Hybrid simulation of an inverted pendulum

Abstract

Hybrid simulation (Hardware-in-the-Loop) of an inverted pendulum is an approach that combines numerical simulation and physical experimentation, with the aim of faithfully replicating real operating conditions in the control of dynamic systems. In this paper, an experimental setup is implemented in which the system dynamics - the cart motion and the pendulum angle - are calculated on a personal computer using the Python environment and the SciPy library, while the control algorithm is executed on the Arduino microcontroller platform. This division enables the simulation and control to run on independent processors, which brings the operating conditions closer to real systems. The mathematical model of the system is based on nonlinear differential equations that describe the cart position and the pendulum deflection angle, while the microcontroller receives the state values in real time and calculates the control signal using the LQR algorithm. In this way, interaction is achieved between the software and hardware parts - Python represents the physics model, while Arduino represents the real controller. The advantage of this approach is the possibility of analyzing delay and time response under conditions close to real ones, which is often neglected in classical simulations. Different microcontroller platforms (ATmega328P, ATmega32u4, ESP32 with FPU) make it possible to experimentally evaluate stability, latency and control-computation speed. The influence of the sampling frequency and communication channels (serial transmission) on system performance is also analyzed. Hybrid simulation represents a bridge between theoretical modeling and practical implementation, enabling safe testing of control algorithms and comparison of hardware platforms in real time.