## Article  
### LMIs-Based LPV Control of Quadrotor with Time-Varying Payload  
[PERSON] 1,*\({}^{\text{(\textregistered)}}\), [PERSON] 1 and [PERSON] 2  
Footnote  
the LPV controller was proposed for high-speed maneuvering of a quadrotor that requires large tilt angles. Tilt angles were accounted up to \(\pm\pi/3\) rad. In [12], a switched LPV control approach was recommended in order to handle huge attitude angles and external disturbances. The region for roll angle \(\phi\) was considered to \(\pm\pi/3\) rad and for pitch angle \(\theta\), the region was limited to \(\pm\pi/8\) rad. Time-varying mass and time-varying inertia were not taken into consideration in the control strategies outlined above. The design of the control system for a quadrotor with variable payload has also been investigated in the literature. In [13], LMI-based static output feedback LPV controller was suggested for Attitude/Altitude control of a quadrotor to handle the rotors' velocity variation and step change in mass. The rotors' velocity and mass were assumed to be measurable. Longitudinal and latitudinal translational motions were ignored, and the small angle assumption (i.e., \(cos\phi cos\theta\approx 1\)) was employed to design the control scheme. Moreover, the mass flow rate was ignored, and the control scheme was conservative due to coupling in the scheduling parameters. In [14], Hybrid LPV control scheme was suggested for the reference tracking of a quadrotor with variable mass and variable inertia. A combination of integral backstepping control and proportional-derivative controls were designed to control the quadrotor's position and altitude. PD controllers were designed using the small angle assumption (i.e., \(sin\phi\approx\phi\), \(sin\eta\approx\theta\), and \(cos\phi\approx cos\theta\approx 1\)). Variation in mass was not considered during the control algorithm design. LPV \(\mathcal{H}_{\infty}\) controller was recommended to control the quadrotor rotational dynamics subject to time-varying inertia and variation in the rotors' speed. Mass and rotor speed were considered measurable. The variations in MOI were recalculated in real-time from the changes in the mass. The mass flow rate was not taken into account and the scheduling parameters selected in the proposed scheme did not vary independently, which led to conservative control. A robust LPV \(\mathcal{H}_{\infty}\) controller was proposed for Altitude/Attitude stabilization of a quadrotor to handle mass, inertia, and rotors velocity variations [15]. The proposed controller was designed using the LMI framework. The small angle approximation was considered to design the LPV scheme for the 4 DOF model of the quadrotor. Moreover, position control and the mass flow rate were not taken into consideration, and the coupling in the scheduling parameters led to conservative control. A switched LPV control technique was suggested for the 3 DOF model of a quadrotor subject to large attitude angles, variable inertia, and outside disturbances [16]. Position control dynamics are not considered. In [17], the author recommended a self-tuning PID control scheme for the reference tracking of a quadrotor. Mass and wind disturbance estimators based on a neural network with online learning were suggested  
Figure 1: The 3D CAD model of quadrotor with Payload. to cope with the system's mass variation and wind disturbances. Variations in MOI due to variable mass and mass flow rate were not taken into consideration. Adaptive sliding mode control (SMC) based on backstepping was advised to reduce the effect of variable load and wind disturbances [18]. Only the changing mass is estimated using the adaptive estimation controller. A fractional SMC was designed to cope with external disturbances and variations in inertia. Actuator limitations and mass flow rate were not considered, and chattering issues existed due to the use of the signum function in the control law. Adaptive non-singular fast terminal SMC was proposed in [19]. External disturbances and mass are estimated online.