Input and output constraints control strategy-based model predictive control for double-link overhead cranes

SummaryIn this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.

Although the literature on control of overhead crane systems is extensive and relatively mature, there is still a need to develop strategies that can simultaneously handle factors such as the double pendulum effect, variable cable length, input saturation, input dead zones, and external disturbances. This article is concerned with adaptive tracking control for underactuated overhead cranes in the presence of the above-mentioned challenging effects. The proposed controller is composed of the following two components. First, a tracking signal vector that effectively reduces system swing magnitudes is constructed to improve the transient performance and guarantee smooth operation of the system. Second, an adaptive law is designed to estimate and compensate for the overall effects of the friction, the external disturbances, and certain nonlinearities. The system stability has been proved rigorously via the Lyapunov method and Barbalat's lemma. Extensions to the cases with input saturation and dead zones have also been discussed. Extensive numerical simulations have been conducted to verify the performance and robustness of the proposed controller, in comparison to some existing methods.

Overhead cranes, which are typically underactuated, are studied systematically nowadays. While, the model widely used in research is ideal. Thus, the corresponding controllers may react badly under external disturbances, unmodeled dynamics and input constraints. To tackle this issue, this paper develops an adaptive version of anti-sway trajectory tracking controller for overhead cranes. First, as to constrained input, we perform a mapping action from the system input to the hyperbolic tangent function. Then adaptation mechanisms are proposed to adjust the modified inputs and the system uncertainty. Such a controller achieves precise positioning and swing suppression despite input saturation, system uncertainty and external disturbances. The crane system proves to be dissipative with the proposed controller. The experiments accomplished on a laboratory-size bridge crane reveal that the proposed controller asymptotically stabilizes all system states.

In this paper, a model-free robust adaptive control scheme with finite-time convergence based on time-delay control is proposed for anti-sway and positioning control of two-dimensional underactuated overhead cranes. First, the whole overhead cranes system is simplified to an ultra-local model for time delay estimation (TDE). TDE brings a direct and effective model-free property but also an estimation error. Second, a sliding mode disturbance observer is designed to estimate and compensate for the TDE error. Third, sliding mode control (SMC) is used to enhance the robustness of the controller. An adaptive integral sliding surface is then designed to accelerate the sliding surface convergence rate and shorten the convergence time. To further optimize the selection of parameters, the parameter estimation is integrated to enhance the performance of model-free control. In the final analysis of the simulation, data yield that the introduction of parameter estimation increases the control performance by more than 20% on average, and the above facts verify the effectiveness of the scheme. Finally, the stability of the closed-loop control system is analyzed by using Lyapunov stability theory, and the effectiveness and robustness of the control scheme are verified through computer simulation results.

This paper proposes an adaptive anti-sway controller for uncertain overhead cranes. The state-space model of the 2D overhead crane with the system parameter uncertainties is shown firstly. Next, the adaptive controller which can adapt with the system uncertainties and input disturbances is established. The proposed controller has ability to move the trolley to the destination in short time and with small oscillation of the load despite the effect of the uncertainties and disturbances. Moreover, the controller has simple structure so it is easy to execute. Also, the stability of the closed-loop system is analytically proven. The proposed algorithm is verified by using Matlab/Simulink simulation tool. The simulation results show that the presented controller gives better performances (i.e., fast transient response, position tracking, and low swing angle) than the state feedback controller when there exist system parameter variations as well as input disturbances.

PID-like coupling control of underactuated overhead cranes with input constraints

In this paper we present the application of an input-output inversion technique for the open-loop control of an overhead crane modelled as a double pendulum. The method is mathematically derived, obtaining a parametric trajectory that ensures reduced residual oscillations. Then, it is shown that the postactuation can be neglected so that the method can be implemented with standard industrial drives. The robustness of the method is evaluated by means of simulations, and the performance of the method is experimentally compared with the well-known input shaping technique. The advantages of using a double pendulum model instead of a simple pendulum one are also shown.

Overhead cranes are used widely in various industrial fields. Crane transportation load must be transported for the work efficiency and safety to the destination without swinging. As a demand of highly precise and safety rises, automation is thought about as a method corresponding to lack of operator of mastery of skills. A transportation load of an overhead crane swings by a traveling acceleration change while doing up-and-down motion of a rope length change. It is necessary to measure this three-dimensional motion for swing suppression control. When it is installed in an overhead crane, a measurement sensor becomes complicated. In this paper, the trial stereovision device is manufactured which is a non-contact sensor, not an installation sensor and tried to control the overhead crane by vision feedback. The vision sensor is a stereovision device of four degree of freedom for tracking and gazing with two CCD cameras. A position measurement of a transportation load and an experiment of tracking control were done. The three-dimensional position of the transportation load is provided with CCD image data of two cameras, the focus distance, and four-vision device drive angles and is used for crane control. The vision device drive target angles that a point of intersection of two camera optical axes seems to always accord with the transportation load center is obtained using inverse kinematics. With these target angles, the control of tracking and gazing about the transportation load can be done. On the other hand, in an overhead crane model, using measured three-dimensional coordinate values, positioning and vibration suppression control of the transportation load was done. The overhead crane model consists of a trolley running on two perpendicular slide guide rails and a hoisting device of the transportation load. The overhead crane model has five degree of freedom, and they are x, y direction displacements of a trolley, a rope length, a swing angle, a swing direction angle. The variable rope length, the swing angle and the swing direction angle are calculated using the load position measured by the vision sensor. Variable digital gains of the trolley in consideration of the rope length change were pursued by this information, and overhead crane control was done. The experiment result of overhead crane control by vision feedback showed that the used control system was effective.

Overhead crane systems play an important role in many engineering sites, such as harbors, factories, construction sites, etc. Traditionally, overhead crane systems are operated by experienced operators. However, due to the increased demand on fast and accurate payload positioning and suppressing of swing angles, as well as safety issues, automation, and control technologies are overwhelmingly applied in controlling of overhead crane systems. Overhead cranes are essentially an underactuated nonlinear system where motions of trolley of the payload are highly coupled, which makes them difficult to control. This chapter presents an autonomous motion control framework for overhead cranes.

Overhead cranes are essentially a kind of complex underactuated nonlinear mechanical systems, and it is a challenge to design an anti-swing controller for overhead cranes, hence, many people design controllers of overhead cranes ignoring the changing of the rope length and other parameters. In this study, we propose a multi-sliding mode controller to solve the problem of anti-swing and positioning controller for an overhead crane with rope length variations. This controller can provide a simultaneous trolley-position regulation, sway suppression, and load hoisting control. Also, this paper adopts a new method to decrease the chattering of the control input. Stability analysis of the proposed controller is given in the paper. The proposed controller does not rely on the accurate knowledge of overhead crane system model, and it is simple and easy to apply, and robust to disturbances. The simulation results show the good performance of the proposed controller.

Energy Efficiency of Overhead Cranes

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.

This paper proposes a new approach for the anti-swing control of overhead cranes, where a coupling control of trolley motion and load swing is adopted for sufficient damping of load swing. A model-based anti-swing trajectory control scheme is designed based on Lyapunov stability theorem, where the stable nonminimum-phase characteristics of the load swing dynamics are used for stability proof. The proposed control guarantees asymptotic stability of the anti-swing trajectory control while keeping all internal signals bounded. In addition, the anti-swing control is solved as a trajectory control problem and hence the proposed control realizes an antiswing control along a typical anti-swing trajectory in practice, which is considered to be the most efficient anti-swing control. Finally, the theoretical results are proven by computer simulation.

This paper proposes a new approach for the design of anti-swing control of overhead cranes. An anti-swing trajectory control scheme is designed based on the trolley and load-hoisting dynamics, and then extended to an adaptive scheme. The load-swing dynamics is controlled by employing a sliding surface that couples the load-swing dynamics with trolley motion. The number of degrees of freedom of the trolley and load-hoisting dynamics is the same as that of the control inputs; therefore, the control problem is reduced to finding a coupled sliding surface that stabilizes the crane control system, based on the load-swing dynamics. In this study, the Lyapunov stability theorem is used as a mathematical design tool. The proposed control guarantees asymptotic stability of the anti-swing trajectory control while keeping all internal signals bounded. The coupled sliding surface allows a direct control of the damping of load swing. In addition, the proposed control provides clear gain-tuning criteria for easy application. Finally, the proposed control realizes an anti-swing control along a typical anti-swing trajectory in practice, with high-speed load hoisting. The validity of the theoretical results is shown by computer simulation.

For anti-swing control of overhead crane, a deflection angle must be estimated. However, it is difficult to estimate deflection angles with a contact sensor such as rotary encoder. Therefore, we show a non-contact measurement method for the deflection angles by using two microphones. This method is based on the sound source location in a human with two ears. The method employs a time delay of arrival (TDOA) of acoustic signals which are picked up by the two microphones. Also, we show an algorithm to obtain the angle from the TDOA by using the Newton’s method. Finally, we show experimental results to demonstrate the effectiveness of the proposed method.