Control algorithm of the unstable 3DOF system
Dragan Erceg, Z Grahovac, Bojan Knežević · Journal of Physics Conference Series · 2023
Abstract The basic characteristics of a system with three degrees of freedom (3DOF) are nonlinearity and instability. An example of such a system is a double pendulum inverted on a moving platform, that is, a pendulum system with two joints and two rods. These characteristics make the system a perfect model for testing various control algorithms such as PID controllers, linear quadrature optimization (LQR) controllers, neural networks, fuzzy logic, etc. This paper presents the mathematical modeling and method for control of the 3DOF system by applying only the force acting on the platform. The system is modeled using Lagrange equations of the second type, which are used as a systematic method for obtaining differential equations of motion systems. To be able to apply the basic concept of control, it is necessary to linearize the system. Differential equations are solved numerically by applying the Runge - Kutta method ode45. A linear quadrature optimization (LQR) controller was used as the controller. The simulation and the results of the proposed control method are verified by computer simulations. This paper presents the difference between a linearized and a non-linearized system. The advantage of the proposed control concept is reflected in the fact that with very small changes it can be extended to the control of many other nonlinear systems.