WSMFindEquilibrium is being phased out in favor of FindSystemModelEquilibrium, which was introduced experimentally in Version 11.3.


searches for an equilibrium to the model "mmodel".


searches for an equilibrium, starting from the point xi=xi0, ui=ui0, and yi=yi0.


searches for an equilibrium, with variable xi constrained to have the value vi etc.


  • WSMFindEquilibrium returns a list {{{x1,},},{{u1,},},{{y1,},}}, where , , and are the computed equilibrium values for states, inputs, and outputs.
  • With no explicit starting point given, WSMModelData["mmodel","GroupedInitialValues"] is used.
  • An equilibrium for a differential algebraic system is a value and such that .
  • WSMFindEquilibrium will attempt to find a local equilibrium point. In general, many equilibrium points may exist for a system.
  • The shortest unique model name mmodel can be used where WSMNames["*.mmodel"] gives a unique match.
  • The following options can be given:
  • WSMProgressMonitorAutomaticcontrol display of progress


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Basic Examples  (4)

Load Wolfram SystemModeler Link:

Find an equilibrium, starting the search at initial values:

Use given start values for states:

Use the diagram representation of a model as input:

Copy and paste the output above:

Scope  (3)

Give start values for states, inputs, and outputs:

Use constraints on inputs and outputs, and start values for states:

Find an equilibrium point with given constraints:

Applications  (5)

Find an equilibrium point for a single water tank with inflow and outflow:

Linearize a model around an equilibrium point:

Linearize around an equilibrium point and analyze the stability:

Design a PI controller for keeping the level in a tank with inflow and outflow constant:

Find the equilibrium where the level "h" is constrained to be 2:

Linearize and close the loop around a PI controller:

Show the closed-loop step response for a family of PI controllers:

Simple pendulum swinging through any angle:

Equilibrium with the pendulum hanging straight down:

Pendulum standing straight up above its axis:

Level curves of the first integral give the potential energy of the system:

The pendulum has one stable and two unstable equilibrium points:

Properties & Relations  (2)

Equilibrium points , for an ODE satisfy :

Find an equilibrium point and :

Verify :

Many equilibrium points may exist: