Automatic Dynamics Equation Generation of Multibody systems

This video demonstrate Automatic Symbolic equation generation of multibody systems using MapleSim, a toolbox from Maplesoft. The example system used for demonstration is Furuta Pendulum


Transcript:

In one of the previous presentations we have seen the steps for MapleSim modeling. Once we have our physical model in block diagram format, we can extract equations using maple templates for MapleSim.

There are a number templates available in the library. For example equation generation template. From documents folder we attach a new equation generation template to our model. This template is written in maple by MapleSoft to generate model equation automatically. Once we open the template, the model is automatically loaded into maple worksheet. By default the parameter names are lengthy. However, we can make use of maples substitution command so that our equations look nice and clean.
For example we replace DFPSubsys1inst.theta_R3 with th2. These are dynamics equations of the system. Although there are number of analysis templates available, we can create our own custom template with maple worksheet. For that I will attach a blank Maple work sheet to the MapleSim model. From maple library I will load the current MapleSim component to our work sheet. We need to specify the file of our model to this component. Now let us see what all commands are available for equation generation within Maple. For that we open Maple help and look for MapleSim. We have Multibody Build equations Package within MapleSim toolbox. This package allows us to use BuildEQs functions with arguments passed as options. This function computed symbolic model equation automatically.There are multiple options available in the library for this function. These options can be assigned to single variable and this variable can be passed to BuildEQs function at single pass without needing to set each and every option individually. For example we assign our options to leArguments .
•Input string is the name of our model and the Maple package, which we are using to input the model into BuildEQs function.
•Model Name is the string indicating the name of the model in the worksheet.
•Then we specify the equation simplification process for kinematic equations and Dynamics Equations.
•And AugType is the string indicating whether the contributions of constraint reactions to the dynamic equations are represented by their actual values (Reaction) or by Lagrange multipliers. Our system is not a constrained system hence there will be no lagrange multiplier generate from the BuildEQs function.
•Now we pass all these options to BuildEQs function.
•We execute the command now..
We can see here that our joint variables are specified. Theta_R3 is the angle of component R3, which is revolute joint at pendulum end—we can see it from GUI. The dynamics equations appear in the same order as the joint variable appear in this verbose output of BuildEQs function.
To extract mass matrix we use a set of commands, which I am going to demonstrate now.
•with(DocumentTools), the document tools package of Maple
•file:=GetProperty(Simulation0,filename); get property of our current model
•file1:=convert(file,name); assign property to a variable
•M:=file1:-xM, extract out our mass matrix
•The coriolis and gravity terms are extracted with
File1:-vF

In this presentation we have seen symbolic automatic equation generation of Multibody systems with MapleSim. I hope you enjoyed this video. Thank you

Category:

Science & Technology

Tags:

• Furuta Pendulum
• MapleSim
• Multibody
• Inverted Pendulum
• QuanserSymbolic
• Computation