables di_signal and di_debounced on the scope • Set the time for 0.1 sec/div and the trigger on Auto • From the communication terminal start buffer 11 at line 1 (“START11, 1”). Follow the instructions on the screen

  19. ACSPL+ Programming Example: 2 Analog Input Filtering: An analog input is being used as accelerometer feedback for increasing the performance of a stage. The accelerometer feedback should be low frequency (< 5 Hz), so it is desired to put a single-pole low pass filter at 50 Hz. • Load program “Programming 08 – AnalogFiltering.prg” to the controller. • Should populate buffer 12 • Open communication terminal and set it up to show DISPmessages • Plot the variables ai_in and ai_filt on the scope • Set the time for 0.1 sec/div and the trigger on Auto • From the communication terminal start buffer 12 at line 1 (“START12, 1”). Follow the instructions on the screen

  20. ACSPL+ Programming Example: 3 X-Y Plane Rotation: • Load program “Programming 08 – XYRotation.prg” to the controller. • Should populate buffer 13 • Modify the program in order to allow the user to specify a rotation in degrees. • Test the program by rotating the plane 45 degrees, and 90 degrees, and running test X and Y axis moves. Hint: A 2-D rotation can be described by the following rotation matrix:

  21. ACSPL+ Programming Example: 4 Simple Digital Controller: An application requires an EtherCAT drive to be run in torque mode in order to give a constant desired torque on a load. A simple PI controller is used with a torque sensor in order to give a steady effective torque. • Open buffer 14 • Write a program to give the desired results. You can create user-defined variables for the drive output command and the torque sensor input.

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