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Similaire à Trajectory generation for Servo motor drives
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Trajectory generation for Servo motor drives
- 1. copyright 2011 controltrix corp www. controltrix.com www.controltrix.com Trajectory generation for Servo motor drives
- 2. copyright 2011 controltrix corp www. controltrix.com Requirement • 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. copyright 2011 controltrix corp www. controltrix.com Requirements. • Minimum distance A to B can be small • Real time computation (though motor is running) • Long trajectories are possible (limited processor memory real time while motor is moving calculations) • Trajectories are always from standstill to standstill • Trajectory is defined as instantaneous value of position, velocity and acceleration to be commanded to the control system
- 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 X data consumption Given
- 5. copyright 2011 controltrix corp www. controltrix.com Divide trajectory into regimes e.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) • midpoint Method
- 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 B Method.
- 7. copyright 2011 controltrix corp www. controltrix.com Ideal case Zone 1 2 3 4 5 6 7 8 Zone1: Standby Zone2: Const +ive jerk Zone3: Const +ive acc Zone4: Const -ive jerk Zone5: Const vel Zone6: Const -ive jerk Zone7: Const -ive acc Zone8: Const +ive jerk Jerk velocity position acceleration
- 8. copyright 2011 controltrix corp www. controltrix.com Simple calculations using basic equations of motion a(k) = a(k-1) + J(k-1).T v(k) = v(k-1) +a(k-1).T S(k) =S(k-1) + v(k-1).T + 1/2 . a(k-1) . T . T Where J=jerk ,a = acc, v =velocity ,S = position Mirror image based solution Real time computation (with motor running) Limiting to maximum permissible limits for (j, a, v) Advantages
- 9. copyright 2011 controltrix corp www. controltrix.com • Overshoot /undershoot at the end (numerical errors , finite sampling, slight unsymmetry between the first and second half) do not allow velocity and acceleration to converge to 0 simultaneously • Small Span trajectories cannot be supported (as midpoint can be hit before cruise mode) • Variable inertia -> maximum acceleration varies hence span varies • Jerky trajectory termination Challenges
- 10. copyright 2011 controltrix corp www. controltrix.com Zone 1 2 3 4 5 6 7 8 9 10 Undershoot due to numerical errors Zone1: Init Zone2: Const +ive jerk Zone3: Const +ive acc Zone4: Const -ive jerk Zone5: Const vel Zone6: Const -ive jerk Zone7: Const -ive acc Zone8: Const +ive jerk Jerk velocity position acceleration A B midpoint
- 11. copyright 2011 controltrix corp www. controltrix.com Jerk acceleration velocity position B A Zone 1 2 3 4 5 6 7 8 9 10 Overshoot due to numerical errors Zone1: Init Zone2: Const +ive jerk Zone3: Const +ive acc Zone4: Const -ive jerk Zone5: Const vel Zone6: Const -ive jerk Zone7: Const -ive acc Zone8: Const +ive jerk midpoint
- 12. copyright 2011 controltrix corp www. controltrix.com • Real time compensation for over/undershoot for smooth termination • Smooth correction • Errors due to discrepancies in symmetry fixed in real time Proposed method
- 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 implementations Proposed method
- 14. copyright 2011 controltrix corp www. controltrix.com Minimum span Zone 1 2 3 4 5 6 7 8 Zone1: Init Zone2: Const +ive jerk Zone3: Const +ive acc Zone4: Const -ive jerk Zone5: Const vel Zone6: Const -ive jerk Zone7: Const -ive acc Zone8: Const +ive jerk midpoint
- 15. copyright 2011 controltrix corp www. controltrix.com • Servo motor drives • Machine tool industry • Position control • Robotics Target Application
- 16. copyright 2011 controltrix corp www. controltrix.com Experimental Results • 30 revolutions • 3X inertia • forward direction • 3200 rpm cruise speed Red : actual velocity Blue: actual position
- 17. copyright 2011 controltrix corp www. controltrix.com Experimental Results. • 30 revolutions • 3X inertia • 3200 rpm cruise speed • opposite direction Red : actual velocity Blue: actual position
- 18. copyright 2011 controltrix corp www. controltrix.com Experimental Results.. Red : velocity Blue: position • 5 revolutions • 3X inertia • 3200 rpm cruise speed • span near limiting span Red : actual velocity Blue: actual position
- 19. copyright 2011 controltrix corp www. controltrix.com Experimental Results… • 5 revolutions • 3X inertia • 3200 rpm cruise speed • near limiting span • opposite direction Red : actual velocity Blue: actual position
- 20. copyright 2011 controltrix corp www. controltrix.com Thank You www.controltrix.com