Diseño e implementación de un péndulo invertido auto balanceado montado en un carro móvil para el análisis de distintas técnicas de control automático

Abstract

The objective of this study was to design, build and implement a self-balancing inverted pendulum mounted on a mobile cart for learning different methods of automatic control for students of the Mechanical Engineering Degree at ESPOCH. The QFD method was applied with which the technical characteristics of the equipment were obtained, later the functional design was carried out describing the operation at its different levels. The 3D design was carried out using the SolidWorks software which allowed the dimensioning and selection of the different mechanical and electronic elements. The dynamic model of the equipment was made and these equations were linearized by representing them in state space that allowed the plant to be represented within Simulink, obtaining the curves where it shows that the system is naturally unstable. A linear quadratic regulator was applied, obtaining the state feedback matrix K using Matlab software, the state feedback was applied by integrating the K matrix to the dynamic model of the equipment, represented in Simulink, this simulation allowed observing the regulation of the variables of State. The equipment was built with precision machines, obtaining great dimensional accuracy and correct assembly. Finally, the LQR control was implemented in the ESP32 module through programming in C language. The curves obtained from the state variables are very similar to the simulated one, where it is shown that the position of the mobile car does not return to its initial zero position. All the variables, except the position, vary around zero degrees and this is due to the control system as it prioritizes control of the pendulum angle sacrificing control of the other variables. It is recommended to add an integrator to the LQR control so that the position of the moving carriage can be maintained at the origin.