Robust adaptive constrained boundary control for a suspension cable system of a helicopter

Ren, Yong; Shi, Peng

doi:10.1002/acs.2826

Cited by 22 publications

(14 citation statements)

References 47 publications

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“…Moreover, considering

T false(z, 0 false) : = T false(z false)

, thus, it has

T false(L false) = m_{p} g + \int_{0}^{L} μ false(z false) d z g

in the vertical direction, where

m_{p}

and g are the mass of payload and the gravitational acceleration, respectively,

μ false(z false)

is the non‐uniform mass per unit length of the suspension cable. Moreover, from [37–39], the translational equation of the helicopter motion with a hanging load can be described as

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \dot{y} (t) & = υ (t), \\ m_{h} \dot{υ} (t) & = - T (L) s^{'} (L, t) - 2 ρ (L) [s^{'} (L, t)]^{3} + u (t) \\ + d (t) - c_{h} υ (t) \end{matrix}

where

- T false(L false) s^{'} false(L, t false) - 2 ρ false(L false) false[s^{'} false(L, t false) false]^{3}

is the tension force exerted on the helicopter in the horizontal direction from the suspension cable.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Invoking (2), considering

s false(L, t false) = y false(t false)

, according to first‐order Taylor series expansion [40], the model for the suspension cable system can be described by [37]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ μ (z) \ddot{s} (z, t) & = T^{'} (z, t) s^{'} (z, t) + T (z, t) s^{″} (z, t) \\ + ρ^{'} (z) [s^{'} (z, t)]^{3} + 3 ρ (z) [s^{'} (z, t)]^{2} s^{″} (z, t) \\ - c \dot{s} (z, t) + f (z, t) \end{matrix}

for

\forall z \in false(0, L false)

and

t \in false[0, \infty false)

, under the boundary conditions of the suspension cable system can be described by

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ m_{h} \ddot{s} (L, t) & = - T (L) s^{'} (L, t) - 2 ρ (L) [s^{'} (L, t)]^{3} + u... \end{matrix}

…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

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Unilateral boundary control for a suspension cable system of a helicopter with horizontal motion

Ren

Liu

2019

IET Control Theory & Applications

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“…Moreover, considering

T false(z, 0 false) : = T false(z false)

, thus, it has

T false(L false) = m_{p} g + \int_{0}^{L} μ false(z false) d z g

in the vertical direction, where

m_{p}

and g are the mass of payload and the gravitational acceleration, respectively,

μ false(z false)

is the non‐uniform mass per unit length of the suspension cable. Moreover, from [37–39], the translational equation of the helicopter motion with a hanging load can be described as

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \dot{y} (t) & = υ (t), \\ m_{h} \dot{υ} (t) & = - T (L) s^{'} (L, t) - 2 ρ (L) [s^{'} (L, t)]^{3} + u (t) \\ + d (t) - c_{h} υ (t) \end{matrix}

where

- T false(L false) s^{'} false(L, t false) - 2 ρ false(L false) false[s^{'} false(L, t false) false]^{3}

is the tension force exerted on the helicopter in the horizontal direction from the suspension cable.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Invoking (2), considering

s false(L, t false) = y false(t false)

, according to first‐order Taylor series expansion [40], the model for the suspension cable system can be described by [37]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ μ (z) \ddot{s} (z, t) & = T^{'} (z, t) s^{'} (z, t) + T (z, t) s^{″} (z, t) \\ + ρ^{'} (z) [s^{'} (z, t)]^{3} + 3 ρ (z) [s^{'} (z, t)]^{2} s^{″} (z, t) \\ - c \dot{s} (z, t) + f (z, t) \end{matrix}

for

\forall z \in false(0, L false)

and

t \in false[0, \infty false)

, under the boundary conditions of the suspension cable system can be described by

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ m_{h} \ddot{s} (L, t) & = - T (L) s^{'} (L, t) - 2 ρ (L) [s^{'} (L, t)]^{3} + u... \end{matrix}

…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Unilateral boundary control for a suspension cable system of a helicopter with horizontal motion

Ren

Liu

2019

IET Control Theory & Applications

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“…Assumption 3 [3]: For the error u(t) between designed control input ν(t) and actual control input u(t), the following conclusion holds:…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…1) Different from the existed results, the vibration reduction and trajectory tracking control problems are investigated by employing backstepping strategy for a suspension cable system of a helicopter. 2) Different from the article [3], [6], [7], [42], an unilateral adaptive boundary control method is adopted to stabilize the closed-loop system. The unilateral control is more easy to implement than bilateral control which has been used in [3], [6], [7], [42].…”

Section: Introductionmentioning

confidence: 99%

“…2) Different from the article [3], [6], [7], [42], an unilateral adaptive boundary control method is adopted to stabilize the closed-loop system. The unilateral control is more easy to implement than bilateral control which has been used in [3], [6], [7], [42]. 3) A numerical simulation is developed to verify that the proposed control scheme in this paper is superior to the proportional-differential (PD) control and the introduced control strategy in [5].…”

Section: Introductionmentioning

confidence: 99%

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Boundary Control for a Suspension Cable System of a Helicopter With Saturation Nonlinearity Using Backstepping Approach

Ren

Song

et al. 2019

IEEE Access

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In this paper, the problems of vibration reduction and trajectory tracking are investigated for a suspension cable system of a helicopter in the presence of input saturation and external disturbances. First, an auxiliary system is proposed to compensate for the error between control input and actuator output which is caused by input saturation. Then, based on the introduced auxiliary system, an adaptive boundary control scheme is proposed to track a desired trajectory and restrain the vibration by using backstepping method. Under the designed control scheme, the uniform ultimate boundedness of closed-loop system is guaranteed. Moreover, the vibration amplitude and the trajectory tracking error will be guaranteed to converge ultimately to a small neighborhood of zero by selecting suitable parameters. The rationality and validity of designed control law is verified by a numerical simulation.

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Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

Aghababa

2018

Adaptive Control & Signal

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SummarySince the introduction of fractional‐order differential equations, there has been much research interest in synthesis and control of oscillatory, periodic, and chaotic fractional‐order dynamical systems. Therefore, in this article, the problem of stabilization and control of nonlinear three‐dimensional perturbed fractional nonlinear systems is considered. The major novelty of this article is handling partially unknown dynamics of nonlinear fractional‐order systems, as well as coping with input saturation along the existence of model variations and high‐frequency sensor noises via just one control input. The method supposes no known knowledge on the upper bounds of the uncertainties and perturbations. It is assumed that the working region of the input saturation function is also unknown. After the introduction of a simple finite‐time stable nonlinear sliding manifold, an adaptive control technique is used to reach the system variables to the sliding surface. Rigorous stability discussions are adopted to prove the convergence of the developed sliding mode controller. The findings of this research are illustrated using providing computer simulations for the control problem of the chaotic unified system and the fractional Chua's circuit model.

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Robust adaptive constrained boundary control for a suspension cable system of a helicopter

Cited by 22 publications

References 47 publications

Unilateral boundary control for a suspension cable system of a helicopter with horizontal motion

Unilateral boundary control for a suspension cable system of a helicopter with horizontal motion

Boundary Control for a Suspension Cable System of a Helicopter With Saturation Nonlinearity Using Backstepping Approach

Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

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