FindSystemModelEquilibrium
FindSystemModelEquilibrium[model]
searches for an equilibrium to the model model.
FindSystemModelEquilibrium[model,{{{x1,x10},…},{{u1,u10},…},{{y1,y10},…}}]
searches for an equilibrium, starting from the points xi=xi0, ui=ui0 and yi=yi0.
FindSystemModelEquilibrium[model,{x1v1,…},…]
searches for an equilibrium, with variable xi constrained to have the value vi etc.
Details and Options
- FindSystemModelEquilibrium is typically used to find values of states, inputs and outputs for which the dynamics of a system model stop.
- The model can be a SystemModel object, a full model name string or a shortened model name accepted by SystemModel.
- FindSystemModelEquilibrium returns a list {{{x1,
},…},{{u1,
},…},{{y1,
},…}}, where 
, 
and 
are the computed equilibrium values for states, inputs and outputs. - With no explicit starting point given, SystemModel[model]["GroupedInitialValues"] is used.
- An equilibrium for a differential algebraic system
is a value 
and 
such that 
. - FindSystemModelEquilibrium will attempt to find a local equilibrium point. In general, many equilibrium points may exist for a system.
- The following option can be given:
-
ProgressReporting $ProgressReporting control display of progress
Examples
open all close allBasic Examples (3)
Find an equilibrium, starting the search at initial values:
Use given start values for states:
Find an equilibrium for one of the included introductory hierarchical examples:
Scope (3)
Options (1)
ProgressReporting (1)
Control progress reporting with ProgressReporting:
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:
Related Links
Wolfram System Modeler DocumentationText
Wolfram Research (2018), FindSystemModelEquilibrium, Wolfram Language function, https://reference.wolfram.com/language/ref/FindSystemModelEquilibrium.html.
CMS
Wolfram Language. 2018. "FindSystemModelEquilibrium." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindSystemModelEquilibrium.html.
APA
Wolfram Language. (2018). FindSystemModelEquilibrium. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindSystemModelEquilibrium.html