Flatness‑Based Control in Successive Loops of an H‑Type Gantry Crane with Dual PMLSM

Purpose In this article, the feedback control and stabilization problem of dual PMLSM-driven H-type gantry cranes is treated with the use of a fatness-based control method which is implemented in successive loops. Dual-drive gantry cranes can achieve high torque and high precision in the tasks’ execution. Such a type of crane can be used in several industrial applications. The solution to the associated nonlinear control problem is a particularly challenging research objective. Methods The integrated system that comprises the H-type gantry crane and two PMLSMs is shown to be diferentially fat. The control problem for this robotic system is solved with the use of a fatness-based control approach which is implemented in successive loops. To apply the multi-loop fatness-based control scheme, the state-space model of the H-type gantry crane with dual PMLSM is separated into subsystems, which are connected in cascading loops. Results For each subsystem, control can be performed with inversion of its dynamics as in the case of input–output linearized fat systems. The state variables of the preceding (ith) subsystem become virtual control inputs for the subsequent (i+1)th subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. Conclusion A novel nonlinear optimal control method has been developed for the dynamic model of a dual PMLSM-driven gantry crane. The proposed method achieves stabilization of the H-type gantry crane with dual PMLSM without the need for difeomorphisms and complicated state-space model transformations. Using the local diferential fatness properties of each one of the subsystems that constitute the gantry crane's model, the design of a stabilizing feedback controller is enabled.This research work has been partially supported by Grant Ref. 301022 ’Nonlinear optimal and fatness-based control methods for complex dynamical systems’ of the Unit of Industrial Automation of the Industrial Systems Institute. Besides, the authors, Pierluigi Siano and Mohammed Al-Numay acknowledge fnancial support from the Researchers Supporting Project Number (RSP2023R150), King Saud University, Riyadh, Saudi Arabia

Controller design for gantry crane system using modified sine cosine optimization algorithm

The objective of this research paper is to design a control system to optimize the operating works of the gantry crane system. The dynamic model of the gantry crane system is derived in terms of trolley position and payload oscillation, which is highly nonlinear. The crane system should have the capability to transfer the material to destination end with desired speed along with reducing the load oscillation, obtain expected trolley position and preserving the safety. Proposed controlling method is based on the proportional-integral-derivative (PID) controller with a series differential compensator to control the swinging of the payload and the system trolley movement in order to perform the optimum utilization of the gantry crane.  Standard sine cosine optimization algorithm is one of the most-recent optimization techniques based on a stochastic algorithm was presented to tune the PID controller with a series differential compensator. Furthermore, the considered optimization algorithm is modified in order to overcome the inherent drawbacks and solve complex benchmark test functions and to find the optimal design's parameters of the proposed controller. The simulation results show that the modified sine cosine optimization algorithm has better global search performance and exhibits good computational robustness based on test functions. Moreover, the results of testing the gantry crane model reveal that the proposed controller with standard and modified algorithms is effective, feasible and robust in achieving the desired requirements

TRACKING CONTROL OF AN UNDERACTUATED GANTRY CRANE USING AN OPTIMAL FEEDBACK CONTROLLER

Gantry cranes have attracted a great deal of interest in transportation and industrial applications. To increase the effectiveness of gantry cranes, the control of such systems is considered vital. This paper is concerned with tracking the control of an underactuated gantry crane using an optimal feedback controller. The optimal control strategy takes into account a performance index, including integrated time and absolute error criterion. To do this, nonlinear dynamic equations of the system are derived using Lagrange’s Principle. The minimum tracking error of the trolley and the minimum oscillation of the hoisting line are assumed as design parameters, and the best gains of the feedback controller are achieved. Finally, some tracking simulations are performed which demonstrate the capability of the simple proposed method in the optimal tracking control of a gantry crane

DYNAMICS AND CONTROL OF FLEXIBLE GANTRY CRANE SYSTEM

Gantry crane system, a non-slewing-luffing crane system is most widely used in many work places. However, the heavier lifting capacities and the greater size of gantry crane, the vibrational motion become more significant during crane operations and it must be considered. The equations of motion of the system can be obtained by modeling the crane framework using finite element in conjuction with moving finite element method and gantry crane by using Lagrange’s equations. The combinational direct integration technique, namely Newmark- and fourth-order Runge-Kutta method is proposed to solve the coupled equations of motion. Numerical simulation results show that the combination of flexibility of crane framework and hoist cable produces greater amplitudes and lower swing angles frequency compared to the gantry crane system with flexible hoist cable or crane framework only with respect to the rigid model. Furthermore, all the flexible models of gantry crane system have lower frequencies in the time histories of swing angles of payload with respect to the rigid model for all the parametric studies. The trends of maximum displacements of crane framework and hoist cable increase with the increase of payload mass and initial swing angle of payload. The increases are slightly linear for payload mass and nonlinear for initial swing angle of payload. Under the increase of structural damping, hoist cable stiffness, cross-sectional dimensions of crane framework and hoist cable length, the trends decrease for all the maximum displacements. Control simulations clearly demonstrate that Zero-Vibration-Derivative-Derivative (ZVDD), Fuzzy Logic Controller (FLC) and Proportional-Integral-Derivative (PID) controllers have rough fluctuations in controlling flexible gantry crane with respect to their performances in controlling the rigid model of gantry crane. Compared to FLC and PID, ZVDD has larger steady state error

Dynamic weighted idle time heuristic for flowshop scheduling

The constructive heuristic of Nawaz, Enscore and Ham (NEH) has been introduced in 1983 to solve flowshop scheduling. Many researchers have continued to improve the NEH by adding new steps and procedures to the existing algorithm. Thus, this study has developed a new heuristic known as Dynamic Weighted Idle Time (DWIT) method by adding dynamic weight factors for solving the partial solution with purpose to obtain optimal makespan and improve the NEH heuristic. The objective of this study are to develop a DWIT heuristic to solve flowshop scheduling problem and to assess the performance of the new DWIT heuristic against the current best scheduling heuristic, ie the NEH. This research developed a computer programming in Microsoft Excel to measure the flowshop scheduling performance for every change of weight factors. The performance measure is done by using n jobs (n=6,10 and 20) and 4 machines. The weight factors were applied with numerical method within the range of zero to one. Different weight factors and machines idle time were used at different problem sizes. For 6 jobs and 4 machines, only idle time before and in between two jobs were used while for 10 jobs and 20 jobs the consideration of idle time was idle time before, in between two jobs and after completion of the last job. In 6 jobs problem, the result was compared between DWIT against Optimum and NEH against Optimum. While in 10 jobs and 20 jobs problem the result was compared between DWIT against the NEH. Overall result shows that the result on 6 and 10 jobs problem the DWIT heuristic obtained better results than NEH heuristic. However, in 20 jobs problem, the result shows that the NEH was better than DWIT. The result of this study can be used for further research in modifying the weight factors and idle time selections in order to improve the NEH heuristic

An experimental study of the efficiency of optimal control for lifting machines

The article is devoted to the synthesis of optimal speed performance control, in which the Pontryagin maximum principle and the phase-plane method are used to search for switching points of the relay control function. A crane trolley model and computer control system, able to implement the automatic movement of the trolley according to the optimal laws, were developed. The conducted experimental study allowed us to establish that the operating cycle of the traveling mechanism can be reduced by 1.5-3.1 times using optimal speed performance control

Input shaping-based control schemes for a three dimensional gantry crane

The motion induced sway of oscillatory systems such as gantry cranes may decrease the efficiency of production lines. In this thesis, modelling and development of input shaping-based control schemes for a three dimensional (3D) lab-scaled gantry crane are proposed. Several input shaping schemes are investigated in open and closed-loop systems. The controller performances are investigated in terms of trolley position and sway responses of the 3D crane. Firstly, a new distributed Delay Zero Vibration (DZV) shaper is implemented and compared with Zero Vibration (ZV) shaper and Zero Vibration Derivative (ZVD) shaper. Simulation and experimental results show that all the shapers are able to reduce payload sway significantly while maintaining desired position response specifications. Robustness tests with ±20% error in natural frequency show that DZV shaper exhibits asymmetric robustness behaviour as compared to ZV and ZVD shapers. Secondly, as analytical technique could only provide good performance for linear systems, meta-heuristic based input shaper is proposed to reduce sway of a gantry crane which is a nonlinear system. The results show that designing meta-heuristic-based input shapers provides 30% to 50% improvement as compared to the analytical-based shapers. Subsequently, a particle swarm optimization based optimal performance control scheme is developed in closed-loop system. Simulation and experimental results demonstrate that the controller gives zero overshoot with 60% and 20% improvements in settling time and integrated absolute error value of position response respectively, as compared to a specific designed PID-PID anti swing controller for the lab-scaled gantry crane. It is found that crane control with changing cable length is still a problem to be solved. An adaptive input shaping control scheme that can adapt to variation of cable’s length is developed. Simulation with real crane dimensions and experimental results verify that the controller provides 50% reduction in payload sway for different operational commands with hoisting as compared to the average travel length approach

Adaptive fuzzy sliding mode control for uncertain nonlinear underactuated mechanical systems

Sliding mode control has been shown to be a robust and effective control approach for stabilization of nonlinear systems. However the dynamic performance of the controller is a complex function of the system parameters, which is often uncertain or partially known. This paper presents an adaptive fuzzy sliding mode control for a class of underactuated nonlinear mechanical systems. An adaptive fuzzy system is used to approximate the uncertain parts of the underactuated system. The adaptive law is designed based on the Lyapunov method. The proof for the stability and the convergence of the system is presented. Robust performance of the adaptive fuzzy sliding mode control is illustrated using a gantry crane system. Simulation results demonstrate that the system output can track the reference signal in the presence of modelling uncertainties, external disturbances and parameter variation. © 2013 IEEE