PLC-Based State-Space Controllers for an Inverted Pendulum: Analysis and Comparison

Calderón J.; Carrillo A.; Alva Alcántara J.; Manzano E.A. · Lecture Notes in Networks and Systems (2026) · DOI: 10.1007/978-3-032-18982-0_9

Resumen

This work presents the design, implementation, analysis and comparison of 4 State-Space controllers (pole placement, LQR, MRAC with pole placement and MRAC with LQR), besides a discrete PID, for a cart inverted pendulum. First, the transfer function of the cart inverted pendulum was obtained, using both DC-motor identification and mathematical equations. Afterwards, this transfer function was transformed into a State-Space representation, in order to design the 4 State-Space controllers previously mentioned. All controllers were implemented using a PLC, and the Django framework was used for the creation of an interface that allowed the selection of the controller and the inverted pendulum’s monitoring. Additionally, a SQLite database was created to register the key variables for the controllers’ evaluation. It was found that all controllers were able to stabilize the pendulum, and the best controller was MRAC with pole placement, with a settling time of 89 ms, an overshoot of 1.75%, MAE of 0.69, MSE of 0.95, and accuracy of 99.79%. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

Instituciones: Universidad Nacional de Trujillo