Fractional Order Modeling and Control of Twin Rotor Aero Dynamical System using Nelder Mead Optimization

Abstract

-This paper presents an application of fractional order controller for the control of multi input multi output twin rotor aerodynamic system. Dynamics of the considered system are highly nonlinear and there exists a significant cross-coupling between the horizontal and vertical axes (pitch & yaw). In this paper, a fractional order model of twin rotor aerodynamic system is identified using input output data from nonlinear system. Based upon identified fractional order model, a fractional order PID controller is designed to control the angular position of level bar of twin rotor aerodynamic system. The parameters of controller are tuned using Nelder-Mead optimization and compared with particle swarm optimization techniques. Simulation results on the nonlinear model show a significant improvement in the performance of fractional order PID controller as compared to a classical PID controller.

Fractional Order Based Computed Torque Control of 2-link Robotic Arm

“…In case of SISO systems, FOPID has been applied for the DC motor speed control in [16], controlling the bioreactor system [17], backlash vibration suppression control for the torsional system [18], and electro-hydraulic servo system (EHSS) position tracking control [19]. For MIMO systems, FOPID controller has also been successfully applied in [20,21,22]. It can be seen from these applications that performance of controller entirely depends on finetuning of controller parameter.…”

“…There are numerous tuning algorithms, which differ in terms of convergence speed. In [20], Nelder-mead is shown better than PSO as it is a geometric algorithm and provides faster convergence. So, this method is chosen in this paper.…”

“…Nelder-Mead tuning is chosen for the robotic arm because it provides faster convergence as compared to other optimization techniques i.e., PSO technique [20].…”

“…Nelder-Mead algorithm requires a continuous search space same way as the original versions of DE and PSO, and the points in space are represented as vectors of real numbers [37]. Nelder-Mead technique has already been applied for the tuning of the PID controller parameters applied for the position tracking control of EHSS [38], [20]. Better and fast tracking performance is achieved as seen from the simulation results in comparison to selftuning fuzzy approach.…”

“…The closed-loop stability of the control scheme can be proved by assuming that CTC [20] drives the open loop gain to unity. However, practically there are incomplete cancellations of nonlinear terms (due to imperfectly known parameters or inevitable friction effects).…”