Discipline: Technology and Engineering
Subcategory: Electrical Engineering
Anayely Saguilan - California State University, Los Angeles
Co-Author(s): Arturo Pacheco-Vega, California State University- Los Angeles, Los Angeles, CA
In this work, we develop intelligent control strategies based on the Fuzzy Logic technique to stabilize a mass-rod inverted pendulum system located on top of a cart. Three types of fuzzy controllers, each with a different amount information about the system being provided to the corresponding controller, are considered. The three controllers use the Mamdani inference method and where operated under the assumption that the starting position of the pendulum is a specific angle θ. The open-loop system takes the inverted pendulum to the stable position of θ = π, while the fuzzy controller is used to maintain the pendulum at the unstable position θ = 0. The behavior of the inverted pendulum on the cart is modeled from applying Newton second law to develop the equations of motion. These equations are then converted into a nonlinear dynamical system. The mathematical model indicates that there are two critical points, an unstable position at θ = 0, and a stable at θ = π. The three types of fuzzy controllers are built with an increasing amount of information about the angle, its rate of change, and its integral. For all of them, triangular membership functions along with if-then rules are used to stabilize the system dynamics under different operating conditions. The manipulated variable is the force exerted on the cart and the controlled variable consist of the angular position of the pendulum. MATLAB is used to implement the fuzzy controllers, along with the corresponding control actions, while numerical tests are conducted to assess their relative performance. Results demonstrate that the reliability of the fuzzy controllers depends on the information given to them, and therefore, the controller that was built the largest amount of information could more effectively stabilize the inverted pendulum-cart system. Future work will include expanding the analysis of the performance on fuzzy logic controllers under the effect of the mass of the pendulum, mass of the cart, and the length of the rod that connects the pendulum to the cart, and to compare stabilization time against similar traditional controllers. References: O. Boubaker, “The inverted pendulum: A fundamental benchmark in control theory and robotics,” in International Conference on Education and e-Learning Innovations, 2012, pp. 1–6.L. Zadeh, “Fuzzy sets,” Information & Control, vol. 8, pp. 338–353, 1965. A. Pacheco-Vega, C. Ruiz-Mercado, K. Peters, and L. Vilchiz-Bravo, “On-line fuzzy-logic-based temperature control of a concentric-tube heat exchanger facility,” Heat Transfer Eng., vol. 30, no. 14, pp. 1208–1215, 2009.
Funder Acknowledgement(s): This project has been supported by NSF/CREST grants: Awards No. HRD-1547723 and HRD-2112554.
Faculty Advisor: Arturo Pacheco-Vega, firstname.lastname@example.org
Role: Equations and code development, and analysis of results.