Comparison of PD, PID and Sliding-Mode Position Controllers for V–Tail Quadcopter Stability

Nonlinear Control of a Multilink Aerial System and ASEKF-Based Disturbances Compensation

“…The estimation of the disturbances is added to the control loop as shown meanwhile, the estimation of the states is used to close the loop when a given sensor fails (doted arrow). A PD control law with disturbances compensation: (38) where K P > 0 ∈ IR 6×6 and K V > 0 ∈ IR 6×6 are diagonal matrices that stand for the proportional and derivative gains, respectively, is applied to the system. The vectors e = q d − q ∈ IR 6 anḋ e =q d −q ∈ IR 6 depend on the desired position q d and the desired velocityq d and correspond to the position and velocity errors, respectively.…”

“…By considering the control law in Eq. (38), taking into account the model of the system introduced in Eq. (5) and assuminĝ ρ ρ ρ ≈ ρ ρ ρ, the closed loop equation can be expressed as:…”

“…The desired thrust and attitude of the vehicles are computed according to Eqs. (8) and (38). Having in mind the overactuation of the ML-UAS is over-actuated since it has 6 DOFs and 8 real control inputs ( f i , θ i d and t β j ); the desired orientation angle of the UAVs is established to be θ…”

Comparison of Linear and Nonlinear Methods for Distributed Control of a Hierarchical Formation of UAVs

“…An SMC PD control scheme from [24] and [25] has been adapted for this study and tailored for the leader-follower tightly coupled formation flight. This technique has been selected because of its high flexibility and reconfigurability for different formations.…”

“…is obtained using nonlinear model Equations (1)- (6). Keeping the control law from Equation (21) in Equation (25), V = −η|s α | < 0 (27) is obtained where η = 1, a strictly positive constant. It is proved from Equation (27) that all the system trajectories point towards the sliding surface s α in a finite time.…”