Lqr-based PID controller with variable load tuned with data-driven methods for double inverted pendulum

Modern controller design is increasingly based on data-driven control methods. PID controllers are still used primarily in the industry, because they are Linear Quadratic Regulator (LQR). The LQR provides an efficient way to tune the parameters of a PID controller. The LQR has the disadvantage of requiring accurate models of the system, as well as reducing a high-order system to a second-order model. First, we explore the new horizons of control theory in the form of the state-space model for high nonlinear systems. Second, the Lagrangian method establishes the new mathematical model of the two-stage linear inverted pendulum system. In addition, real-time LQR parameters are calculated under variable load. This method has been demonstrated to be highly applicable and accurate through simulations and experiments using the Double Inverted Pendulum model.