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WSMFindEquilibrium


searches for an equilibrium to the model .

searches for an equilibrium, starting from the point , , and .

searches for an equilibrium, with variable constrained to have the value etc.
  • returns a list , where , , and are the computed equilibrium values for states, inputs, and outputs.
  • With no explicit starting point given, WSMModelData is used.
  • An equilibrium for a differential algebraic system is a value and such that .
  • will attempt to find a local equilibrium point. In general, many equilibrium points may exist for a system.
  • The following options can be given:
ModelicaConversionAutomaticvariable name conversion rule
Load Wolfram SystemModeler Link:
Find an equilibrium, starting the search at initial values:
Use given start values for states:
Load Wolfram SystemModeler Link:
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Find an equilibrium, starting the search at initial values:
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Use given start values for states:
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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:
Find the equilibrium of a model by using the variables from WSMModelData:
Conversion method uses Modelica-like symbols for variable names:
Use conversion method to get generic variable names:
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 is constrained to be :
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:
Equilibrium points , for an ODE satisfy :
Find an equilibrium point and :
Verify :
Many equilibrium points may exist: