Payload Swing Research Articles

Exponential stabilization of flexural sway vibration of gantry crane via boundary control method

This paper aims to develop a boundary control solution for complicated gantry crane coupled motions. In addition to the large angle sway motion, the crane cable has a flexural transverse vibration. The Hamilton principle has been utilized to derive the governing partial differential equations of motion. The control objectives which are sought include: moving the payload to the desired position; reducing the payload swing with large sway angle; and finally suppressing the cable transverse vibrations in the presence of boundary disturbances simultaneously. These simultaneous boundary control objectives make the problem challenging. The proposed control approach is based on the original nonlinear hybrid partial differential equation–ordinary differential equation model without any simplifications of sway motion nonlinearities, coupling effects, and the effect of gravitational force. Using the Lyapunov method, a boundary control law has been designed which guarantees the exponential stability and uniform boundedness of the closed-loop system. In order to demonstrate the effectiveness of the proposed control method, numerical simulation results are provided by applying the finite difference method.

Payload twisting dynamics and oscillation suppression of tower cranes during slewing motions

Challenging and dangerous material-handling applications in construction have motivated the study of the dynamics and control of tower cranes. Manipulating tower cranes is difficult while moving large-size payloads because of the inevitable payload swing and twisting about the cables. Although significant work has been directed at reducing the swing of point-mass loads, much less effort has been directed at limiting the payload twisting. A nonlinear dynamic model of tower cranes carrying distributed-mass beams is described. Furthermore, an open-loop control method is proposed to reduce both the swing and twisting of the payloads during slewing motions. Simulations and experiments demonstrate the theoretical dynamic behavior of the model and validate the effectiveness of the proposed control method.

An Online Trajectory Planning Approach for a Quadrotor UAV With a Slung Payload

In this article, a novel online antiswing trajectory planning approach is proposed for a quadrotor slung-load system, which is an underacuated, strong coupling, and nonlinear system so that it is difficult to achieve the quadrotor's precise positioning and the payload's swing suppression simultaneously. The proposed trajectory planning approach is efficient and convenient without iterative optimizations. Specially, the proposed trajectory planning strategy is composed of two parts: a target positioning part and an antiswing part. The convergence of the quadrotor's positioning and payload's swing suppression is proved by Lyapunov-based analysis. Experimental results show that the proposed trajectory has achieved satisfied control performance.

Efficient swing control of an overhead crane with simultaneous payload hoisting and external disturbances

Abstract The effects of time varying parameters and external disturbances on a flexible system may badly degrade the control performance resulting in excessive induced vibrations/oscillations. For an overhead crane, the oscillation can be even worse when both factors occur simultaneously. This paper proposes a novel swing control approach for an underactuated overhead crane having payload hoisting and external disturbance simultaneously. The proposed scheme is designed based on a predictive unity magnitude shaper and an adaptive feedback control which efficiently suppress payload swing to handle both effects. Furthermore, the control parameters can be updated online in real time to progressively suppress the payload swing. To evaluate the effectiveness of the proposed method, experiments are carried out with a simultaneous payload hoisting and external disturbances including a non-zero initial condition, persistent disturbance (wind) and instant disturbance. The developed controller achieves higher robustness under all testing conditions with significant swing reductions of at least 45% and 69% in the overall and residual swing responses, respectively over a comparative control method. It is envisaged that the proposed method can be very beneficial as an anti-swing controller for various cranes under the influence of disturbance and hoisting simultaneously.

Adaptive Output-Feedback Control for Dual Overhead Crane System With Enhanced Anti-Swing Performance

In industrial practice, to improve transportation capability, there has been increasing applications for dual overhead crane systems (DOCSs). Compared with single overhead crane systems (SOCSs), DOCSs are more dangerous and difficult for human operators to manipulate due to their extremely complex system dynamics. Furthermore, more people, usually not less than three, are required to guarantee the safety of a typical transportation process of DOCS, which is not only of low efficiency but also causes a waste of human resources. Due to the above facts, it is concluded that automation of DOCS has great practical significance. To promote this process, a high-performance nonlinear controller is proposed in this article, which can better suppress the payload swing due to the incorporation of more swing-related information. Besides, only position signals are required for feedback, which is more practical for industrial application. Another highlight of the proposed method lies in the fact that it can well conquer the payload mass uncertainty with an adaption law, so that many corresponding adverse effects are eliminated. The performance of the proposed method is not only theoretically proved by rigorous mathematical analysis, but also validated with convincing hardware experiments.

Adaptive Nonlinear Hierarchical Control for a Rotorcraft Transporting a Cable-Suspended Payload

Rotorcrafts, with satisfactory maneuver performance and ability under complex terrains unreachable for ground robots, are playing important roles for goods transportation. In this article, we focus on the control of the cable-suspended transportation way due to its lower costs and more agility of the rotorcraft's rotational motion. Compared with traditional crane systems and single rotorcrafts without loads, the aerial transportation system presents “double” underactuated property, stronger system nonlinearity, and more complex dynamic coupling, which are huge challenges for control schemes design. Meanwhile, aerial transportation usually suffers from external disturbances and uncertainties presented with aerodynamic damping coefficients and rope length. Additionally, overshoots of the rotorcraft's position are potential threats for flight safety, especially in confined and complex environments. To address these problems, a novel adaptive control scheme is designed, which ensures effective rotorcraft positioning and payload swing suppression with restricted overshoot amplitudes. Asymptotic results are obtained with rigorous theoretical derivations provided by the Lyapunov-based stability analysis and LaSalle's invariance theorem. Real-time experiments are performed to validate the effectiveness of the proposed control scheme even in the presence of external disturbances. To the best of our knowledge, this is the first method designed for aerial transportation systems which achieves simultaneous rotorcraft positioning and swing suppression, together with insurance for overshoot restriction even in the presence of parametric uncertainties.

A family of anti-swing motion controllers for 2D-cranes with load hoisting/lowering

Abstract This paper presents a methodology for designing controllers that attenuate the payload swing angle in two-dimensional overhead crane systems with varying rope length. The proposed scheme is based on the proper construction of a design function, which combines the coordinate of the translational motion of the crane with that corresponding to the swing angle. The proposed methodology shows how to design a family of functions that can be used not only to attenuate the swing angle but also to follow a desired motion. Then, the controller is implemented in combination with a trajectory design stage based on S-curves. The proposed scheme is compared with a controller with a proportional derivative structure and an adaptive controller. Numerical and experimental results validate the proposed methodology and show the effectiveness of the proposed controller even when the system is being affected by state estimation errors and external disturbances.

Adaptive Anti-Swing and Positioning Control for 4-DOF Rotary Cranes Subject to Uncertain/Unknown Parameters With Hardware Experiments

Among various large-scale mechanical equipments, a rotary crane is one of the most practical hoisting machineries utilized in factories and docks. However, the inaccurate measurement of friction coefficients and the requirement of accurate gravity-related compensation may inevitably increase the difficulty for controlling such systems. For most existing control methods, the exact model knowledge is required; otherwise, positioning errors would unavoidably appear, which brings many limitations for their practical applications. To deal with these problems, in this paper, a novel adaptive control approach is suggested, in which a novel update law is designed to achieve accurate identifications of unknown parameters as well as exact compensation of the gravity-related lumped term. Moreover, the payload can be transported to its specified location precisely via the boom’s rotation with effective payload swing suppression. Specifically, without linearizing the nonlinear dynamic model of the rotary crane system, the state variables are ensured to be asymptotically convergent to the equilibrium point, which is proven strictly in theory by utilizing Lyapunov techniques and LaSalle’s invariance principle. Finally, experimental results indicate the effectiveness and practicability of the proposed approach.

An Enhanced Coupling PD with Sliding Mode Control Method for Underactuated Double-pendulum Overhead Crane Systems

An enhanced coupling PD with sliding mode control method, called ECPD-SMC in short, is presented for double-pendulum overhead crane systems in this paper. The proposed method replaces the PD controller with the equivalent part of traditional SMC method, without any system parameters. The ECPD-SMC algorithm is composed of PD control part and the SMC control part. The SMC part is utilized for constructing the frame of a controller, providing strong robustness with uncertain model, different system parameters, and external disturbances. The PD control part is used to stabilize the control system. Moreover, the coupling behavior between the trolley movement and the payload swing is enhanced, and hence, leads to an improved control performance. As shown by Lyapunov techniques and Schur complement, the proposed ECPD-SMC guarantees asymptotic result even in the presence of uncertainties, including model, system parameters, and various disturbances. Some simulation results are included to demonstrate the correctness and superior control performance of the designed controller.

Neural Network-Based Adaptive Antiswing Control of an Underactuated Ship-Mounted Crane With Roll Motions and Input Dead Zones.

As a type of indispensable oceanic transportation tools, ship-mounted crane systems are widely employed to transport cargoes and containers on vessels due to their extraordinary flexibility. However, various working requirements and the oceanic environment may cause some uncertain and unfavorable factors for ship-mounted crane control. In particular, to accomplish different control tasks, some plant parameters (e.g., boom lengths, payload masses, and so on) frequently change; hence, most existing model-based controllers cannot ensure satisfactory control performance any longer. For example, inaccurate gravity compensation may result in positioning errors. Additionally, due to ship roll motions caused by sea waves, residual payload swing generally exists, which may result in safety risks in practice. To solve the above-mentioned issues, this paper designs a neural network-based adaptive control method that can provide effective control for both actuated and unactuated state variables based on the original nonlinear ship-mounted crane dynamics without any linearizing operations. In particular, the proposed update law availably compensates parameter/structure uncertainties for ship-mounted crane systems. Based on a 2-D sliding surface, the boom and rope can arrive at their preset positions in finite time, and the payload swing can be completely suppressed. Furthermore, the problem of nonlinear input dead zones is also taken into account. The stability of the equilibrium point of all state variables in ship-mounted crane systems is theoretically proven by a rigorous Lyapunov-based analysis. The hardware experimental results verify the practicability and robustness of the presented control approach.

Model-independent PD-SMC method with payload swing suppression for 3D overhead crane systems

Abstract A model-independent control method, called proportional-derivative with sliding mode control method or PD-SMC in short, is designed for 3D overhead crane systems, where external disturbances, unmodeled and parametric uncertainties are present, to achieve simultaneous trolley positioning and payload swing suppression. One great benefit of the designed controller is its model-independent feature that can avoid requiring exact model knowledge. The proposed control method has the advantages of both simple structure of the PD control method and strong robustness of the SMC method. The PD control is utilized to stabilize the nominal model and the SMC is utilized to provide the robustness and to compensate the uncertainty and external disturbance of the controlled overhead crane systems. Moreover, to enhance the control performance of payload swing suppression and elimination, one additional term is introduced to the designed controller. Lyapunov techniques and Schur complement are utilized to analyze the asymptotically stable of the closed-loop system. Experimental results are illustrated to validate the effective and robustness of the new proposed control law.

Motion Trajectory-Based Transportation Control for 3-D Boom Cranes: Analysis, Design, and Experiments

Boom crane systems with high practicality, the control problems of which are more complex than those of most other underactuated systems due to their strongly nonlinear dynamical coupling characteristics, are widely applied in various places. In addition to the basic control objectives of accurate boom positioning and payload swing suppression, another challenging aspect is how to improve the transient performance of the state variables while ensuring time (sub)optimality during transportation. In this paper, to address the two aforementioned issues, i.e., complicated nonlinear dynamics and ensuring transient performance, a new nonlinear time suboptimal trajectory planning approach, which does not require linearizing the original nonlinear dynamics, is proposed to achieve efficient control results for the boom crane system. After performing an in-depth analysis, we find a transformation relationship between four tip signals and the state variables. Then, by planning proper trajectories for the tip signals based on the original nonlinear boom crane dynamics, we obtain swing-free time suboptimal trajectories for the boom pitch and yaw movements; hence, the boom can reach its destination accurately, and the payload swing can be suppressed. Moreover, the state variables can be restricted within specified ranges as required. The presented trajectory planner can be considered as the first solution for generating trajectories for the boom crane system, respecting various state constraints without the need for any linearization operations. Finally, some hardware experiments are introduced to verify the effectiveness of the presented control strategy.

Dynamic Feedback Antiswing Control of Shipboard Cranes Without Velocity Measurement: Theory and Hardware Experiments

As a class of typical representatives for conveyance, shipboard crane systems are usually fixed on ship decks to transport cargoes on the sea, which is greatly different from land-fixed cranes. Due to some disturbances induced by sea waves, payload positions are always difficult to control precisely. In addition, unless equipped with velocity sensors, it would be difficult to obtain velocity signals for feedback control, by noting that the traditional way of numerical differentiation operations (to recover velocities from positions/angles) may induce extra noises in practice. In this paper, we propose an observer-based dynamic feedback control method to deal with the foregoing issues. Specifically, both boom/rope positioning and payload swing elimination can be achieved simultaneously by utilizing only measurable displacement/angle feedback signals. Moreover, as far as we know, this paper gives the first input-saturated control method including nonlinear coupling terms to realize the objective of effective positioning and swing suppression without the requirement of velocity feedback, which is developed on the basis of the complicated nonlinear shipboard crane dynamics with no linearization operations during controller design or stability analysis. Meanwhile, the corresponding velocity signals are accurately recovered online by means of the suggested observer. In addition, the amplitudes of the control inputs can be guaranteed within the allowable ranges to avoid falling into saturation. The asymptotic stability for the equilibrium point of the crane system in closed loop with the controller and the observer is proven by rigorous analysis with Lyapunov techniques and LaSalle's invariance theorem. After a series of hardware experiments, we validate the effectiveness and robustness of the presented controller.

Swing angle estimation for multicopter slung load applications

A filtering technique based on a set of recursive equations is analyzed and applied to swing angle estimation for multicopter slung load applications. Starting from the equations of motion of the coupled slung load system, an observation model is derived to autonomously measure the swing angle by means of the data available from the onboard IMU, without the need to rely on extra sensors. Provided the multicopter is subject to known control inputs, data-fusion is performed through a Fading Gaussian Deterministic approach, whose theoretical background was recently investigated by the author. In particular, the algorithm is based on a two-step set of equations derived from the minimization of a cost function where earlier data are progressively de-weighted by a fading factor, making the estimation less prone to problem unknowns. The validity of the approach is investigated by means of numerical simulations, where a tuning criterion is shown to provide the fading factor that best dampens the modeling errors with respect to the measurement noise. Estimated swing angles are then used in a sample feedback control application with the aim to simultaneously perform trajectory tracking and payload swing damping.

Fractional-order fast terminal back-stepping sliding mode control of crawler cranes

Crawler crane is an under-actuated system whose five outputs are tracked by only two actuators. Crawler crane also comprises complex dynamic model with nonlinear kinematic constraints while suffering from strong wind and uncertainties. This study proposes a robust control system for crawler cranes by combining five techniques: fractional-order differential, back-stepping, sliding mode control, finite-time Lyapunov stability, and Mittag–Leffler theory. The proposed control approach is investigated by simulating on a practical Manitowoc® crane. Results reveal that the controller works well, that is, crane tracks boom and payload to destinations while keeping payload swing small during operation. However, the locally tiny oscillations of boom and payload remain due to handling cable elasticity.

Energy-Based Nonlinear Adaptive Control Design for the Quadrotor UAV System With a Suspended Payload

In this paper, the control problem for an underactuated quadrotor unmanned aerial vehicle (UAV) with a suspended payload is investigated. An energy-based nonlinear controller is proposed that is able to control the quadrotor UAV's position and the payload's swing angle asymptotically. An adaptive control design is developed to compensate for the unknown length of the cable which is used to connect the UAV and the payload. The Lyapunov-based stability analysis is employed together to prove the stability of the closed-loop system. Detailed real-time experimental results illustrate the good performance of the proposed controller.

Tracking control design for a multi-degree underactuated flexible-cable overhead crane system with large swing angle based on singular perturbation method and an energy-shaping technique

A flexible-cable overhead crane system having large swing is studied as a multi-degree underactuated system. To resolve the system dynamics complexities, a second order singular perturbation (SP) formulation is developed to divide the crane dynamics into two one-degree underactuated fast and slow subsystems. Then, a control system is designed based on the two-time scale control (TTSC) method to: (a) transfer the payload to a desired location and decrease the payload swing, by a nonlinear controller for slow dynamics; and (b) suppress transverse vibrations of the cable, by a linear controller for fast dynamics. The nonlinear controller is designed based on an energy shaping technique according to the controlled Lagrangian method. To demonstrate the control system effectiveness, an example of the flexible cable crane systems with a lightweight payload is considered to perform simulations. In addition to the proposed control system, two other controllers; namely, a linear controller based on the linear–quadratic regulator method and a TTSC based on the approximate SP model and partial feedback linearization, are applied to the system for comparison. Also, by applying a disturbance force to the trolley and considering 10% uncertainty in crane parameters, the control performance against disturbances and parameter uncertainties is investigated.

Distributed-mass payload dynamics and control of dual cranes undergoing planar motions

Abstract Unwanted oscillations caused by the operator-commanded motions lower the capable operating speeds and degrade the safety of dual cranes moving distributed-mass payloads. Mounting numbers of works have been devoted to the dynamics and control of dual cranes. However, few studies have been dedicated to the accurate estimation of natural frequency, which is a critical factor for controlling the dual cranes. This paper develops a new method to predict the natural frequency of dual planar cranes with different cable lengths. Furthermore, a modified extra-insensitive (MEI) input shaper is proposed to suppress the oscillations of the payload swing and pitch in the dual cranes. The MEI shaper has good robustness to large changes in the frequency, and has good performance in the jerk limitation. Simulated and experimental investigations are performed on small-scale dual cranes transporting a slender beam to validate the system dynamic behavior and the effectiveness of the MEI shaper.

Explicit GPC Control Applied to an Approximated Linearized Crane System

This paper proposes a MIMO Explicit Generalized Predictive Control (EGPC) for minimizing payload oscillation of a Gantry Crane System subject to input and output constraints. In order to control the crane system efficiently, the traditional GPC formulation, based on online Quadratic Programming (QP), is rewritten as a multiparametric quadratic programming problem (mp-QP). An explicit Piecewise Affine (PWA) control law is obtained and holds the same performance as online QP. To test effectiveness, the proposed method is compared with two GPC formulations: one that handle constraints (CGPC) and another that does not handle constraints (UGPC). Results show that both EGPC and CGPC have better performance, reducing the payload swing when compared to UGPC. Also both EGPC and CGPC are able to control the system without constraint violation. When comparing EGPC to CGPC, the first is able to calculate (during time step) the control action faster than the second. The simulations prove that the overall performance of EGPC is superior to the other used formulations.

A Novel Energy-Coupling-Based Hierarchical Control Approach for Unmanned Quadrotor Transportation Systems

Cable-suspended transportation is an important way of transferring goods and materials by rotorcraft in complex and hazardous environments, where external disturbances, system uncertainties, and, especially, the underactuated characteristic bring great challenges to realize safe and smooth deliveries. In terms of the aforementioned problems, this paper presents an enhanced coupling hierarchical control scheme for both quadrotor positioning and payload swing elimination. By exploiting the cascade property of quadrotor transportation systems, we can design controllers for the inner loop and the outer one separately, provided that the growth restriction condition is well satisfied, which greatly simplifies the design procedure. As the outer loop describes the quadrotor translation and payload swing motion, our central work focuses on the controller design of this subsystem. Specifically, a generalized payload signal is introduced to increase the state coupling, based on which we construct a novel energy storage function. Consequently, an energy coupling control law is proposed, which ensures that the equilibrium point of the system is asymptotically stable by using Lyapunov techniques and LaSalle's invariance theorem. Experimental results are presented to illustrate the superior control performance, even in the presence of external disturbances and parameter uncertainties.