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. 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 Red : velocity Blue: position
- 17. copyright 2011 controltrix corp www. controltrix.com Experimental Results. Red : velocity Blue: position
- 18. copyright 2011 controltrix corp www. controltrix.com Experimental Results.. Red : velocity Blue: position
- 19. copyright 2011 controltrix corp www. controltrix.com Experimental Results… Red : velocity Blue: position
- 20. copyright 2011 controltrix corp www. controltrix.com Thank You www.controltrix.com