Simulink Model for Inverted Pendulum System with PID Controller Implementation

In this technical article, we present the development of a Simulink model for an inverted pendulum system and the implementation of a classical PID controller. To provide detailed insights into the modeling and control implementation process, we begin by introducing the fundamental principles and dynamic equations governing inverted pendulum systems. The mathematical formulation includes deriving the nonlinear dynamics using Lagrange's equations, which forms the foundation for our Simulink implementation. We then comprehensively discuss how these theoretical principles and equations are translated into specific components and connections within the Simulink environment. This includes creating subsystems for pendulum dynamics, cart movement, and sensor feedback loops using Simulink blocks like Integrators, Gains, and Summing Junctions. The model incorporates state-space representation blocks for real-time system simulation. Subsequently, we explain the operational principles of the PID controller and demonstrate the methodology for tuning its parameters (proportional, integral, and derivative gains) to achieve stable inverted pendulum control. The PID implementation uses Simulink's PID Controller block with anti-windup protection and saturation limits to prevent integral windup during aggressive maneuvers. We detail the Ziegler-Nichols tuning method and manual optimization techniques for determining optimal controller parameters. Finally, we validate the effectiveness and performance of our designed model and controller through extensive simulation studies and experimental results. The validation process includes stability analysis, disturbance rejection tests, and set-point tracking performance evaluation using Simulink's Simulation Data Inspector for data logging and analysis. Through this article, readers will gain comprehensive understanding of inverted pendulum simulation and control, along with practical knowledge of applying Simulink and PID controllers to achieve robust stabilization of inverted pendulum systems.