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graphequationmodelicaderivative
B.Castarunza
B.Castarunza

Reputation: 167

Modelica, what's der(x)

in the modelica language I found the time derivative of x used in this equation:

der(x) = 1 - x

as always the x is set to 0 by default, what I don't understand is how this equation drives the value of x towards 1.0.

reached the 2 seconds mark, shouldn't it go to negative instead of stabilizing to 1.0?

source: https://mbe.modelica.university/behavior/equations/first_order/

Thank you

Upvotes: 1

Views: 256

Answers (1)

Atiyah Elsheikh
Atiyah Elsheikh

Reputation: 578

From Calculus, time derivative of x (i.e. dx/dt (t0) ) represents the amount of increase or decrease of a variable as simulation proceeds at time point t0. Remember Taylor series expansion:

x(t0 + dt) = x(t0) + dx/dt(t0) . dt + O(dt^2)

So from this Calculus-based observation it is straightforward to see that:

  • if der(x) > 0, then x will increase as the simulation runs and vise versa.
  • x will increase as time increases but der(x) would decrease as x increases.
  • As der(x) approaches 0, then the increase of x will slow down and x tends to 1.
  • If the initial value of x is equal to 2, then der(x) = -1 at the start of the simulation and it approaches 0 as time increases and meanwhile x approaches 1.
  • If x = 1, then der(x) = 0 and x would neither increase nor decrease. The value of x = 1 is the steady-state of the given ODE system that makes der(x) = 0

Upvotes: 4

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