Navid Razmjooy - Department of Electrical Engineering, University of Tafresh, Tafresh, Iran.
Mehdi Ramezani - Department of Mathematics, University of Tafresh, Tafresh, Iran.
Ali Namadchian - Department of Electrical Engineering, University of Tafresh, Tafresh, Iran.

Flexible manipulators are very commonly used in industries. In this paper a single-link flexible joint robot is modeled firstly by using Euler–Lagrange energy equation. An optimized Linear Quadratic Regulator is employed to control the manipulator. After that, a Linear Quadratic Regulator (LQR) controller is used for optimal control of the manipulator. For optimizing the LQR, the regulator term weighting of the LQR is achieved by using the newly introduced grey wolf optimizer technique. With the optimized LQR controller based on the proposed performance index, it is tried to have a system with the minimum overshoot and settling time. By considering the proposed performance index and comparing with the PSO-based controller as a popular algorithm, the superiority of the proposed LQR controller in improving the stability and performance of the manipulator is shown. The simulations are performed in MATLAB environment and the results confirm the efficiency of the proposed controller.

Single-link flexible-joint Manipulator, en, Linear Quadratic Regulator, Optimal Control, Gray Wolf Optimizer, particle swarm optimization