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Tower cranes are very complex mechanical systems and have been the subject of research investigations for several decades. Research on tower cranes has focused on the development of dynamical models (linear and nonlinear) as well as control techniques to reduce the swaying of the payload. Inherently, the dynamical model of the tower crane is highly nonlinear and classified as under-actuated. The crane system has potentially six degrees of freedom but only three actuators. Also, the actuators are far from the payload which makes the system non-colocated. The dynamic model describing the motion of the payload from point to point is affected by uncertainties, time delays and external disturbances which may lead to inaccurate positioning, reduce safety and efficacy of the overall system. It is proposed here to use an H∞ based adaptive fuzzy control technique to control the swaying motion of a tower crane. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed disturbances, as well as parameter uncertainties. The proposed control law for payload positioning is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the tower crane; then, an indirect adaptive fuzzy scheme is developed for overriding the nonlinearities and time delays. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme fuses a Variable Structure (VS) scheme to resolve the system uncertainties, and the external disturbances such that H∞ tracking performance is achieved. A control law is derived based on a Lyapunov criterion and the Riccati-inequality to compensate for the effect of the external disturbances on tracking error so that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H∞ tracking performance. Simulations are presented here to illustrate the performance of the proposed control design.

Complex mechanical systems, such as tower cranes, are known to be highly nonlinear, under-actuated, and non-colocated, which makes their closed-loop control very challenging. The interconnected components of these systems undergo complex dynamic phenomena, such as friction, which lead to energy or momentum transmission delays. The complexity of such systems is further complicated by external disturbances and nonlinearities resulting from using hydraulic and/or electrical actuators, mechanical joints, gears, etc., which result in the formation of dead-zones, backlash, and hysteresis. A dead-zone, which constitutes a significant non-smooth nonlinearity, severely limits the performance of many mechanical systems such as the tower crane. Previous works on the control of tower cranes were based on accurate determination of their actuated states. In this work, a robust control technique based on adaptive fuzzy theory is investigated for anti-swing and trajectory tracking of tower crane systems. The system is subject to uncertainties in parameter parameters, time delays, external disturbances, and unknown actuator nonlinearities. The unknown actuator nonlinearities, from the jib and tower motors, are characterized by dead-zone bands (as opposed to the typical crisp dead-zone functions). First, fuzzy logic systems with on-line adaptations are utilized to evaluate the unknown nonlinear functions. The proposed control scheme uses the H∞ control technique to develop compensators to overcome the effects of parameter variations, time delays, external disturbances, and unknown actuator dead-zone band nonlinearities. The proposed control scheme ensures the stability of the closed-loop system and achieves desired tracking precision such that the states of the tower crane system are ultimately uniformly bounded (UUB) and guarantees an H∞ norm bound constraint on disturbance attenuation for all admissible uncertainties based on the Lyapunov criterion. Simulation results show the validity of this approach for the tower crane system.

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