The Inverted Pendulum Problem

Overview

The primary objective of this project is to establish a thorough understanding of dynamics and control of a system. This project comprises of balancing an inverted pendulum on a cart, the premise being — use a simple yet classical control problem that provides an in depth and comprehensive working of the mechanics involved in building a single degree of freedom controller. Here we have analysed the system using various tools to determine the stability, sensitivity, phase and gain margins. The system was modelled using Simulink and Simscape. We used several controllers to draw out the distinctions in their results and this includes — PID, LQR and MPC.

Objectives

  • Understand the dynamics of inverted pendulum on a cart
  • Define the dynamics in classical and Lagrangian mechanics
  • Model the dynamics using Transfer functions and State-space representation
  • Develop a PID controller on Simulink
  • Simulate the dynamics on Simscape
  • Develop a LQR controller and a full state estimator
  • Compare the outputs from PID, LQR, and MPC controller

Why NMP?

Thrust Test