Simulating LQR and PID controllers to stabilise a three-link robotic system

The study reported here concerns stabilisation control in a multiple-link robotic gymnast (Robogymnast) MATLAB model. The Robot Gymnast represents a high-complexity, triple-inverted pendulum system. The gymnast imitates a human gymnast hanging from an elevated bar and swinging up to increasing heights until it reaches full rotation. The Robogymnast is a 3-link structure, with components analogous to the legs, arms and torso, and has 3 joints: one operating passively, without power; and two other joints which use power. The overhead joint is a significant problem for the controlled motion of the robot and in achieving the smoothness necessary in its operation. The robot gymnast system has been built in reality. However, this paper will focus on the MATLAB model, and illustrate systems features as well as linearisation of the mathematical model for the system, the paper will investigate ways of identifying state space using Lagrange equations. A proportional-integral-derivative controller is applied to operate the system, to measure the degree of response stabilisation. Additionally, use is made of MATLAB Simulink for system simulations and displaying results for overshoot and rise and settle times. The primary purpose of this study was to investigate how linear quadratic regulators and proportional-integral-derivative controllers can be applied in robotic gymnastics.