Modeling and Nonlinear Control of a Quadcopter for Stabilization and Trajectory Tracking

Abstract

This paper presents an adequate mathematical representation of a quadcopter’s system dynamics and effective control techniques. A quadcopter is an unmanned aerial vehicle (UAV) that is able to do vertical take-off and landing. This study presents a nonlinear quadcopter system’s mathematical modeling and control for stabilization and trajectory tracking. The mathematical model of the system dynamics of the quadcopter is derived using Newton and Euler equations with proper references to the appropriate frame or coordinate system. A PD control algorithm is developed for the nonlinear system for stabilization. Another nonlinear control technique called full state feedback linearization (FBL) using nonlinear dynamic inversion (NDI) is developed and implemented on the quadcopter system. However, there is a problem with the normal approach of the complete derivation of the full state FBL system using NDI as gathered from the literature review. In such an approach, the PD controller that was used for attitude stabilization was able to stabilize the angles to zero states, but the position variables cannot be stabilized because the state variables are not observable. Thus, a new approach where the position variables are mapped to the angle variables which are controllable so as to drive all states to zero stability was proposed in this study. The aim of the study was achieved but the downside is that it takes a longer time to achieve this stability so it is not efficient and should only be considered when absolute zero stability is the aim without considering time efficiency. The study further investigates the problem of nonlinear quadcopter system’s mathematical modelling and control for stabilization and trajectory tracking using the feedback linearization (FBL) technique combined with the PD controller. The proposed control algorithms are implemented on the quadcopter model using MATLAB and analyzed in terms of system stabilization and trajectory tracking. The PD controller produces satisfactory results for system stabilization, but the FBL system combined with the PD controller performs better for trajectory tracking of the quadcopter system.

Evaluation of the Success of Simulation of the Unmanned Aerial Vehicle Precision Landing Provided by a Newly Designed System for Precision Landing in a Mountainous Area

“…The mathematical model of the chosen unmanned aerial vehicle was created based on the general motion Equations ( 1)- (10) for a quadcopter [20][21][22][23][24] (Figure 3). microcontroller works with a frequency of 12 MHz, and the sampling frequency of the used analogue converter is 32 kHz, thanks to which the necessary frequency range of the system is covered (from 88 MHz to 500 MHz).…”

“…The mathematical model of the chosen unmanned aerial vehicle was created based on the general motion Equations ( 1)- (10) for a quadcopter [20][21][22][23][24] (Figure 3). The movement of the UAV can be expressed in four basic movements, the change in altitude a 1 , roll a 2 , pitch a 3 and yaw a 4 , which are given as follows in Equations ( 1)-(4):…”

An optimal hybrid quadcopter control technique with MPC-based backstepping

“…Using the Newton-Euler method, a dynamic model of the quadcopter is developed. The translational and rotational dynamic equations of the body frame of the quadcopter are expressed with respect to the Earth-fixed frame in [40]. The forces involved in the translational dynamics of the quadcopter are thrust, and the force applied along the 𝑧-axis against gravity [41].…”

“…where 𝑢 𝑣 𝑤 𝑇 = 𝑥 𝑦 𝑧 𝑇 . The rotational dynamic of the quadcopter according to the Newton-Euler second law of motion, 𝑀 is the sum of the quadcopter torque vector, − → 𝑈 𝜏 and the quadcopter gyroscopic effects as defined in (8) [40]:…”

Control strategies in enhanced stand-alone mini-grid operations for the NESI–an overview

“…Moreover, with the proliferation of renewable energy sources (RESs) in the energy mix because of near zero carbon footprints, micro-/mini-grids are becoming more competitive and attractive for investors than legacy grids. The reason for such competitiveness is partly because most RESs are usually integrated at the distribution buses (Arfeen et al, 2019), which will not require huge capital investment on equipment and manpower because of lower voltage levels of integration (Lovejoy, 1992;Bidram and Davoudi, 2012;Hazelton et al, 2014;Mipoung et al, 2014;Dang et al, 2015;Singh et al, 2015;Unamuno and Barrena, 2015;Nasirian et al, 2016;Dehkordi et al, 2017b;Arcos-Aviles et al, 2018;Castilla et al, 2019;Flowers, 1997;Lasseter, 2002;Lasseter and Paigi, 2004;Lasseter, 2011;Olivares et al, 2014;Tahir and Mazumder, 2015;Chen et al, 2016;Fioriti et al, 2017;Li et al, 2017;Moayedi and Davoudi, 2017;Chen et al, 2018;Sen and Kumar, 2018;Xu et al, 2019;Jumani et al, 2020;Mujtaba et al, 2020;Shrestha et al, 2020;Abdulkareem et al, 2022;Anand et al, 2013;Awelewa et al, 2016;Awelewa et al, 2020;Buja and Kazmierkowski, 2004;Concari et al, 2016;De Carne et al, 2015;De Carne et al, 2018;…”