Double-pendulum Overhead Cranes Research Articles

Artificial Intelligence based LQR and PID Controller Design of 3 Degree of Freedom System

In this study, the position control of a 3 DoF underactuated system is carried out. The developed approach is tested on a double pendulum overhead crane. Considering the nonlinear dynamics of the system, its mathematical model is first obtained by Euler-Lagrange model. Then, since PID and LQR controllers are used in the simulations, the nonlinear model is linearized around the equilibrium point of the system. Using the linear model, the parameters of LQR and PID controllers are tuned by Artificial Bee Colony Algorithm. In the optimization process, the Integral Time Absolute Error function is chosen from traditional fitness functions to minimize the error in each single-degree-of-freedom joint of the system. Additionally, to ensure the precise movement of the car, the objective function is improved in a way to include unit step response characteristics. The control performance is evaluated in the simulations. The results are presented in tables and graphs. The proposed approach can be used to control multi-degree of freedom underactuated systems.

Finite-time plant-parameter-free trajectory tracking control for overhead cranes with double-pendulum dynamics and uncertain disturbances

In this paper, a novel finite-time plant-parameter-free trajectory tracking control method, along with a finite-time disturbance estimator, is developed for the overhead crane system with double-pendulum dynamics and uncertain disturbances. Compared with existing works for the double-pendulum overhead crane system, the proposed control scheme possesses three remarkable advantages: free of any plant parameters, finite-time trajectory tracking, and uncertain disturbance rejection. Specifically, the dynamic equation of the double-pendulum overhead crane system is transformed into a new form by introducing auxiliary signals. Then, a finite-time disturbance estimator is constructed based on the transformed dynamic equation, and a corresponding finite-time trajectory tracking control scheme is proposed for the double-pendulum overhead crane system. The stability of the closed-loop system is given through rigorous theoretical proof. Finally, numerical simulation results are provided to demonstrate the effectiveness of the presented control scheme.

Oscillation Control of a Double-Pendulum Overhead Crane Using Positive and Negative Input Shaping Techniques

A double-pendulum overhead crane system exhibits significant nonlinearity and is classified as an under-actuated system, making control more complex. This study focuses on designing a robust shaper to effectively mitigate oscillations in such systems. Two robust shapers, which are Zero Vibration Derivative (ZVD) and Negative Equal-Magnitude (NEM), are considered. These are obtained by convolving two input shapers that are designed based on the hook and payload oscillation frequencies. Matlab simulations are utilized to evaluate the performance of the shapers, using a nonlinear dynamic model of the crane to assess their effectiveness. Simulation results show that the ZVD shaper has a better performance in oscillation reduction, with 81% and 76% reductions for the hook and payload oscillations, respectively. In addition, the ZVD provides the lowest mean average error by achieving 87% and 83% reductions in the hook and payload as compared to the case with an unshaped input. However, the NEM shaper provides less delay in the trolley response.

Finite-time distributed state and disturbance estimation for LTI systems with disturbance: a PEBO-based approach

For a class of linear time-invariant (LTI) systems with disturbance, the finite-time distributed estimation problem of both system state and disturbance was investigated. First, observability decomposition is performed to transform the original system into a cascaded one that is composed of multiple subsystems, and the system disturbance is modelled as the output of an external system. Second, the first substate and external system state are augmented into a new state, and the explicit relationships between state and unknown parameters are established by applying global filtering transformation. Subsequently, the DREM-based parameter estimator and parameter estimation-based observer are developed to simultaneously estimate the first substate and disturbance in finite time. Then, under a unidirectional communication mechanism between adjacent nodes, the subsequent nodes can obtain the estimates of disturbance and substates of all precursor subsystems and only need to estimate the state of current subsystem. Finally, the effectiveness of the proposed methods is illustrated by a numerical example and double-pendulum overhead crane system.

Control of a Multimode Double-Pendulum Overhead Crane System Using Input Shaping Controllers

This paper investigates the impact of higher derivative input shaping for minimizing both oscillations, namely hook and payload of a multimode double-pendulum overhead crane (MDPOC) system. The MDPOC has greater nonlinearities and stronger internal couplings, especially when involving two oscillation frequencies with multimode dynamic effects. With a suitable system’s natural frequency and damping ratio of the hook and payload oscillations, multimode zero-vibration (ZV-ZV), multimode zero-vibration derivative (ZVD-ZVD) and multimode zero-vibration derivative-derivative (ZVDD-ZVDD) shapers are successfully designed. More interestingly, two scenarios under a fixed cable length and a payload hoisting are considered which are closer to the real practical crane. Thus, an average travel length (ATL)-based shaper method is also considered to further verify the effectiveness and robustness of efficient hook and payload oscillation control under payload hoisting. All the multimode input shaping is simulated using the Matlab software. The simulation results of multimode ZVDD-ZVDD shaper successfully reduced in the overall hook and payload oscillations by 97.9% and 97.2%, respectively, compared to the unshaped system, whereas the multimode ATL-ZVDD shaper reduced hook and payload oscillations by 94.8% and 94.0%, respectively. In fact, the multimode ZVDD-ZVDD and multimode ATL-ZVDD shapers demonstrate the superiority in minimizing the hook and payload oscillations compared to the multimode ZV-ZV, multimode ZVD-ZVD, ATL-ZV and ATL-ZVD shapers. This significant reduction in oscillations enhances the precision and safety of real-world crane operations in industrial settings. It has been proven that considering the additional derivative of input shaping results in a higher level of hook and payload oscillations reduction.

Neural network–based adaptive sliding mode control of three-dimensional double-pendulum overhead cranes with prescribed performance

In order to tackle the uncertainties encountered in the operation of three-dimensional (3D) overhead crane systems and enhance the overall robustness of the control system, an adaptive sliding mode control (SMC) method based on prescribed performance is proposed in this work. Specifically, an integral sliding mode controller (ISMC) based on prescribed performance is designed for the 3D overhead crane dynamics model with double-pendulum effect, which is used to constrict system error. By considering the case of model uncertainty, time-varying parameters, track friction, and so on, the neural network (NN) is employed to estimate unknown terms in the controller design, and the Lyapunov function is applied to analyze the stability of the close-loop system. The results demonstrated that the proposed method can effectively improve the positioning accuracy and payload swing suppression performance of the overhead crane system, and also improve the robustness of the control system to deal with uncertainties.

Adaptive coupled double-pendulum overhead crane control strategy with enhanced attitude suppression under initial input constraints

Adaptive coupled double-pendulum overhead crane control strategy with enhanced attitude suppression under initial input constraints

Modelling and dynamic characterisation of a double-pendulum overhead crane carrying a distributed-mass payload

Modelling and dynamic characterisation of a double-pendulum overhead crane carrying a distributed-mass payload

Research on adaptive coupling trajectory tracking anti-swing control strategy for three-dimensional double-pendulum overhead crane

In the transportation process of a three-dimensional double-pendulum overhead crane, the system is significantly influenced by the pronounced coupling introduced by the double-pendulum effect, posing a considerable challenge for the development of effective anti-swing control strategies. Moreover, uncertainties in certain system parameters and errors in trolley positioning contribute to the complexity of anti-swing control strategy design. To address these practical issues, a control strategy is proposed: First, an S-shaped transport trajectory with minimal positioning error is introduced, incorporating more system parameters into the coupling signal design to enhance system coupling. Based on this, an error-coupled trajectory signal is introduced. Second, the error-coupled trajectory signal is integrated into the energy function, and leveraging adaptive principles, an adaptive coupled trajectory tracking anti-swing control strategy is proposed to estimate uncertain system parameters online. Subsequently, the asymptotic stability of the equilibrium point of the closed-loop system is verified using the Lyapunov techniques and the Barbalat lemma. Finally, through simulations and experiments, it is demonstrated that the proposed control strategy not only ensures precise positioning of the trolley and bridge but also effectively suppresses oscillations of the hook and load, exhibiting excellent control performance. Even in scenarios where system parameters undergo changes or external disturbances are introduced, the proposed control strategy exhibits strong robustness and holds significant practical potential.

Distributed delay adaptive output-based command shaping for different cable lengths of double-pendulum overhead cranes

Distributed delay adaptive output-based command shaping for different cable lengths of double-pendulum overhead cranes

Control of a Double-Pendulum Overhead Crane System Based on Hierarchical Sliding Mode Control Techniques

The double-pendulum overhead crane system belongs to a class of underactuated mechanical systems, which is challenging to control due to its strong nonlinearities. This study deals with the nonlinear controller design for a double-pendulum overhead crane based on hierarchical sliding mode control with state-dependent switching gain. The equivalent and switching controls are obtained with the aid of first-level and second-level sliding surfaces. The asymptotic stability of sliding surfaces is proved theoretically and also shown graphically. Numerical simulations show that the proposed controller performs better than conventional hierarchical sliding mode control. The proposed controller effectively suppresses the load and hook swing and precisely controls the trolley’s displacement. It has strong robustness to the payload displacement and the change of the crane parameters.

Robust Control Method Design for Underactuated Double-Pendulum Overhead Cranes

Overhead travelling cranes are infrastructure for building construction and their main purpose is to ensure accurate and rapid transport of goods to a given location in the shortest possible time without any residual oscillation. The overhead crane is also a typical underdrive method, which has fewer inputs than the amount being controlled. In some practical applications, uneven weight and f-loads on the hook can lead to load and hook oscillations and the bridge crane can develop the so-called double-pendulum properties. This leads to a high degree of coupling and a high degree of non-linearity between the various state variables of the crane system. The study that follows suggests a new energy-coupled control strategy for an underactuated double-pendulum overhead crane with initial control force constraints. Strong robustness and superior control performance to parameter changes and external disturbances are the proposed controller’s noticeable characteristics. To ensure the smooth start of the trolley, a robust control adds the hyperbolic tangent function to the control procedure. In addition, the stability analysis and stability verification of the control system is given by using the LaSalle’s invariance principle and Lyapunov techniques. The simulation results show that the new energy coupling control method has stability and strong robustness under various conditions such as different rope lengths, load quality, target position and external disturbance when the initial control force decreases.

Design and Real-time Implementation of a Distributed-Delay Input Shaper for Sway Control of a Double-Pendulum Overhead Crane

Design and Real-time Implementation of a Distributed-Delay Input Shaper for Sway Control of a Double-Pendulum Overhead Crane

Design and real-time implementation of a distributed-delay input shaper for sway control of a double-pendulum overhead crane

Design and real-time implementation of a distributed-delay input shaper for sway control of a double-pendulum overhead crane

Motion Trajectory Tracking and Sway Reduction for Double-Pendulum Overhead Cranes Using Improved Adaptive Control Without Velocity Feedback

The dynamic characteristics of 3-D overhead cranes with double-pendulum effect are complex, which makes the controller design particularly challenging. Besides, in actual conditions, external disturbances cause interference to the system, and the model parameters are uncertain, which further increase the difficulty of controller design. In order to improve the control performance, two composite displacement signals are constructed to increase the coupling relationship of state vectors, and then new error signals and a total mechanicallike energy function are derived. Based on the new energy function, an adaptive control method with enhanced swing suppression is derived. Furthermore, considering the costs of sensors, the velocity signals cannot be obtained directly in many cases of practical application. Hence, auxiliary functions are constructed to replace the velocity feedback signals, and then an improved adaptive tracking control strategy is proposed. Theoretical analysis and experimental results prove that the proposed method can fulfill the control task. Its control result is significantly better than that of the comparison methods. Meanwhile, the experimental results in three different scenarios verify the strong robustness of this method.

A novel hybrid of Nonlinear Sine Cosine Algorithm and Safe Experimentation Dynamics for model order reduction

ABSTRACT The current study introduces the hybridization of the Nonlinear Sine Cosine Algorithm (NSCA) and Safe Experimentation Dynamics (SED) as a novel optimization method for model order reduction of high-order single-input single-output (SISO) systems. Reciprocated synergism between both meta-heuristic algorithms is achieved by appropriating the nonlinear position-updated mechanism of NSCA for enhanced exploration/exploitation competencies and proficiency of SED in maximizing stagnation avoidance within the local optima. Named the NSCA-SED algorithm, the applicability of the proposed method is assessed by scholastic adoption of a sixth-order numerical transfer function towards two independent high-order systems enclosing Double-Pendulum Overhead Crane and Flexible Manipulator. Experimentation results further suggested NSCA-SED as the superior alternative in terms of execution robustness and consistency excellence against other available optimization-based methods for tackling model order reduction. Exemplified simulations sequentially demonstrated considerable improvements by the employment of NSCA-SED over conventional SCA following respective enhanced proportions of 97.17%, 13.17% and 29.03% for Example 1, Example 2 and Example 3.

Trolley regulation and swing reduction of underactuated double-pendulum overhead cranes using fuzzy adaptive nonlinear control

Trolley regulation and swing reduction of underactuated double-pendulum overhead cranes using fuzzy adaptive nonlinear control

Partial state feedback sliding mode control for double-pendulum overhead cranes with unknown disturbances

In this paper, a novel sliding mode controller which requires partial state feedback is proposed for double-pendulum overhead cranes subject to unknown payload parameters and unknown external disturbances. Firstly, it is theoretically proved that the hook and payload tend to their respective equilibrium points concurrently. Secondly, a decoupling transformation is performed on the original nonlinear dynamics of double-pendulum overhead cranes. The novel sliding mode controller that does not require the prior information and motion signals of the payload is designed based on the decoupled nonlinear dynamics. Then, the asymptotic stability of the equilibrium point of double-pendulum overhead cranes is proved by rigorous analysis. Finally, several simulations are conducted to validate the effectiveness and robustness of the proposed controller.

Frequency-Modulation Input-Shaping Strategy for Double-Pendulum Overhead Cranes Undergoing Simultaneous Hoist and Travel Maneuvers

Large payloads hoisted by overhead cranes exhibit the same behavior as that of a double pendulum. Changes in the hoisting cable length during payload transfer maneuvers gives rise to time-dependent system frequencies rendering input-shaped commands ineffective. In this paper, a frequency-modulation input-shaping strategy that enables simultaneous hoist and travel maneuvers using single-mode input-shaping is presented. This strategy utilizes model-based feedback and partial feedback linearization techniques. Simulations are carried out using arbitrary travel and hoist commands combined with the common single-mode zero-vibration (ZV) and zero-vibration-derivative (ZVD) input-shapers. Sensitivity analysis reveals robust performance in the presence of high system uncertainties.

Linear Active Disturbance Rejection Control for Double-Pendulum Overhead Cranes

Because of the complexity, non-linearity, and under-actuated features of double pendulum overhead cranes, a control method based on linear active disturbance rejection control (LADRC) and differential flatness theory is proposed to realize accurate trolley positioning and effective swing eliminating. Specifically, in order to simplify the system model, we introduce the differential flatness theory to construct system output. Based on this method, the uncertainty and system external disturbance become total disturbance. The control method of the crane is designed according to LADRC. Then, we use the bird swarm algorithm (BSA) to optimize controller’s parameters. Finally, the double-pendulum crane control method based on the LADRC can better accomplish the crane’s anti-swing and location in the real environment according to simulation and experimental results, which confirms its effectiveness and robustness in existing system.