MATLAB Simulation for Crane-Double Pendulum System Control (Two-Stage Inverted Pendulum)

This document provides a detailed explanation of MATLAB simulation techniques for controlling a crane-double pendulum system, also known as a two-stage inverted pendulum. The simulation compares two distinct control methodologies: S=1 LQR (Linear Quadratic Regulator) control and S=2 PID (Proportional-Integral-Derivative) control.

The implementation begins with establishing the fundamental principles and dynamic modeling of the crane-double pendulum system. We then demonstrate how to construct the simulation model using MATLAB's Simulink environment or state-space representation. For the S=1 LQR control approach, we design the controller using MATLAB's lqr() function, which requires defining the weight matrices Q and R to optimize the quadratic cost function. The implementation involves linearizing the system around equilibrium points and computing optimal feedback gains. For the S=2 PID control method, we utilize proportional, integral, and derivative components adjusted through MATLAB's pidtune() function or manual parameter optimization, where the control signal is generated based on real-time error calculations between desired and actual system states.

Through comprehensive simulation experiments, we evaluate and compare the performance characteristics and stability margins of both control strategies. The simulation includes benchmarking metrics such as settling time, overshoot analysis, and disturbance rejection capabilities. This comparative analysis provides valuable insights into control system design for underactuated mechanical systems and offers practical guidance for real-world applications.

This technical documentation aims to enhance understanding of crane-double pendulum control challenges and serve as a valuable reference for academic research or industrial projects involving complex mechanical system control.