MinVal

Computes the minimum value of a user specified function, which could be a MotionSolve expression or a user subroutine.

The minimum value of a signal $f (q (t))$ satisfies the following condition: If T* is the point in time when is $f (q (t))$ minimum, then $f (q (T *)) \geq f (q (t))$ when t ≠T*. If the expression has no minimum value, the initial value will be returned as the minimum value.

A smooth approximation to the MIN function is implemented in MotionSolve, so that its sensitivities are analytically computed. The smooth approximation, known as the alpha soft approximation, is:(1)

M i n v a l (x) = \frac{\int_{0}^{T} x (t) e^{a x (t)} d t}{\int_{0}^{T} e^{a x (t)} d t}

The parameter

a < 0

is used to control the accuracy of the calculations.

Note:

M i n (x) = \lim_{⍺ \to \infty} M i n v a l (x)

Example

Assume that you want to put a lower limit on the velocity of a vehicle.

Here is a code snippet that shows how the response should be defined with MinVal:


>>> # Define the minimum of velocity
>>> minVel = MinVal(function = "VZ({},{})".format(p.cm.id,ref.id))