Control Methodologies for Tip Stabilization in Flexible Robotic Manipulators: An Analysis of LQR, LQG, and PID Controllers

Flexible robotic manipulators are increasingly utilized in the aerospace industry, leading to continuous advancements in their control methodologies. While PID controllers have traditionally been predominant in this field, there is a shift toward exploring and implementing new control strategies. This paper employs the finite element method to develop the dynamics of a single-link flexible robotic manipulator, calculating the generalized inertia and stiffness matrices for a specified manipulator length. It also formulates both the linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers. The system is linearized to create a state-space representation, and the dynamic responses, including tip deflections and velocities, are analyzed under a bang-bang torque scenario. The study examines LQR and LQG controllers with both partial and full state feedback. The tip deflections of the manipulator are compared to those produced by a PID controller. The performance of all controllers is evaluated based on the time required for tip stabilization, with conclusions drawn from the collected data.