Double-pendulum Effect Research Articles

Novel Adaptive Hierarchical Sliding Mode Control for Trajectory Tracking and Load Sway Rejection in Double-Pendulum Overhead Cranes

Overhead cranes with double-pendulum effect seem more practical than those with single-pendulum effect. However, in this case, the dynamic performance analysis and the controller design become more difficult. Moreover, achieving both high-precision trajectory tracking and load sway rejection is a more significant issue for crane systems. For these purposes, the nonlinear dynamics of an overhead crane with double-pendulum effect is derived for the controller design. Then, a novel adaptive hierarchical sliding mode controller is presented. Unlike a traditional approach, the proposed one can make fixed sliding mode surface active to search the state trajectories. Such an adaptive design can make the states of the system to enter the desired sliding surface as soon as possible and, at the same time, can also improve the cart tracking precision. The Lyapunov technique and LaSalle's principle are employed to confirm the stability of the whole system. The experimental results validate that the proposed method has superior control performance and robustness with respect to parameter variations.

Decoupled linear model and S-shaped curve motion trajectory for load sway reduction control in overhead cranes with double-pendulum effect

Overhead cranes with double-pendulum effect seem more practical than those with single-pendulum effect. However, in this case, it is difficult to find an applicable controller for such systems. Hence, a linearized and decoupled double-pendulum overhead crane dynamic model is derived by adopting a disturbance observer and modal analysis technique. The S-shaped trajectory is planned by solving algebraic equations, and the stability of the system is confirmed by the Routh–Hurwitz stability theory. Experimental results and simulations demonstrate the effectiveness of the proposed method. It could be realized to operate the crane accurately without sensor systems for measuring load sways by using the proposed method.

Novel robust controller design for load sway reduction in double-pendulum overhead cranes

It is seen that when the hook mass is larger than the load mass or the load has distributed mass property, the load sway of the crane system presents as double-pendulum effect. In this situation, crane system has two different natural frequencies so that the sway characteristic becomes more complex and greatly increases the difficulty of the dynamic performance analysis and controller design. Moreover, the rope length changes significantly affect the stability and control performance of the crane system. In order to solve the aforementioned problems, the linear dynamics of a two-dimensional overhead crane with double-pendulum effect is derived based on a disturbance observer, and is decoupled for controller design by modal analysis. Next, a state feedback controller is presented to achieve robust control performance for a given range of rope length changes. The controller gains are obtained via linear matrix inequality optimization method. Finally, numerical simulations and experimental results validate that the proposed method has superior control performance.

Nonlinear Antiswing Control for Crane Systems With Double-Pendulum Swing Effects and Uncertain Parameters: Design and Experiments

In practical applications, industrial cranes may exhibit double-pendulum swing effects, due to many factors, such as large payload scales and non-negligible hook masses. Currently, for double-pendulum cranes, most available methods are open-loop controllers designed based on linearized crane dynamics; even for existing closed-loop approaches, they are also mostly developed using linearized dynamics and require the exact knowledge of system parameters, which makes them sensitive to parametric uncertainties. To handle these issues, we present an adaptive antiswing control strategy for crane systems with double-pendulum swing effects and uncertain/unknown parameters, which can make the trolley accurately reach the target position with reduced overshoots and effectively eliminate the double-pendulum swing angles at the same time. A complete stability analysis, based upon the full nonlinear dynamics (i.e., without linearizing the dynamics), is included to support the theoretical derivations. We present hardware experimental results to demonstrate that the proposed controller achieves better performance than existing ones and exhibits good robustness. Note to Practitioners —This paper is motivated by the issue of controlling a crane system when double-pendulum swing effects are excited and present. The double-pendulum effects can happen in many practical scenarios and make the crane manual operation very challenging. Moreover, most existing crane control approaches are developed based upon single-pendulum crane models and they may not work normally in the presence of the double-pendulum phenomenon. In addition, usually, the model parameters, including rope length and trolley/hook/payload masses, are not exactly known in practice, which may badly degrade the performance of the control approaches requiring exact model knowledge. Toward this end, we suggest a new control method for cranes suffering from double-pendulum effects to achieve satisfactory performance. The presented control method is robust against parametric uncertainties and it can suppress the double-pendulum swing, reduce the trolley overshoots, and improve the efficiency. Preliminary physical experiments carried out on a double-pendulum crane hardware test bed indicate the effectiveness of the proposed method. In our future work, we will apply the suggested control approach to industrial crane systems to improve their working efficiency.

Amplitude-Saturated Nonlinear Output Feedback Antiswing Control for Underactuated Cranes With Double-Pendulum Cargo Dynamics

When modeling cranes, the hook and the suspended cargo are usually regarded roughly as one mass point for simplicity, i.e., the cargo swing is modeled as that of a single pendulum. However, in practice, when the hook mass is nonnegligible or the cargo has a large size, the crane always exhibits double-pendulum swing dynamics, which is much more complicated and makes most existing control methods unapplicable. In addition, all existing closed-loop controllers for (double-pendulum) cranes require full state feedback, while velocities are unavailable in most cases. Moreover, they need to linearize the nonlinear crane model and cannot respect the actuator's practical saturation constraint, which may probably lead to actuator saturation and badly degrade the control performance (even unstable). In response to these practical issues, we suggest a novel amplitude-saturated output feedback (OFB) control approach for underactuated crane systems exhibiting double-pendulum effects. We provide explicit Lyapunov-based analysis to rigorously prove that the equilibrium point of the closed-loop system is almost globally asymptotically stable, without any approximation to the original nonlinear dynamics. As far as we know, this paper presents the first closed-loop control method that can achieve control for an underactuated double-pendulum crane with merely OFB and theoretically-guaranteed saturated control efforts. Hardware experimental results demonstrate the superior performance of the proposed approach over existing methods and its strong robustness as well.

Adaptive tracking control for double-pendulum overhead cranes subject to tracking error limitation, parametric uncertainties and external disturbances

In a practical application, overhead cranes are usually subjected to system parameter uncertainties, such as uncertain payload masses, cable lengths, frictions, and external disturbances, such as air resistance. Most existing crane control methods treat the payload swing as that of a single-pendulum. However, certain types of payloads and hoisting mechanisms result in double-pendulum dynamics. The double-pendulum effects will make most existing crane control methods fail to work normally. Therefore, an adaptive tracking controller for double-pendulum overhead cranes subject to parametric uncertainties and external disturbances is developed in this paper. The proposed adaptive tracking control method guarantees that the trolley tracking error is always within a prior set of boundary conditions and converges to zero rapidly. The asymptotic stability of the closed-loop system׳s equilibrium point is assured by Lyapunov techniques and Barbalat׳s Lemma. Simulation results show that the proposed adaptive tracking control method is robust with respect to system parametric uncertainties and external disturbances.

Performance studies of human operators driving double-pendulum bridge cranes

Oscillation of crane payloads makes it challenging to manipulate payloads quickly, accurately, and safely. The problem is compounded when the payload creates a double-pendulum effect. This paper evaluates an input-shaping control method for reducing double-pendulum oscillations. Human operator performance testing on a 10-ton industrial bridge crane is used to verify the effectiveness and robustness of the method. Fifty operators drove the crane with a standard control pendent, as well as a wireless touchscreen interface. Data from these experiments show that human operators drive the crane much faster and safer with the input-shaping control scheme. Furthermore, considerably less operator effort is required when input shaping is used to limit the oscillation. Additional tests required the operators to drive the crane numerous times over a period of eight days. These experiments show that significant learning occurred when operators did not have the aid of input shaping. However, the performance never approached that achieved by untrained operators using input shaping.

Dynamics and Control of Bridge Cranes Transporting Distributed-Mass Payloads

The large-amplitude and lightly-damped oscillation of crane payloads is detrimental to safe and efficient operation. The problem is further complicated when the payload creates a double-pendulum effect. Previous researches have shown that single-mode oscillations can be greatly reduced by properly shaping the inputs to the crane motors. This paper builds on previous developments by thoroughly describing the double-pendulum dynamic effects as a function of payload parameters and the crane configuration. Furthermore, an input-shaping control method is developed to suppress double-pendulum oscillations created by a payload with distributed-mass properties. Experiments performed on a 10-ton industrial bridge crane verify the effectiveness of the method. A critical aspect of the testing was human operator studies, wherein numerous operators utilized the input-shaping controller to perform manipulation tasks. The performance improvements provided by the input-shaping controller, as well as operator learning effects, are reported.

Input Shaping Control of Double-Pendulum Bridge Crane Oscillations

Large amplitude oscillation of crane payloads is detrimental to safe and efficient operation. Under certain conditions, the problem is compounded when the payload creates a double-pendulum effect. Most crane control research to date has focused on single-pendulum dynamics. Several researchers have shown that single-mode oscillations can be greatly reduced by properly shaping the inputs to the crane motors. This paper builds on those previous developments to create a method for suppressing double-pendulum payload oscillations. The input shaping controller is designed to have robustness to changes in the two operating frequencies. Experiments performed on a portable bridge crane are used to verify the effectiveness of this method and the robustness of the input shaper.