Tuning of PID Controllers for Quadcopter System using Hybrid Memory based Gravitational Search Algorithm – Particle Swarm Optimization

Abstract

Quadrotors are coming up as an attractive platform for unmanned aerial vehicle (UAV) research, due to the simplicity of their structure and maintenance, their ability to hover, and their vertical take-off and landing (VTOL) capability. With the vast advancements in small-size sensors, actuators and processors, researches are now focusing on developing mini UAV's to be used in both research and commercial applications. This work presents a detailed mathematical nonlinear dynamic model of the quadrotor which is formulated using the Newton-Euler method. Although the quadrotor is a 6 DOF under-actuated system, the derived rotational subsystem is fully actuated, while the translational subsystem is under-actuated. The derivation of the mathematical model was followed by the development of the controller to control the altitude, attitude, heading and position of the quadrotor in space, which is, based on the linear Proportional-Derivative-Integral (PID) controller; thus, a simplified version of the model is obtained. The gains of the controllers will be tuned using optimization techniques to improve the system's dynamic response. The standard Gravitational Search Algorithm (GSA) was applied to tune the PID parameters and then it was compared to Hybrid Memory Based Gravitational Search Algorithm -Particle Swarm Optimization tuning, and the results shows improvement in the new algorithm, which produced enhancements by ( %) compared to the standard algorithm.

Dodecarotor İHA'nın Yörünge Takibi için Bozkurt Optimizasyon Algoritması Temelli Optimal PID Denetleyici Tasarımı

“…In order to describe this relationship, the equations of motion representing the 3D motion of the system are derived based on the Euler-Newton formulation. A linear relationship between the body forces and the vector Ω forming the angular velocities of the motors can be obtained with a constant matrix C as in (1)(2)(3). Depending on the configuration of the vehicle, the C matrix can be calculated as in (3).…”

“…Many in the research community focused on the design of position controllers for autonomous flights, resulting in remarkable advances in the field of rotor aircraft. PID controllers are the most common type of controller in many fields due to their simplicity, ease of implementation and efficiency [1][2][3]. If the parameters of the PID controller are not determined correctly, no matter which area of the industry is used, the system to which the controller is applied cannot perform at a satisfactory level.…”

Nonlinear PID controller design for a 6-DOF UAV quadrotor system

“…The four possible movements of the 6-DOF quadrotor are shown in Figure 1. Some researchers [13][14][15]27] depend only on the equations of acceleration for the 6-DOF quadrotor system without taking the velocities into account. In this paper the mathimatical model of the 6-DOF quadrotor system is crafted in such a way that the acceleration and velocity vectors are taken into consideration resulting in a more accurate nonlinear model for the 6-DOF quadrotor system and closer to the actual one.…”

“…where f xi , f yi , i = 1, 2, 3 are the NLPID controller gains given in (6). By taking into considerationẍ de andÿ de = 0, then (14) can be written as,…”

“…Many researchers studied the quadrotor control design with different types of controllers. One of the most used controllers is the LPID control because of its simplicity [13][14][15][16] but on the other hand it has many disadvantages: 1) sometimes it gives a high control signal due to the fact of windup, thus, overshooting and continuing to increase as the accumulated error is unwound (offset by errors in the other direction, 2) the differentiator Email address: ibraheem.i.k@ieee.org (Ibraheem Kasim Ibraheem) leads to noise amplification. Other used controllers like: NLPID control [17] and [18], LQR [19], geometric control [20], nonlinear model predictive control [21], L1 control [22], fuzzy control [23,24].…”