copyright 2011 controltrix corp www. controltrix.comwww.controltrix.comTrajectory generation for Servo motordrives
copyright 2011 controltrix corp www. controltrix.comRequirement• To move (linear or rotary )motor from point A to B• Gener...
copyright 2011 controltrix corp www. controltrix.comRequirements.• Minimum distance A to B can be small• Real time computa...
copyright 2011 controltrix corp www. controltrix.com• Floating point (Pseudo (IQ) or true) support• Digital signal process...
copyright 2011 controltrix corp www. controltrix.comDivide trajectory into regimese.g. for positive direction movement• Co...
copyright 2011 controltrix corp www. controltrix.com• Constant positive velocity (cruise mode) (jerk=0,acc=0)• Constant ne...
copyright 2011 controltrix corp www. controltrix.comIdeal caseZone 1 2 3 4 5 6 7 8Zone1: StandbyZone2: Const +ive jerkZone...
copyright 2011 controltrix corp www. controltrix.comSimple calculations using basic equations of motiona(k) = a(k-1) + J(k...
copyright 2011 controltrix corp www. controltrix.com• Overshoot /undershoot at the end (numerical errors , finitesampling,...
copyright 2011 controltrix corp www. controltrix.comZone 1 2 3 4 5 6 7 8 9 10Undershoot due to numerical errorsZone1: Init...
copyright 2011 controltrix corp www. controltrix.comJerkaccelerationvelocitypositionBAZone 1 2 3 4 5 6 7 8 9 10Overshoot d...
copyright 2011 controltrix corp www. controltrix.com• Real time compensation for over/undershoot for smoothtermination• Sm...
copyright 2011 controltrix corp www. controltrix.com• Smaller spans supported (by backward scaling)• Variable inertia prog...
copyright 2011 controltrix corp www. controltrix.comMinimum spanZone 1 2 3 4 5 6 7 8Zone1: InitZone2: Const +ive jerkZone3...
copyright 2011 controltrix corp www. controltrix.com• Servo motor drives• Machine tool industry• Position control• Robotic...
copyright 2011 controltrix corp www. controltrix.comExperimental ResultsRed : velocityBlue: position
copyright 2011 controltrix corp www. controltrix.comExperimental Results.Red : velocityBlue: position
copyright 2011 controltrix corp www. controltrix.comExperimental Results..Red : velocityBlue: position
copyright 2011 controltrix corp www. controltrix.comExperimental Results…Red : velocityBlue: position
copyright 2011 controltrix corp www. controltrix.comThank Youwww.controltrix.com
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Trajectory generation for Servo motor drives

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Trajectory generation for servo motor drives to move from point A to point B with a smooth motion, as fast as possible limiting the jerks, acceleration and speed to specified value. Long trajectories are possible. Simple and real time computation (when the motor is running). Also errors due to discrepancies in symmetry is fixed in real time.

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Trajectory generation for Servo motor drives

  1. 1. copyright 2011 controltrix corp www. controltrix.comwww.controltrix.comTrajectory generation for Servo motordrives
  2. 2. copyright 2011 controltrix corp www. controltrix.comRequirement• To move (linear or rotary )motor from point A to B• Generate a trajectory (periodic position command )• Smooth motion• As fast as possible• Limit jerks, acceleration and speed to specified value• Load inertia is known but variable
  3. 3. copyright 2011 controltrix corp www. controltrix.comRequirements.• Minimum distance A to B can be small• Real time computation (though motor is running)• Long trajectories are possible (limited processor memory realtime while motor is moving calculations)• Trajectories are always from standstill to standstill• Trajectory is defined as instantaneous value of position, velocityand acceleration to be commanded to the control system
  4. 4. copyright 2011 controltrix corp www. controltrix.com• Floating point (Pseudo (IQ) or true) support• Digital signal processor (finite periodic sampling time ~ 1ms)• Memory is limited to 500 samples• Trajectory generation and data use occurs in a circular buffer• Trajectory generation will fill buffer (provided it is empty ) at 10 Xdata consumptionGiven
  5. 5. copyright 2011 controltrix corp www. controltrix.comDivide trajectory into regimese.g. for positive direction movement• Constant positive jerk (acceleration increase )• Constant positive acceleration (vel increase ,jerk =0)• Constant negative jerk (acceleration decrease to 0)• Constant positive velocity(cruise mode) (jerk=0,acc=0)• midpointMethod
  6. 6. copyright 2011 controltrix corp www. controltrix.com• Constant positive velocity (cruise mode) (jerk=0,acc=0)• Constant negative jerk (acceleration decrease to –ve value)• Constant negative acceleration (vel decrease ,jerk = 0 )• Constant positive jerk (acceleration increase to 0)• Stop is position BMethod.
  7. 7. copyright 2011 controltrix corp www. controltrix.comIdeal caseZone 1 2 3 4 5 6 7 8Zone1: StandbyZone2: Const +ive jerkZone3: Const +ive accZone4: Const -ive jerkZone5: Const velZone6: Const -ive jerkZone7: Const -ive accZone8: Const +ive jerkJerkvelocitypositionacceleration
  8. 8. copyright 2011 controltrix corp www. controltrix.comSimple calculations using basic equations of motiona(k) = a(k-1) + J(k-1).Tv(k) = v(k-1) +a(k-1).TS(k) =S(k-1) + v(k-1).T + 1/2 . a(k-1) . T . TWhereJ=jerk ,a = acc, v =velocity ,S = positionMirror image based solutionReal time computation (with motor running)Limiting to maximum permissible limits for (j, a, v)Advantages
  9. 9. copyright 2011 controltrix corp www. controltrix.com• Overshoot /undershoot at the end (numerical errors , finitesampling, slight unsymmetry between the first and second half) donot allow velocity and acceleration to converge to 0 simultaneously• Small Span trajectories cannot be supported (as midpoint can behit before cruise mode)• Variable inertia -> maximum acceleration varies  hence spanvaries• Jerky trajectory terminationChallenges
  10. 10. copyright 2011 controltrix corp www. controltrix.comZone 1 2 3 4 5 6 7 8 9 10Undershoot due to numerical errorsZone1: InitZone2: Const +ive jerkZone3: Const +ive accZone4: Const -ive jerkZone5: Const velZone6: Const -ive jerkZone7: Const -ive accZone8: Const +ive jerkJerkvelocitypositionaccelerationABmidpoint
  11. 11. copyright 2011 controltrix corp www. controltrix.comJerkaccelerationvelocitypositionBAZone 1 2 3 4 5 6 7 8 9 10Overshoot due to numerical errorsZone1: InitZone2: Const +ive jerkZone3: Const +ive accZone4: Const -ive jerkZone5: Const velZone6: Const -ive jerkZone7: Const -ive accZone8: Const +ive jerkmidpoint
  12. 12. copyright 2011 controltrix corp www. controltrix.com• Real time compensation for over/undershoot for smoothtermination• Smooth correction• Errors due to discrepancies in symmetry fixed in real timeProposed method
  13. 13. copyright 2011 controltrix corp www. controltrix.com• Smaller spans supported (by backward scaling)• Variable inertia programmable (by scaling)• Trajectory is almost always nearly symmetric• Simple computation• Fixed and floating point implementationsProposed method
  14. 14. copyright 2011 controltrix corp www. controltrix.comMinimum spanZone 1 2 3 4 5 6 7 8Zone1: InitZone2: Const +ive jerkZone3: Const +ive accZone4: Const -ive jerkZone5: Const velZone6: Const -ive jerkZone7: Const -ive accZone8: Const +ive jerkmidpoint
  15. 15. copyright 2011 controltrix corp www. controltrix.com• Servo motor drives• Machine tool industry• Position control• RoboticsTarget Application
  16. 16. copyright 2011 controltrix corp www. controltrix.comExperimental ResultsRed : velocityBlue: position
  17. 17. copyright 2011 controltrix corp www. controltrix.comExperimental Results.Red : velocityBlue: position
  18. 18. copyright 2011 controltrix corp www. controltrix.comExperimental Results..Red : velocityBlue: position
  19. 19. copyright 2011 controltrix corp www. controltrix.comExperimental Results…Red : velocityBlue: position
  20. 20. copyright 2011 controltrix corp www. controltrix.comThank Youwww.controltrix.com
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