Model Of Overhead Crane Research Articles

Robust Trajectory Tracking Control of a Differentially Flat Overhead Crane Using Sliding Mode

The control of overhead cranes is a benchmark problem, since it is an underactuated mechanism and its mathematical model is nonlinear. During operation the mass of the load is unknown, representing an uncertainty in the inertial parameters, which requires robustness of the controlled system. Our paper proposes a novel robust control method, that combines the differentially flat property of the dynamics with the robustness of the sliding mode control. The sliding surface is constructed to ensure the tracking of the configuration variables whose accelerations is calculated using the flatness property of the dynamic model. This formulation also allows achieving the matching conditions of the parameter uncertainties. Considering a simplified overhead crane model where the load motion is restricted in a vertical plane, two sliding surfaces are defined for the rope angle and rope length, since the cart position can be calculated from the previous two. The suggested control method is successfully validated in simulations as well as using a reduced-size overhead crane. For the real crane, the rope angle was estimated by utilizing the dynamical model, which uses the estimated cart acceleration.

Passivity and underactuated modeling-based load energy coupling control for three-dimensional overhead crane systems

The conventional control strategies and methods with the three-dimensional model of overhead crane system are excessively dependent on model parameters and lead to the controllers design complex on position and anti-swing of overhead crane systems. With analysis on the coupling relationship among various state variables of overhead crane, the three-dimensional dynamic model of overhead crane based on mechanical virtual displacement and Lagrangian equation is constructed. A novel control strategy based on load energy coupling is designed to realize system positioning and eliminate the problem of residual load swing. The passivity of the three-dimensional overhead crane system is judged, and the energy composition of the system is deduced. The energy coupling function based on load displacement and swing angle is built. The control strategy of three-dimensional overhead crane system based on load energy coupling is designed by the Lyapunov stability theory and function construction method. The stability of the system is verified by the Lasalle invariance principle. With the experimental and programming, the proposed method is compared with different control methods. The results show that this method can realize the accurate positioning of the trolley more quickly and restrain the load swing more effectively.

Settling Time Optimization of a Critically Damped System with Input Shaping for Vibration Suppression Control

The input shaping technique is widely used as feedforward control for vibration suppression of flexible dynamic systems. The main disadvantage of the input shaping technique is the increasing system time response since the input shaper contains time delay parts. However, with the same reference input, the actuator effort in the case of using an input shaper is smaller than the one in the case without an input shaper. Thus, it is possible to decrease the system response time by designing the feedback controller to maximize the actuator effort. This paper proposes a design approach to design the Proportional-Derivative (PD) controller for position control of the actuator so that the settling time of the flexible system with input shaper is minimized. The actuator system with a PD controller is equivalent to a critically damped system, and the condition for the controller gains is established. In addition, the settling time and actuator effort with shaped step input are calculated. The controller gains can be determined by solving the settling time optimization problem with the actuator effort constraint. The effectiveness of the proposed approach is verified via experiments with an overhead crane model.

Study of adaptive control law of overhead crane using its model

Nowadays, cargo cranes are widely used in various areas of industries. Many of cranes use suspended load fastening, which is associated with load swinging during transportation. Load swinging is most often caused by acceleration or deceleration of the crane trolley, less often it occurs due to external disturbances, such as wind. One of the key directions of the development of this kind of cranes is the development of an automated control system that can dampen pendular oscillations of the load. At present, a considerable number of control systems have been developed, but most of them require preset adjustment of specific parameters of the transported load. The task of this study is to develop and debug a control algorithm using a model of an overhead crane of previously developed adaptive control law that can provide fine positioning and damping of load oscillations under the current parametric uncertainty. The study using the pilot plant will allow us to determine and analyze the features of the implementation of the control law before its application for industrial cranes. An adaptive control law is studied using the model of overhead crane under conditions of a current parametric uncertainty of the load and external disturbances. This control method is based on an adaptive control approach with an identifier and an implicit reference model using “simplified” adaptation conditions. A previously developed adaptive control law for an overhead crane is described. An experimental model of an overhead crane is described. An algorithm for adaptive control of an overhead crane model has been developed. The first experimental studies of the proposed control method have been carried out. They confirm its performance in real conditions. The results of experimental tests have shown the effectiveness of the adaptive control law. The system ensures fine motion of the load in a short period of time, dampens the pendular oscillations of the load during acceleration and deceleration of the trolley, as well as during external disturbances. The adaptive control law allows you to move the load to the designated position and dampen the pendular oscillations with minimal preset adjustment of the control system. Since the identification of parameters occurs at the current time, the changes of the parameters of the load and the length of suspension do not affect the quality of control.

New results on sampled‐data output‐feedback control of linear parameter‐varying systems

AbstractThis article presents a novel sampled‐data static output‐feedback control technique for continuous‐time linear parameter‐varying (LPV) systems. Particularly, the input‐delay approach is introduced to map the sample‐and‐hold dynamics into the continuous‐time domain with delay in the states. This, together with a new parameter‐dependent Lyapunov–Krasovskii functional, results in a bounded real lemma for the underlying closed‐loop LPV systems. Furthermore, application of convex optimization techniques transforms the controller synthesis problem into the feasibility of a group of parameterized matrix inequalities. It is also shown that the convexification procedures allow for controller dependence on time‐varying parameters. Simulation studies are conducted on a case comparison and an overhead crane model to validate the efficacy and less conservatism of the result.

Robust motion trajectory optimization of overhead cranes based on polynomial chaos expansion

In this paper, we present a polynomial chaos-based framework for the trajectory optimization of an overhead crane system under uncertainty. The main research described in this paper is as follows. First, the deterministic trajectory optimization problem formulation of a two-dimensional overhead crane model is constructed. Based on this basic mathematical formulation, the uncertainty trajectory optimization problem is formed considering the uncertainty of initial state and system parameter. Then, to solve the uncertainty trajectory optimization problem efficiently, a robust trajectory optimization problem formulation is proposed. However, it is difficult to solve the robust trajectory optimization problem directly because it contains stochastic function terms, such as stochastic dynamic equations, constraint functions and objective functions. We consider both the system state and control input as functions of uncertainty and use polynomial chaos expansion to quantify these stochastic functions. An augmented deterministic trajectory optimization problem which can be solved directly is finally obtained. Based on the proposed robust trajectory optimization formation, the motion trajectory optimization of an overhead crane system under two different uncertainty types of is solved. All simulation results are compared with traditional sampling-based Monte Carlo simulations to demonstrate the feasibility and effectiveness of the proposed method.

A software tool to make primary school students aware of control systems

In this paper we present a simple software tool, designed as a game, that can be used to make (especially primary) school students aware of the importance of control systems. An overhead crane model is used as an effective dynamic system to show the difficulty of applying manual control in some contexts and how a control system can help to achieve the required performance. In addition to the technical details of the tool, which has been developed in Matlab, the overall experience with the students is explained in the paper and some preliminary results of its use with people without expertise in control are discussed.

Design and implementation of finite time sliding mode controller for fuzzy overhead crane system

This paper considers the problem of fuzzy overhead crane system modelling and finite-time stability/boundedness via sliding mode control (SMC) method. Due to the strong coupling of control input, the fuzzy technique is utilized to linearize the overhead crane system and a fuzzy overhead crane model is established with appropriate membership functions. Considering the bad effect, including the swing of hook and plates, the external disturbances of the friction and air resistances, is inevitable during the transportation of copper electrode plates, the SMC method is adopted to stabilize the fuzzy system and robust to these interference signals. Furthermore, taking the time cost of actual industry into account, the finite-time stability/boundedness is introduced to achieve the state of system could be stable in a specified finite time. Moreover, the reaching law of sliding mode dynamics is analysed and the sufficient conditions for finite-time stability/boundedness of system state are formulated, respectively. Finally, the simulation results of the control strategy put forward in this article with the comparisons on some existing algorithms are provided to verify the effectiveness of the control strategy in the copper electrolytic overhead crane system.

Modeling of overloads of raising mechanism in metallurgical overhead cranes

Electromechanical processes occurring when the load is lifted by an overhead crane are considered. The main idea of the work is to identify emergency mode (crane overload) by a method based on control of stator current of lift motor. To obtain stator current diagrams of electric motor, mathematical model of overhead crane (three-mass circuit) has been developed, which includes equations describing elastic properties of crane beams and its rope. A system of (α, β) coordinates, fixed relative to electric motor stator, is adopted to describe the drive asynchronous motor. Lifting cycle is considered as sequence of three steps: choice of the rope “slack”; rope tension; separation of cargo lifting. For each stage, a system of differential equations has been compiled describing motion of masses of overhead crane elements and electrical parameters of electric motor. Initial and boundary conditions for each of the stages were determined. Preliminary transformations of the system of equations to their solution by numerical methods and subsequent modeling of stages of lifting loads were carried out for different weights. Sequential solution of three boundary value problems allows obtaining values of stator currents at time of load separation. Diagrams of stator phase currents of an electric motor were obtained for loads of different mass. Simulation results indicate the presence of fixable difference in magnitudes of stator currents after the load is separated from the support surface. On basis of the developed model and the study results, a functional diagram of crane overload protection device is proposed and its principle of operation is described. It consists in controlling lifted load mass and stator current when liftingthe load. Conclusion is made about feasibility and effectiveness of monitoring electrical values of lifting motor for development of overhead crane protection against overloads. Effectiveness of the proposed system was evaluated.

An Input Shaping Control Scheme with Application on Overhead Cranes

Abstract A new optimization technique is developed to generate a step-input acceleration function for an input shaping harmonic system. This approach is integrated into an overhead crane model for a rest-to-rest maneuver with standard and nonstandard maneuver settings. The proposed method guarantees the satisfaction of the system constraints and desired final conditions, while it minimizes the system sensitivity to crane cable-length variations. The minimal system sensitivity is achieved through an optimization algorithm that provides zero vibration and a minimum integral of system sensitivity over a continuous range of crane cable length. Numerical simulations are conducted to demonstrate the feasibility of the proposed shaper in eliminating the residual vibration at the end of a programmed maneuver. Sensitivity analyses are also performed to verify the robustness of the new shaper. In comparison to the previous shapers, the new methodology is significantly less sensitive and can effectively handle different arbitrary maneuver times.

Takagi-Sugeno Fuzzy Modeling and PSO-Based Robust LQR Anti-Swing Control for Overhead Crane

The dynamic model of overhead crane is highly nonlinear and uncertain. In this paper, Takagi-Sugeno (T-S) fuzzy modeling and PSO-based robust linear quadratic regulator (LQR) are proposed for anti-swing and positioning control of the system. First, on the basis of sector nonlinear theory, the two T-S fuzzy models are established by using the virtual control variables and approximate method. Then, considering the uncertainty of the model, robust LQR controllers with parallel distributed compensation (PDC) structure are designed. The feedback gain matrices are obtained by transforming the stability and robustness of the system into linear matrix inequalities (LMIs) problem. In addition, particle swarm optimization (PSO) algorithm is used to overcome the blindness of LQR weight matrix selection in the design process. The proposed control methods are simple, feasible, and robust. Finally, the numeral simulations are carried out to prove the effectiveness of the methods.

Funnel control for overhead crane model

AbstractWe consider an overhead crane whose control variables are the length of the rope and force/velocity at the gantry. The output consists of the position of the load. The objective is to design a closed‐loop tracking controller which also takes into account the transient behavior. First we show that this system has no well‐defined relative degree, which unfortunately does not allow to apply established methods for adaptive control to achieve the objective. To circumvent this problem, we design a dynamic state feedback which results in a system with relative degree four. Thereafter, we apply a funnel controller to this feedback system. We show that our approach can be used to move loads from one to another given position in the situation where there are several obstacles which have to be circumnavigated.

Stabilization and Riesz basis property for an overhead crane model with feedback in velocity and rotating velocity

This paper studies a variant of an overhead crane model's problem, with a control force in velocity and rotating velocity on the platform. We obtain under certain conditions the well-posedness and the strong stabilization of the closed-loop system. We then analyze the spectrum of the system. Using a method due to Shkalikov, we prove the existence of a sequence of generalized eigenvectors of the system, which forms a Riesz basis for the state energy Hilbert space.

Frequency-Modulation Input Shaping Control of Double-Pendulum Overhead Cranes

Traditionally, multimode input shaping controllers are tuned to systems' frequencies. This work suggests an alternative approach. A frequency-modulation (FM) input shaping technique is developed to tune the resonant frequencies of a system to a set of frequencies that can be eliminated by a single-mode primary input shaper. Most of the current input shaping techniques can be used as primary input shapers for the FM input shaping technique. Virtual feedback is used to modulate the closed-loop frequencies of a simulated double-pendulum model of an overhead crane to the point where the closed-loop second mode frequency becomes an odd-multiple of the closed-loop first mode frequency, which is the necessary condition for a satisfactory performance of most single-mode input shapers. The primary input shaper is based on the first mode frequency of the closed-loop system model. The input commands to the plant of the virtual feedback system are then used to drive the physical double-pendulum. Simulations results, using primary zero-vibration (ZV) and zero-vibration-derivative (ZVD) input shapers, are presented. The performance is validated experimentally on a scaled model of a double-pendulum overhead crane.

Optimum controller design of an overhead crane: Monte Carlo versus pre-filter-based designs

In this paper, we consider an overhead crane model with some of its parameters known within given upper and lower bounds. It is shown that a controller with single valued gains based on the nominal values of the parameters could lead to unsatisfactory performance. Two design methodologies are applied to guarantee the desired performance of the considered overhead crane model and their results are compared. The first method utilizes the Monte Carlo approach to find optimum values of the controller gains based on minimizing a least-square error function representing the deviation of the swing angle from a desired trajectory. The second method uses a pre-filter to ensure that the closed-loop performance lies within two given desired responses. Simulation results are provided to compare the performance of the two methods where both show reasonable responses. The Monte Carlo-based approach, however, does not require additional hardware components, compared with the pre-filter technique.

Modeling of an Underactuated Nonlinear Double-Container Overhead Crane

Compared with a traditional single-container overhead crane, the double-container overhead crane is a type of new efficient container stevedoring machinery, however, it is actually a complicated nonlinear system. In this brief, both the kinematic and dynamic characteristics concerning the double-container crane are investigated, and then an accurate dynamic model of the underactuated double-container overhead crane is established by utilizing Euler-Lagrange's method. Not only is the variation of the rope and payloads, but also some uncertainties such as mechanical frictions and air-resistance in the environment are taken into account in modeling. Simulation results show the validity of the established double-container overhead crane model.

비정합 불확실성을 갖는 시스템을 위한 적응 슬라이딩 모드 제어기 설계

초록·키워드 목차 오류제보하기 본 논문에서는 불확실한 다변수 시스템을 위한 적응 슬라이딩 모드 제어기의 LMI 기반 설계방법이 제시된다. LMI를 사용하여 슬라이딩 평면의 존재조건을 구한다. 그리고 외란의 놈 경계치를 추정하고 안정성을 보장할 적응 스위칭 궤환 제어기 알고리즘을 제시한다. 마지막으로 제안된 방법의 유효성을 보이기 위해 크레인 모델을 제어하기 위한 설계 예를 제시한다. #Linear Matrix Inequality(Lmi) #Adaptive Control #Sliding Mode #Polytopic Model 요약Abstract1. 서론2. 문제 설정3. 주요 결과4. 수치적인 예5. 결론References저자소개

Concept Of Decomposition And Aggregation Method With Application: Part II

This paper describes the application of Decomposition and Aggregation method to a model of a practical system so as to analyse its effectiveness. A computer programme (Fortran) have been developed to evaluate and simulate specific parameter of the model. By evaluating the model through simulation the stable condition of the model can be obtained. The procedure for analysing the stability of this system is also shown in detail. The model used in this paper is the overhead crane model and it will be used as an example in understanding the analysis performed by the prescribed method.

Time‐optimal control of an overhead crane model

AbstractTime‐optimal solutions for a simple crane model have been arrived at by a number of authors using expensive analogue methods. The method described in this paper also gives time‐optimal solutions but these can be obtained using a very simple microprocessor. These solutions are obtained quickly and inexpensively and thus can be used for comparison with other suboptimal solutions based on more complex and less idealized models. An extension of the method is also outlined which covers certain variants of the simple model.