Trajectory generation for Servo motor drives

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Trajectory generation for Servo motor drives


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


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


• 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


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


• 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.


Ideal caseZone 1 2 3 4 5 6 7 8

Zone1: StandbyZone2: Const +ive jerk Zone3: Const +ive accZone4: Const -ive jerk Zone5: Const velZone6: Const -ive jerk Zone7: Const -ive accZone8: Const +ive jerk

Jerk

velocity

position

acceleration


Simple calculations using basic equations of motion

a(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 = position

Mirror image based solutionReal time computation (with motor running)Limiting to maximum permissible limits for (j, a, v)

Advantages


• 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


Zone 1 2 3 4 5 6 7 8 9 10

Undershoot due to numerical errors

Zone1: InitZone2: Const +ive jerk Zone3: Const +ive accZone4: Const -ive jerk Zone5: Const velZone6: Const -ive jerk Zone7: Const -ive accZone8: Const +ive jerk

Jerk

velocity

position

acceleration

A

B

midpoint


Jerk

acceleration

velocity

position

B

A

Zone 1 2 3 4 5 6 7 8 9 10

Overshoot due to numerical errors


midpoint


• Real time compensation for over/undershoot for smooth termination• Smooth correction• Errors due to discrepancies in symmetry fixed in real time

Proposed method


• 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


Minimum spanZone 1 2 3 4 5 6 7 8


midpoint


• Servo motor drives • Machine tool industry • Position control• Robotics

Target Application


Experimental Results

Red : velocityBlue: position


Experimental Results.



Experimental Results..



Experimental Results…



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Trajectory generation for Servo motor drives

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