Inverted-pendulum---PINN

Inverted Pendulum on Circular Cart (Quanser)

Physics-Informed Neural Network (PINN) model for simulating the inverted pendulum on a circular cart.

The equations and parameters used in this project are based on the file System_identification_of_a_2DOF_pe .

Code Structure

The code is organized into the following sections:

• Training dataset creation
• Neural network (NN) architecture definition
• NN training using ADAM optimizer
• Validation plots
• Error analysis

Implemented Functions

The file PINN_pendolo includes the following main functions:

• model_loss: main function for computing the total loss
• pinn_loss: PDE-based loss function
• lossIC: loss for initial condition enforcement

The function pendolo_soluzioneNumerica calculates the numerical solution of the system's differential equations.
It outputs time, input voltage, cart angle, and pendulum angle:

[t, x] = [(t, Vm_values), (gamma, phi)]

Within pendolo_soluzioneNumerica, the following helper functions are used:

• Vm_fun: defines the input voltage signal applied to the system

• pendulum_ODE: defines the system's ordinary differential equations (ODEs).
  It returns the angular velocities (first derivatives) and angular accelerations (second derivatives) of the cart and the pendulum:

  dxdt = [gamma_d; gamma_dd; phi_d; phi_dd];