The Modelling and Control for Design Aero-Pendulum via Proportional–Integral–Derivative and Integral-Proportional Derivative

The article aims to clarify the essential design principles behind Aero pendulum balancing and its two related controllers: Proportional–Integral–Derivative (PID) and Integral-Proportional Derivative (I-PD). The design incorporates dynamic principles and Newton’s laws, leading to a non-linear mathematical model that must be converted into a linear form for effective control design. The PID controller serves as the primary controller, forming the foundation for developing I-PD controllers to ensure stability and the elimination of interference within the Aero pendulum system. MATLAB’s Simulink program is employed due to its smooth compatibility with the Arduino board and the Aero pendulum, facilitating simulation and experimentation. The controller’s logic capitalizes on the system’s capabilities to stabilize the Aero pendulum and sustain the targeted angle via simulation. The article explores the design of the controller based on the structural design derived from dynamic principles and parameters of Newton’s laws, assessing the angular performance of the Aero pendulum and its mathematical model-derived design while reviewing the control system’s performance index. Ultimately, the article focuses on using PID and I-PD controllers to stabilize the Aero pendulum, underlining how effective the non-linear equations from the mathematical model are in controlling and stabilizing the system. The findings reveal that the I-PD controller exhibits a higher amplitude with a time-setting point ranging from 2.1 to 2.3 seconds. In contrast, the PID controller demonstrates a lower amplitude than the PID controller, with a time-setting point of 2.3 to 2.5 seconds, making it slower than the I-PD controller.