Simulink Diagram for Solving a Nonlinear Second-Order Differential Equation

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SUMMARY

The discussion focuses on creating a Simulink diagram to solve the nonlinear second-order differential equation \(\frac{d^2 \theta}{dx^2}=-\frac{x}{10}\cos \theta - \frac{9.8}{10}\sin \theta\). The user seeks assistance in finding the system's response to both a unit step function and a unit pulse function. A warning regarding the simulation step size is addressed, with a recommendation to adjust the settings in the model configuration parameters to optimize the simulation performance.

PREREQUISITES
  • Understanding of nonlinear differential equations
  • Familiarity with Simulink 2023a
  • Knowledge of simulation step sizes and solvers
  • Experience with block diagram arrangement in Simulink
NEXT STEPS
  • Learn how to configure simulation parameters in Simulink
  • Explore the use of pulse generators in Simulink simulations
  • Study methods for solving nonlinear differential equations using Simulink
  • Investigate the implications of step size settings on simulation accuracy
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Engineers, students, and researchers involved in control systems, simulation modeling, and those specifically working with nonlinear differential equations in Simulink.

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< Mentor Note -- thread moved to HH from the technical engineering forums, so no HH Template is shown >[/color]

\frac{d^2 \theta}{dx^2}=-\frac{x}{10}\cos \theta - \frac{9.8}{10}\sin \theta

I'm supposed to draw a simulink diagram for this equation and find the response to a unit step function

This is what I did so far but I don't know if its right
http://postimg.org/image/64mm8rjhv/
 
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looks good. typically i like to arrange the block diagram so the input is on the left, but that is just a matter of preference.
 
donpacino said:
looks good. typically i like to arrange the block diagram so the input is on the left, but that is just a matter of preference.

thanks Also, I'm supposed to find the response to a unit pulse function.
But when I replace the step function with a pulse generator and try running, I get this:
"Using a default value of 0.2 for maximum step size. The simulation step size will be equal to or less than this value. You can disable this diagnostic by setting 'Automatic solver parameter selection' diagnostic to 'none' in the Diagnostics page of the configuration parameters dialog"
 
is that a warning or an error.
typically that step size refers to the simulation step size in the solver. Go to simulation;model config parameters and you can change the step sizes. You can also change it from variable to set step sizes, which i typically recommend.
 

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