Design, modeling, and control of a ball-on-T-shaped inverted pendulum system with experimental validation

This paper presents the design, modeling, and real-time control of a recently developed Ball-on-T-shaped Inverted Pendulum (BTIP) system mounted on a motorized cart, serving as a novel experimental platform for advanced control validation. The nonlinear dynamics are derived using the Euler–Lagrange formulation and expressed in state-space form to facilitate controller design. Two model- based control strategies—pole placement and Linear Quadratic Regulator (LQR), including an extended LQR with integral action—are developed to stabilize the under-actuated and highly unstable system. A full-state observer is implemented to estimate unmeasured states and integrated into the closed-loop framework. The controllers are validated through MATLAB/Simulink simulations and real- time implementation using the Simulink Real-Time environment and National Instruments data acquisition (DAQ) hardware. Experimental results demonstrate that both control strategies successfully stabilize the BTIP system. The LQR controller achieved full stabilization within approximately 2.8 s, with a maximum pendulum deviation of ±0.015 rad and ball–position error below 5 cm, while maintaining the control effort within ±5 N. In comparison, the pole–placement state–feedback controller stabilized the system within about 3.2 s, with slightly higher noise and control effort. The BTIP platform thus provides a robust benchmark for evaluating advanced control algorithms in nonlinear, under-actuated systems and an effective educational tool for real-time control and mechatronics applications.