Fractional Order Particle Swarm Optimization to Optimize a Fractional Order PID Controller for a Vertical Take-Off and Landing System

A Vertical Take-Off and Landing (VTOL) system is highly unstable and hence a robust controller is needed to stabilize it in finite time. This work presents the design of a Fractional Order Proportional-Integral-Derivative (FOPID) controller to stabilize the VTOL system. The applied FOPID controller has been tuned, to achieve the desired performance and robustness, by Fractional Order Particle Swarm Optimization (FOPSO), which is a modified form of the original PSO obtained by generalizing the order of the velocity derivative to a real number \(0 \le \alpha \le 1\). This helps in smoother transitions, better exploration and longer memory of the particles. The results obtained using the FOPID controller has been compared with the conventional PID controller. It has been found that the FOPID controller exhibits superior performance and robustness.