Ramps.jl

Provides a function for ramping up from one level to another.
Author TomRottier
Github
Popularity
0 Stars
Updated Last
2 Years Ago
Started In
December 2022

Ramps.jl

Overview

Exports the Ramp type which, when evaluated, smoothly ramp up from one level to another over a specified time, with zero first and second derivatives at endpoints, MultiRamp type which chains together multiple ramps, and evaluate to evaluate the ramp, or its derivative, at any given time.

Maths

Solve system of equations to determine coefficients for a quintic polynomial (chosen so that the second derivative is a cubic) so that the quintic polynomial $x(t)$ gives $x(0) = 0$, $x(1) = 1$, $x'(0) = 0$, $x'(1) = 0$, $x''(0) = 0$, and $x''(1) = 0$. Resulting polynomial is then scaled for any range $(x_0, x_1)$ and any domain $(t_0,t_1)$. If $t < t_0$ then $x(t) = x_0$ and if $t > t_1$ then $x(t) = x_1$. The ramp is shown below:

ramp pic

Installation

  pkg> add Ramps

Example usage

using Ramps

# create a ramp from 0 to 10 from 0 to 2
r = Ramp(0,10,0,2)

# evaluate ramp at start, middle, and end
evaluate(r, 0) == 0
evaluate(r, 1) == 5
evaluate(r, 2) == 10

# evaluate first and second derivative at start and end (third arguement is the derivative, default = 0)
evaluate(r, 0, 1) == 0
evaluate(r, 2, 2) == 0

# evaluate out of domain of ramp
evaluate(r, -100) == 0
evaluate(r, 100, 2) == 0

# create multiple ramps - must ensure ramps begin one after the other and start value is same as previous end value
r1 = Ramp(0, 10, 2, 4)
r2 = Ramp(10, 2, 5, 6)
mr = MultiRamp([r1,r2]) # will check ramps

# evaluate
evaluate(mr, 0) == 0
evaluate(mr, 2.3) ≈ 0.2661187...
evaluate(mr, 4.5) == 10
evaluate(mr, 4.5, 2) == 0
evaluate(mr, 5.7) ≈ 3.30464...
evaluate(mr, 6) == 2
evaluate(mr, 100) == 2
evaluate(mr, 100, 2) == 0