Motion System Specification and Design

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Motion System Specification and Design

• ME4803 Motion Control
• Wayne J. Book
• G.W.Woodruff School of Mechanical Engineering
• Georgia Institute of Technology

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Issues in the Load and Performance Specification

• What is the nature of the load (Modeled)
• Inertia
• Friction
• Spring
• Higher order
• Forces (e.g. gravity)
• What motions must be made
• point to point
• continuous travel
• trajectory following
• index relative to another motion
• force application

• What measures the level of performance
• cycle time
• accuracy end point, static
• payload
• overshoot, damping, rise time characteristics
• disturbance rejection
• reliability

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Nature of the motion

• Point to point very common
• Get there in a nice way
• Fast
• Efficiently
• Dont exceed actuator limitations
• Dont overly stress or vibrate structure
• Exact position versus time not important
• Step change not feasible
• Next simplest trapezoidal velocity profile

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Motion ProfilesSimple Trapezoidal Velocity
Profile

• Max acceleration up to max velocity
• Max deceleration to desired position
• Cruise at constant speed in between
• For short moves max velocity not reached
• Min time trajectory for acceleration and speed
  limited actuators
• For pure intertial loads, max accel max torque

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Math of Simple Trapezoidal Profile
area under accel velocity
ta
tc
ta
area under velocity position
t2tatc
t1ta
tftc2 ta
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Constrained Jerk Motion Profile

• Abrupt application of acceleration
• May be impossible due to inductance of windings,
  other dynamics of actuators
• Is stressful on equipment
• Excites vibrations
• A reasonable alternative is to ramp up
  acceleration by using a constrained rate of
  acceleration, or jerk.
• The constrained jerk profile is now examined

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Start with Max Jerk, Hold to Max Accel
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Hold Max Accel
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Ramp Accel Down as Max Vel Approached
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Hold Max Vel as Needed
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Begin to Slow, Ramp Decel
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Hold Max Decel
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Ramp Decel to Zero as Vel Goes to Zero and
Desired Position is Approached
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Jerk Limited Trajectory(Case IA all maximums
reached)
Area distance traveled. Move time longer than
trapezoid by tj
tj
ta
tv
tj/2
t5
t4
t6
t1
t2
t3
t7
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Jerk Limited Equations

• Basic constraints are jmax, amax, vmax and
  pmax(final position)
• Define intervals tj, ta, tv for constant j, a or
  v
• Jerk j is either jmax, -jmax or 0 to minimize
  move time
• Integrate this constant one, two, and three times
  for a, v, and p
• Define seven switching times (in addition to
  start)
• Use symmetry of curves where possible

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Determine Time Intervals
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Determine Time Intervals (cont.)
Time cost of limiting jerk is tjamax/jmax
pbefore
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Other Cases

• Case I Max accel can be reached without
  violating max vel
• Move is long enough to reach max accel vel (see
  analysis completed above.)
• Move is long enough only to reach max accel, max
  accel time is used to adjust final pos
• Move is short, dont reach max accel either,
  adjust positon with max jerk time
• Case II Max accel can never be reached without
  violating max vel
• Move is long enough to reach max vel, adjust
  final position with max vel time.
• Move is short, same trajectory as 3 above
• The analysis is in the document provided.

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Compare the Vibration Effects on Base
Mass to move

• Support structure holds actuator to move mass m2
• Motion profile will be
• Trapezoidal Trajectory
• Constrained Jerk Trajectory
• Solution by Matlab using solver ode23

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Comparison of Base Vibration
Constrained Jerk Velocity Profile
Trapezoidal Velocity Profile
In this example vibration resulting from
Constrained Jerk is less than ½ that from
Trapezoidal