org.lsst.ccs.subsystems.shutter.sim

Class CubicSCurve

java.lang.Object

org.lsst.ccs.subsystems.shutter.sim.CubicSCurve

All Implemented Interfaces:

MotionProfile

public class CubicSCurve
extends Object
implements MotionProfile

Defines a piecewise cubic S-curve motion profile. Acceleration is linearly ramping up or down at all times so that there are no intervals of constant velocity.

In motion controller parlance an S-curve motion profile is one that ramps acceleration using a constant "jerk" (da/dt). The alternative is a so-called "trapezoidal" profile in which acceleration changes discontinuously (infinite jerk). S-curve motion is smoother, with no sharp bends in the velocity curve.

The S-curve is generated by scaling the following basic profile starting at distance = 0 dUnit, velocity = 0 dUnit/tUnit and acceleration = 0 dUnit/tUnit*2:

• Phase 0, t in [0, 1/4] tUnit: Jerk = +4 dUnit/tUnit^3, acceleration ramps from 0 to 1 dUnit/tUnit^2.
• Phase 1, t in [1/4, 3/4] tUnit: Jerk = -4 sUnit/tUnit^3, acceleration ramps from 1 to -1 sUnit/tUnit^2.
• Phase 2, t in [3/4, 1] tUnit: Jerk = +4 sUnit/tUnit^3, acceleration ramps from -1 to 0 sUnit/tUnit^2.

The basic profile d(t), v(t), a(t) represents of motion of +1/8 dUnit in 1 tUnit. A motion of D distance units in T time units is represented by 8D*d(t/T), (8D/T)*v(t/T), (8D/T**2)*a(t/T). D is positive for an extension and negative for a retraction.

Instances of this class are immutable.

Distance traveled, velocity and acceleration all refer to the leading edge of the blade set though for brevity we just say "the blade set".

This motion profile was first used with the one-bladed shutter prototype.

Author:

tether

Constructor Summary

Constructors

Constructor and Description
CubicSCurve(double totalDistance, double totalTime) Sets the scale factors for distance moved and total elapsed time.

Method Summary

Modifier and Type	Method and Description
double	acceleration(double t) Gives the acceleration of the blade set at time t.
double	distance(double t) Gives the distance traveled by the blade set at time t.
double	inverseDistance(double dtarget) Provides the time t at which the distance had a given value d.
double	velocity(double t) Gives the velocity of the blade set at time t.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CubicSCurve

public CubicSCurve(double totalDistance,
                   double totalTime)

Sets the scale factors for distance moved and total elapsed time.

Parameters:

totalDistance - The total distance D to move. Negative for a retraction.

totalTime - The elapsed time T allowed for the move.

Throws:

IllegalArgumentException - if totalTime is zero or negative.

Method Detail

distance

public double distance(double t)

Description copied from interface: MotionProfile

Gives the distance traveled by the blade set at time t.

Specified by:

distance in interface MotionProfile

Parameters:

t - a time between 0.0 and the amount of time allowed for the motion, inclusive

Returns:

the distance traveled at time t. Negative for a retraction

velocity

public double velocity(double t)

Description copied from interface: MotionProfile

Gives the velocity of the blade set at time t.

Specified by:

velocity in interface MotionProfile

Parameters:

t - a time between 0.0 and the amount of time allowed for the motion, inclusive

Returns:

the velocity at time t

acceleration

public double acceleration(double t)

Description copied from interface: MotionProfile

Gives the acceleration of the blade set at time t.

Specified by:

acceleration in interface MotionProfile

Parameters:

t - a time between 0.0 and the amount of time allowed for the motion, inclusive.

Returns:

the acceleration at time t.

inverseDistance

public double inverseDistance(double dtarget)

Description copied from interface: MotionProfile

Provides the time t at which the distance had a given value d. Assumes that the motion is monotonic; no reversals of the direction of travel.

Specified by:

inverseDistance in interface MotionProfile

Parameters:

dtarget - the distance, between 0.0 and the total distance traveled, inclusive. Negative for a retraction.

Returns:

the time at which the distance traveled was d