Function Repository Resource:

SystemModelManipulate

Manipulate parameters or initial values in plots of model simulation results

Contributed by: Wolfram MathCore

ResourceFunction["SystemModelManipulate"][model]

creates a Manipulate object from model showing the resulting plots of a simulation with controllers for parameters and initial values.

ResourceFunction["SystemModelManipulate"][model,{u}]

creates a control only for the top-level parameter or variable u.

ResourceFunction["SystemModelManipulate"][model,{u,u_min,u_max}]

allows the value for u to vary between u_min and u_max.

ResourceFunction["SystemModelManipulate"][model,{{u,u_init},u_min,u_max,…}]

takes the initial value of u to be u_init.

ResourceFunction["SystemModelManipulate"][model,{u,{u₁,u₂,…}}]

allows u to take on discrete values u₁,u₂,….

ResourceFunction["SystemModelManipulate"][model,{u,func}]

creates a control from the function func.

ResourceFunction["SystemModelManipulate"][model,{u,…},{v,…},…]

provides controls to manipuate each u,v,….

Details and Options

The model can have the following forms:

SystemModel[…]

general system model

StateSpaceModel[…]

state-space model

TransferFunctionModel[…]

transfer function model

AffineStateSpaceModel[…]

affine state-space model

NonlinearStateSpaceModel[…]

nonlinear state-space model

DiscreteInputOutputModel[…]

discrete input-output model

ResourceFunction["SystemModelManipulate"] by default provides controls for top-level parameters and initial values of top-level variables.

For a SystemModel model, model["TopParameterNames"] and model["TopSystemVariables"] provide names for top-level parameters and variables in model.

ResourceFunction["SystemModelManipulate"][model] by default picks a range for the controls depending on its type, initial value and min or max values, if given in the model.

For a SystemModel model with stored control annotations, ResourceFunction["SystemModelManipulate"][model] reproduces them.

ResourceFunction["SystemModelManipulate"][model,{tmin,tmax},…] simulates and plots from time tmin to time tmax.

ResourceFunction["SystemModelManipulate"][model] shows all the default plots specified in the model. "Plots" is accepted as a special value in ResourceFunction["SystemModelManipulate"][model,…,{"Plots",…},…] to include a controller for switching the plots.

ResourceFunction["SystemModelManipulate"][model, {u,u_min,u_max,du}] allows the value for u to vary between u_min and u_max in steps du.

ResourceFunction["SystemModelManipulate"][model, {{u,u_init,u_lbl},…}] labels the controls for u with u_lbl.

ResourceFunction["SystemModelManipulate"][model, {u,{u₁→lbl₁,u₂→lbl₂,…}}] labels the controls values u₁,u₂,… with labels lbl₁,lbl₂,…

ResourceFunction["SystemModelManipulate"][…,spec] uses Association spec to set inputs, or additional parameter or initial values:

"ParameterValues"

{p₁→val₁,…}

set parameter p_i to value val_i

"InitialValues"

{v₁→val₁,…}

set initial value of variable v_i to val_i

"Inputs"

{in₁→fun₁,…}

set input in_i to value fun_i[t] at time t

If the parameters and variables have descriptions in the model, these are displayed with a Tooltip in their corresponding controllers.

ResourceFunction["SystemModelManipulate"] has the same options as SystemModelSimulate, SystemModelPlot and Manipulate, with the following additions and changes:

Appearance

"Open"

appearance of controls for real and integer values

ContinuousAction

False

whether to update continuously when controls are changed

SynchronousInitialization

False

whether to perform initialization synchronously

SynchronousUpdating

False

whether to update synchronously

Options such as ControlType and Appearance can be given separately for each variable, in the form {u,spec,opts}.

Available example models can be found using SystemModelExamples.

Examples

Basic Examples (3)

Create a dynamic interface for a model simulation:

In[1]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/986c6990-5a44-4fb2-97e8-fc72bb6ea190"]

Out[1]=

Manipulate an initial value in a simulation:

In[2]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/8054af49-c6ce-4037-9437-b1f9e1a116ce"]

Out[2]=

Specify the model by name and manipulate a specific parameter value in a simulation:

In[3]:=

Out[3]=

Scope (23)

Models (5)

Control initial values in an AffineStateSpaceModel:

In[4]:=

$ResourceFunction["SystemModelManipulate"][ AffineStateSpaceModel[{{-(x1/10) - Cos[x2^2], Cos[x1]}, {{0}, {1}}, {x1}, {{0}}}, {x1, x2}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None] ]$

Out[4]=

Control initial and parameter values in a NonlinearStateSpaceModel:

In[5]:=

Out[5]=

Control parameter and initial values in a StateSpaceModel with a given input:

In[6]:=

ResourceFunction["SystemModelManipulate"][
StateSpaceModel[{{{0, 1}, {1/4 (-2 - 4 a), -(5/2) - a}}, {{0}, {1}}, {{1, -1}}, {{0}}},
SamplingPeriod ->None, SystemsModelLabels -> None], <|
"Inputs" -> {1 -> UnitStep}|>]

Out[6]=

Control a parameter value in a TransferFunctionModel with a given input:

In[7]:=

$ResourceFunction["SystemModelManipulate"][ TransferFunctionModel[ Unevaluated[{{(s - 1)/(s^2 + (5/2 + a) s + 1/2 + a)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], <| "Inputs" -> {1 -> Tanh}|>]$

Out[7]=

Control a parameter value in a DiscreteInputOutputModel with a given input:

In[8]:=

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In[9]:=

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Content (6)

Reproduce control annotations for a SystemModel:

In[10]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/ee24562f-d7e9-4952-8506-04e44cae8d82"]

Out[10]=

For a SystemModel all default plots are shown by default:

In[11]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/528c7503-0df2-41d8-b5f4-e0aebea9634f"]

Out[11]=

Manipulate all plots individually with a "Plots" control:

In[12]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/16fb2da8-41e2-48cb-bddc-d9e64b31ff06"]

Out[12]=

Select which plots to make available:

In[13]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/3bc8c753-0ce6-4c08-84a3-cbb2744ecc51"]

Out[13]=

Use variables or list of variables to specify plots:

In[14]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/d59945cd-9edd-4562-bb50-4f81bdb6b185"]

Out[14]=

Specify a custom simulation interval:

In[15]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/ce64f30e-862c-4ac9-9196-d7db8e662c2b"]

Out[15]=

Controls (5)

Pick minimum and maximum values for the control of a parameter value:

In[16]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/f4a8ed15-176a-4dfd-8a94-1f9f225e541c"]

Out[16]=

Pick minimum, maximum and jump values for the control of a parameter value:

In[17]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/01ac37eb-77b3-4c9f-ac02-d4b2caa72af8"]

Out[17]=

Pick an initial value for the control of a parameter value:

In[18]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/77b61f29-4c3c-438d-911f-bd268d59520b"]

Out[18]=

Pick a list of discrete values for the control of a parameter:

In[19]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/98981c9a-4e58-4756-98ff-60a1d49ab238"]

Out[19]=

Pick a function for the control of a parameter:

In[20]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/5fb88e0d-7987-4ade-a36b-4a9bdf030131"]

Out[20]=

Presentation (4)

Pick a label for the control of an initial value:

In[21]:=

$ResourceFunction["SystemModelManipulate"][ AffineStateSpaceModel[{{-(x1/10) - Cos[x2^2], Cos[x1]}, {{0}, {1}}, {x1}, {{0}}}, {x1, x2}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None] , {{x1, 5, Style["State 1", Bold]}, 0, 10}]$