Simulation and Fuzzy controller design for a second-order inverted pendulum system

The inverted pendulums constitute a large family of mechanical devices whose dynamic behavior has been widely studied in the control of systems and their construction leads to very complete pilot plants, of interest and motivation for researchers in the area of control engineering, due to the non-linear component of the process.

The mathematical representation that describes the dynamic behavior of the inverted pendulum can be obtained from the application of the Newtonian, Lagrangian or Hamiltonian mechanical theory, which in general terms leads to a non-homogeneous second order difference equation with constant coefficients, which for simulation and methodology validation purposes does not take into account the dynamics of the actuator and the friction in the joints.

The fuzzy control developed for the control of the inverted pendulum was selected as inputs to the controller two variables that are considered of great relevance in the mathematical behavior of the system, which were the error of the angular position and change ratio of this. The output is defined as the manipulated variable, which in this case is the torque applied to the actuator.

Figure below shows the fuzzy controller simulation in MATLAB. If you are interested, please visit my implementation and codes in GitHub repository.