Control System Model for a Quadruple Inverted Pendulum

This document presents a comprehensive control system model for a quadruple inverted pendulum developed using MATLAB/Simulink. The model is designed to simulate and study control methodologies for quadruple inverted pendulum systems. Initially, we constructed an accurate mathematical model within the MATLAB/Simulink environment that precisely replicates the physical characteristics and dynamic behavior of the four-link pendulum system. The implementation involves defining the system's state-space equations and configuring the Simulink blocks to represent the pendulum's nonlinear dynamics.

We then implemented a sophisticated control algorithm employing state-feedback control techniques to achieve stabilization of the quadruple inverted pendulum. The control system design incorporates pole placement methods and LQR (Linear Quadratic Regulator) optimization to calculate optimal gain matrices. Through systematic adjustment of control parameters and design of appropriate feedback control strategies, we optimized the system's performance metrics including settling time, overshoot, and stability margins.

The validation process involved extensive simulation studies and experimental verification to confirm the model's accuracy and the control algorithm's effectiveness. Key Simulink features used include variable-step solvers for handling stiff systems, scopes for real-time visualization of system states, and MATLAB functions for implementing custom control logic. The primary objective of this project is to provide an in-depth understanding of quadruple inverted pendulum control principles and deliver a reliable control system framework suitable for advanced research and practical applications in nonlinear control theory.