Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties

Mofid, Omid; Mobayen, Saleh

doi:10.1016/j.isatra.2017.11.010

Cited by 293 publications

(125 citation statements)

References 78 publications

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“…One supposes that the state measurement is affected by a white noise with a standard deviation equal to 0.0001 and a sampling time equal to 0.001s. 16 Remark 4. The external perturbations, introduced in the mathematical model of the quarotor, represent the fluctuations force produced by rotors.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…According to Moussid et al and Mofid and Mobayen the dynamical model of a quadrotor aircraft describing the translational and the rotational motions, represented in a body‐fixed coordinate frame with the origin at the center mass, is given by

\begin{matrix} right \ddot{X} & left = (s_{ψ} s_{ϕ} + c_{ψ} c_{ϕ} s_{θ}) \frac{U_{c}}{m} + δ_{x}, & right \\ right Ÿ & left = (- c_{ψ} s_{ϕ} + s_{ψ} s_{θ} c_{ϕ}) \frac{U_{c}}{m} + δ_{y}, \\ right \ddot{Z} & left = (c_{ϕ} c_{θ}) \frac{U_{c}}{m} - g + δ_{z}, \\ right \ddot{ϕ} & left = U_{ϕ} I_{x}^{- 1} - (I_{z} - I_{y}) \dot{θ} \dot{ψ} I_{x}^{- 1} + δ_{ϕ}, \\ right \ddot{θ} & left = U_{θ} I_{y}^{- 1} - (I_{x} - I_{z}) \dot{ϕ} \dot{ψ} I_{y}^{- 1} + δ_{θ}, \\ right \ddot{ψ} & left = U_{ψ} I_{z}^{} \end{matrix}

…”

Section: Applicationmentioning

confidence: 99%

“…The reference trajectories in X and Y are defined as circular path whereas altitude Z is forced to be constant ( Z ref =1 m ), and ψ ref =0. The initial values are defined as

{[X (0) Y (0) Z (0) ϕ (0) θ (0) ψ (0)]}^{T} = {[0 1.5 0 0.5 0.5 0.5]}^{T} .

In order to demonstrate the robustness properties of the proposed algorithm, the following external disturbances have been introduced:

\begin{matrix} alignleft \\ align-1 δ_{X} & align-2 = \sin (t), δ_{Y} = \cos (t), δ_{Z} = 0.5 \sin (0.5 t) \cos (0.5 t), \\ align-1 δ_{ϕ} & align-2 = 0.5 \sin (0.5 t), δ_{θ} = 0.5 \cos (0.5 t), δ_{ψ} = 0.5 \cos (0.5 t) \sin (0.5 t) . \end{matrix}

One supposes that the state measurement is affected by a white noise with a standard deviation equal to 0.0001 and a sampling time equal to 0.001 s …”

Section: Applicationmentioning

confidence: 99%

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A simplified version of adaptive super‐twisting control

Gutierrez

León-Morales

Plestan

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, a simplified super‐twisting control with adaptive gain is proposed for a class of nonlinear uncertain systems. A strong Lyapunov function is constructed to design a sliding mode controller with adaptive gain. Furthermore, the analysis of the finite time convergence towards the equilibrium point of the closed‐loop system is detailed. Regarding previous works from literature, the main contribution of this approach is the simplification of the gain tuning process by maintaining a high level of performance. Finally, simulation results for tracking control of a quadrotor are given to show the performance of the proposed algorithm.

show abstract

Section: Simulation Resultsmentioning

confidence: 99%

\begin{matrix} right \ddot{X} & left = (s_{ψ} s_{ϕ} + c_{ψ} c_{ϕ} s_{θ}) \frac{U_{c}}{m} + δ_{x}, & right \\ right Ÿ & left = (- c_{ψ} s_{ϕ} + s_{ψ} s_{θ} c_{ϕ}) \frac{U_{c}}{m} + δ_{y}, \\ right \ddot{Z} & left = (c_{ϕ} c_{θ}) \frac{U_{c}}{m} - g + δ_{z}, \\ right \ddot{ϕ} & left = U_{ϕ} I_{x}^{- 1} - (I_{z} - I_{y}) \dot{θ} \dot{ψ} I_{x}^{- 1} + δ_{ϕ}, \\ right \ddot{θ} & left = U_{θ} I_{y}^{- 1} - (I_{x} - I_{z}) \dot{ϕ} \dot{ψ} I_{y}^{- 1} + δ_{θ}, \\ right \ddot{ψ} & left = U_{ψ} I_{z}^{} \end{matrix}

…”

Section: Applicationmentioning

confidence: 99%

“…The reference trajectories in X and Y are defined as circular path whereas altitude Z is forced to be constant ( Z ref =1 m ), and ψ ref =0. The initial values are defined as

{[X (0) Y (0) Z (0) ϕ (0) θ (0) ψ (0)]}^{T} = {[0 1.5 0 0.5 0.5 0.5]}^{T} .

In order to demonstrate the robustness properties of the proposed algorithm, the following external disturbances have been introduced:

\begin{matrix} alignleft \\ align-1 δ_{X} & align-2 = \sin (t), δ_{Y} = \cos (t), δ_{Z} = 0.5 \sin (0.5 t) \cos (0.5 t), \\ align-1 δ_{ϕ} & align-2 = 0.5 \sin (0.5 t), δ_{θ} = 0.5 \cos (0.5 t), δ_{ψ} = 0.5 \cos (0.5 t) \sin (0.5 t) . \end{matrix}

One supposes that the state measurement is affected by a white noise with a standard deviation equal to 0.0001 and a sampling time equal to 0.001 s …”

Section: Applicationmentioning

confidence: 99%

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A simplified version of adaptive super‐twisting control

Gutierrez

León-Morales

Plestan

et al. 2019

Intl J Robust & Nonlinear

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show abstract

“…The dynamic model of a quadcopter has been reported in many related studies [56][57][58][59][60][61][62][63][64][65][66][67]. In this section, the mathematic model is briefly presented.…”

Section: Mathematic Model Of a Quadcoptermentioning

confidence: 99%

Nonlinear Control for Autonomous Trajectory Tracking while Considering Collision Avoidance of UAVs Based on Geometric Relations

2019

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Trajectory tracking with collision avoidance for a multicopter is solved based on geometrical relations. In this paper, a new method is proposed for a multicopter to move from the start position to a desired destination and track a pre-planned trajectory, while avoiding collisions with obstacles. The controller consists of two parts: First, a tracking control is introduced based on the errors between the relative position of the multicopter and the reference path. Second, once the obstacles with a high possibility of collision are detected, a boundary sphere/cylinder of the obstacle is generated by the dimensions of the vehicle and the obstacles, so as to define the safety and risk areas. Afterwards, from the relation between the vehicle’s motion direction, and the tangential lines from the vehicle’s current position to the sphere/cylinder of the obstacle, a collision detection angle is computed to decide the fastest direction to take in order to avoid a collision. The obstacle/collision avoidance control is activated locally when an object is close, and null if the vehicle moves away from the obstacles. The velocity control law and the guidance law are obtained from the Lyapunov stability. In addition, a proportional controller is used at the end of vehicle’s journey to ensure the vehicle stops at the target position. A numerical simulation in different scenarios was performed to prove the effectiveness of the proposed algorithm.

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“…The algorithm can also be extended to a general class of unstructured disturbances. In [12], an adaptive SMC method based on an adaptive law to estimate the unknown parameters of UAVs for stabilizing and tracking control of the vehicles is introduced. Although the procedure of designing controllers is very obvious, it is not easy to achieve the satisfactory controller gains.…”

Section: Related Workmentioning

confidence: 99%

Robust Dynamic Sliding Mode Control-Based PID–Super Twisting Algorithm and Disturbance Observer for Second-Order Nonlinear Systems: Application to UAVs

Thanh

Hong

2019

Electronics

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This paper introduces a robust dynamic sliding mode control algorithm using a nonlinear disturbance observer for system dynamics. The proposed method is applied to provide a rapid adaptation and strictly robust performance for the attitude and altitude control of unmanned aerial vehicles (UAVs). The procedure of the proposed method consists of two stages. First, a nonlinear disturbance observer is applied to estimate the exogenous perturbation. Second, a robust dynamic sliding mode controller integrated with the estimated values of disturbances is presented by a combination of a proportional–integral–derivative (PID) sliding surface and super twisting technique to compensate for the effect of these perturbations on the system. In addition, the stability of a control system is established by Lyapunov theory. A numerical simulation was performed and compared to recently alternative methods. An excellent tracking performance and superior stability of the attitude and altitude control of UAVs, exhibiting a fast response, good adaptation, and no chattering effect in the simulation results proved the robustness and effectiveness of the proposed method.

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Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties

Cited by 293 publications

References 78 publications

A simplified version of adaptive super‐twisting control

A simplified version of adaptive super‐twisting control

Nonlinear Control for Autonomous Trajectory Tracking while Considering Collision Avoidance of UAVs Based on Geometric Relations

Robust Dynamic Sliding Mode Control-Based PID–Super Twisting Algorithm and Disturbance Observer for Second-Order Nonlinear Systems: Application to UAVs

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