Artificial Intelligence based LQR and PID Controller Design of 3 Degree of Freedom System

In this study, the position control of a 3 DoF underactuated system is carried out. The developed approach is tested on a double pendulum overhead crane. Considering the nonlinear dynamics of the system, its mathematical model is first obtained by Euler-Lagrange model. Then, since PID and LQR controllers are used in the simulations, the nonlinear model is linearized around the equilibrium point of the system. Using the linear model, the parameters of LQR and PID controllers are tuned by Artificial Bee Colony Algorithm. In the optimization process, the Integral Time Absolute Error function is chosen from traditional fitness functions to minimize the error in each single-degree-of-freedom joint of the system. Additionally, to ensure the precise movement of the car, the objective function is improved in a way to include unit step response characteristics. The control performance is evaluated in the simulations. The results are presented in tables and graphs. The proposed approach can be used to control multi-degree of freedom underactuated systems.