Combined control with sliding mode and partial feedback linearization for 3D overhead cranes

Abstract

A 3D overhead crane is an underactuated system consisting of five outputs: trolley position, bridge translation, cable length, and two cargo swings. These outputs are controlled by three actuators for cargo hoisting, trolley motion, and bridge traveling. This study proposes the use of a nonlinear controller that performs five tasks concurrently: cargo hoisting, trolley tracking, bridge motion, payload vibration suppression during transport, and cargo swing elimination at the destination. The proposed algorithm is combined with two control components: (i) partial feedback linearization, which is a precursor to controller design, to suppress cargo vibration; and (ii) sliding mode method, which provides robust control in lifting the payload and driving trolley and bridge motions against model imprecision and uncertainty. These two control mechanisms are successfully merged into a combined controller because the kinematic relationships between the state variables are made apparent in the system dynamics. Simulation and experimental results show that the proposed controller asymptotically stabilizes all system responses.COMBINED CONTROL WITH SLIDING MODE AND PFL 3373 parameter-varying model, Giua [13] designed a controller-observer with state-feedback stabilization for time-varying systems. Park [14] proposed a nonlinear controller for a 2D container crane to suppress cargo swing, track the trolley, and lift the cargo. FLC was applied to the trolley and cargo hoisting dynamics to obtain one controller component; the antiswing component was obtained with an energy-based nonlinear control design. Cho [15] proposed a scheme linearly composed of two controls: nominal proportional-derivative (PD) control designed through feedback linearization and corrective control. Cho expanded this so-called PFL controller with an adaptive component in [16].Studies on SMC for crane systems have also been published. The general theory of SMC for a class of underactuated systems was first presented by Bergeman [17], developed by Lee [18], and completed by Ashrafiuon [19] and Sankaranarayanan [20]. Focusing on overhead crane control, Karkoub [21] introduced a variable structure controller in conjunction with state feedback control andţ-synthesis control. Bartolini [22] proposed a simple control scheme based on second-order sliding modes for a payload-cart system with constant cable length. In another study by Bartolini [23], two SMC laws were constructed: a proportional-integral controller and a linear, observer-based, time-varying feedback scheme. Liu [24] combined fuzzy logic with SMC for an overhead crane based on a linearized mathematical model. Lee [25] developed an SMC controller by analyzing sliding surface stability to concurrently control cargo swing and trolley motion. With the simplest crane model wherein cable length is constant, an adaptive fuzzy SMC control was proposed by Park [26] for cargo antiswing and trolley tracking. Almutrairi [27] adopted the SMC scheme developed by Lee [25] to develop a 3D crane control system. An ...

Simplified input-output inversion control of a double pendulum overhead crane for residual oscillations reduction

“…In the case of velocity control, the transfer function to be inverted is the one between the force applied to the cart and the velocity of the payload (16). The feedforward input force signal can be obtained by applying the simplified inversion procedure to (16), obtaining…”

“…Many of the different proposed methodologies are related to the closed-loop control of the system, in which the angle of the payload is measured. In this context, for example, a Lyapunov approach [5,6], a fuzzy logic mechanism [7][8][9], the model predictive control concept [10][11][12], a gain scheduling technique [13,14], sliding mode approach [15,16] and adaptive schemes [17] have been exploited. However, it has to be recognized that the simplest approach is to apply an openloop controller, that is, a motion planning method for which the cart motion is determined in order to obtain an efficient motion of the payload [18].…”

Boom motion trajectory generation approach for load sway rejection in rotary cranes considering double-pendulum effect

“…This load sway will not only reduce the working efficiency of the crane but also bring potential safety hazards and even cause accidents. Because the closedloop methods can provide strong robustness performance, a large number of related control methods, including adaptive control, [1][2][3][4] sliding mode control, [5][6][7] Lyapunov-based nonlinear method, [8][9][10][11][12][13][14][15] fuzzy control, [16][17][18] and so on, have been proposed. However, these methods need to feedback the load sway information; therefore, the control performance entirely depends on the accuracy of the information.…”

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

“…Due to their inability to cope with perturbations and disturbances, some researchers combined them with closed‐loop controllers to improve the control performance . As for closed‐loop control schemes, it can be further categorized into proportional integral derivative, linear quadratic regulator, model predictive control (MPC), adaptive control, sliding mode control, etc. The closed‐loop control schemes listed above are all model‐based methods, which suggests that their control performances severely depend on the accurate mathematical modeling of overhead crane systems.…”