Partial feedback linearization control for 3-D underactuated overhead crane systems

Wu, Xianqing; He, Xiongxiong

doi:10.1016/j.isatra.2016.06.015

Cited by 72 publications

(38 citation statements)

References 45 publications

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“…External disturbances are imposed as follows: (i) to simulate the possible collision between of payload and obstacles, impulse disturbances (with an amplitude of 2° to θ x and 2° to θ y ) are imposed at t = 2 seconds; (ii) to simulate the possible influence of wind, continuous random disturbances with amplitudes of 1° are imposed between 15 seconds and 17 seconds. In addition, the partial feedback linearization (PFL) controller (the control gains are fully tuned and chosen as k a = 1, k ε = 1, k θ = 0.5) developed in the work of Wu and He is taken for comparison. Profiles of state variables and control variables are given in Figure and Figure , respectively.…”

Section: Simulation Results and Analysismentioning

confidence: 99%

“…Profiles of state variables, including (A) x , (B) y , (C) θ x , and (D) θ y (blue solid line in (A) and (B): reference trajectory; red dash line: results obtained by the proposed MPC controller; green dotted line: results obtained by the PFL controller in the work of Wu and He). MPC, model predictive control; PFL, partial feedback linearization [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Simulation Results and Analysismentioning

confidence: 99%

“…In Figure B, x and y represent the displacements of the trolley and the girder along the X‐axis and Y‐axis, respectively; θ x and θ y describe the position of the payload; the rope is considered to be massless and its length is l ; m g , m t , and m p are the masses of the girder, the trolley, and the payload, respectively; and u x and u y are the control forces applied to the trolley and the girder, respectively. By selecting the generalized coordination as q = [ x , y , θ x , θ y ] T , the dynamic equations of the 3D overhead crane can be derived using the Lagrange's method as follows:

bold-scriptM ((), q) \overset{q}{true} + bold-scriptV ((),, q, \dot{boldq}) \overset{q}{true} + bold-scriptG ((), q) = bold-scriptF,

where

bold-scriptM false(boldq false) \in R^{4 \times 4}

is the inertia matrix;

bold-scriptV ((),, q, \dot{boldq}) \in ℝ^{4 \times 4}

represents the centripetal‐Coriolis matrix;

bold-scriptG ((), q) \in ℝ^{4}

is the gravity vector; and

bold-scriptF \in R^{4}

represents the control vector, which can be expressed explicitly as

scriptM = ([], \begin{array}{c} m_{p} + m_{t} & 0 & m_{p} {l C}_{x} C_{y} & - m_{p} {l S}_{x} S_{y} \\ 0 & m_{p} + m_{t} + m_{g} & 0 & m_{p} {l C}_{y} \\ m_{p} {l C}_{x} C_{y} & 0 & ... \end{array})

…”

Section: Problem Formulationmentioning

confidence: 99%

“…In Figure 1B, x and y represent the displacements of the trolley and the girder along the X-axis and Y-axis, respectively; x and y describe the position of the payload; the rope is considered to be massless and its length is l; m g , m t , and m p are the masses of the girder, the trolley, and the payload, respectively; and u x and u y are the control forces applied to the trolley and the girder, respectively. By selecting the generalized coordination as q = [x, y, x , y ] T , the dynamic equations of the 3D overhead crane can be derived using the Lagrange's method as follows 34 :…”

Section: System Dynamics Of 3d Overhead Cranesmentioning

confidence: 99%

“…Hence, most of the state‐of‐the‐art control methods for overhead cranes are regulation control methods. In fact, the regulation control can be seen as a special kind of trajectory tracking control where the reference trajectory is selected as the desired final position . However, trajectory tracking control has its own merits: (i) the corresponding control inputs can be obtained when the reference trajectory is generated; therefore, operators can evaluate the safety of actuators before the transferring mission; (ii) for missions to be operated in an environment where obstacles exist, a feasible collision‐free reference trajectory can be generated in advance; comparing to detecting and avoiding obstacles in the online regulation control method, tracking the reference trajectory by a trajectory tracking controller is more appealing for its online computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

Wang

Liu

Zhang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.

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Section: Simulation Results and Analysismentioning

confidence: 99%

Section: Simulation Results and Analysismentioning

confidence: 99%

bold-scriptM ((), q) \overset{q}{true} + bold-scriptV ((),, q, \dot{boldq}) \overset{q}{true} + bold-scriptG ((), q) = bold-scriptF,

where

bold-scriptM false(boldq false) \in R^{4 \times 4}

is the inertia matrix;

bold-scriptV ((),, q, \dot{boldq}) \in ℝ^{4 \times 4}

represents the centripetal‐Coriolis matrix;

bold-scriptG ((), q) \in ℝ^{4}

is the gravity vector; and

bold-scriptF \in R^{4}

represents the control vector, which can be expressed explicitly as

scriptM = ([], \begin{array}{c} m_{p} + m_{t} & 0 & m_{p} {l C}_{x} C_{y} & - m_{p} {l S}_{x} S_{y} \\ 0 & m_{p} + m_{t} + m_{g} & 0 & m_{p} {l C}_{y} \\ m_{p} {l C}_{x} C_{y} & 0 & ... \end{array})

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: System Dynamics Of 3d Overhead Cranesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

Wang

Liu

Zhang

et al. 2019

Intl J Robust & Nonlinear

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Adaptive neural network hierarchical sliding mode control for six degrees of freedom overhead crane

Kim

Nguyen

Manh

et al. 2022

Asian Journal of Control

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This paper presents an effective control method for three-dimensional (3D) overhead cranes with six degrees of freedom (DOF). Two payload swings and an axial payload oscillation should be minimized besides driving the bridge, trolley, and hoisting drum to bring the payload to the desired position in space. First, a novel 3D-6DOF crane model is developed, where the sixth degree of freedom is axial cargo oscillation that has never been considered in previous studies. A controller is then designed using the hierarchical sliding mode control method. Moreover, a radial basis function neural network (RBFNN) is used to approximate the system's unknown dynamic model accurately. According to the Lyapunov principle, a control law and an updated law for the neural network's weight matrices are designed to ensure the stability of the closed-loop system. Simulation results on Matlab software show the proposed approach's effectiveness, such as smaller swing, minor axial oscillation, and precise position as desired.

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Nonlinear coordination control of offshore boom cranes with bounded control inputs

Fang

Sun

2018

Intl J Robust & Nonlinear

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Offshore cranes are complicated underactuated systems, which work in harsh sea conditions. Due to the various severe disturbances, the control of offshore cranes has always been a great challenge, which is made even more complicated when considering some practical issues such as actuator saturation and coordination. Until now, few results have been published in the literature on this topic. To address this problem, an efficient nonlinear control method is proposed for offshore boom cranes suffering from both ship roll and heave motion in this paper, which takes full consideration of actuator saturation, as well as the coordination problem between actuators. Furthermore, regarding the various extra nonvanishing disturbances, such as winds, frictions, and unmodeled dynamics, a disturbance observer is designed to estimate and eliminate these uncertainties. The asymptotic stability of the desired equilibrium point is rigorously guaranteed by Lyapunov techniques and LaSalle's invariance theorem. Finally, extensive hardware experimental tests are carried out to demonstrate the feasibility and efficiency of the proposed method. To the best of our knowledge, this paper proposes the first method that considers the saturation and coordination problem for offshore cranes while guaranteeing the asymptotic stability of the desired equilibrium point.

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Partial feedback linearization control for 3-D underactuated overhead crane systems

Cited by 72 publications

References 45 publications

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

Adaptive neural network hierarchical sliding mode control for six degrees of freedom overhead crane

Nonlinear coordination control of offshore boom cranes with bounded control inputs

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