MaxVal

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

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

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

(1)

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

The default value of $a$ is +10 and it should work for most of use cases.

Example

Assume that you are designing a suspension system and there is an upper limit on the maximum acceleration of the chassis.

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

>>> # Define the maximum of acceleration
>>> maxAcc = MaxVal(function = "ACCZ({})".format(p.cm.id))