NONLINEAR DYNAMIC MODELING AND PID ATTITUDE CONTROL OF A QUAD (+) CONFIGURATION UAV: A MATLAB-BASED SIMULATION STUDY

Quadrotor unmanned aerial vehicles (UAVs) are increasingly deployed in aerial photography, search and rescue, surveillance, and logistics applications, yet their inherently unstable and nonlinear dynamics make controller design and validation a central challenge. This paper presents the derivation of a full twelve-state nonlinear dynamic model for a Quad(+) configuration UAV and the design of a cascaded proportional-integral-derivative (PID) attitude controller for roll, pitch, yaw, and vertical-velocity regulation. The model incorporates rigid-body translational and rotational equations of motion expressed in Euler-angle parameterization, together with the thrust and moment allocation relating individual rotor speeds to total thrust and body-axis moments. The controller and plant were implemented and simulated in MATLAB over a two-second horizon subject to step commands of −10° roll, 10° pitch, 10° yaw, and 1 m/s descent rate. Simulation results show that all four attitude channels converge to their commanded values, with the roll response tracking without overshoot and the pitch, yaw, and vertical-velocity channels exhibiting bounded overshoot of approximately 10–20% before settling within 1.2–1.5 seconds. These results confirm that a linear PID scheme, despite neglecting the higher-order nonlinearities of the plant, can provide adequate attitude regulation near hover for a Quad(+) UAV, while also revealing the coupling between attitude and lateral translation that motivates more advanced nonlinear control strategies for aggressive maneuvers.