| Abstract: |
A generalized model of a complicated overhead crane system of flexible cable and time dependent cable length is considered for the first time. The analysis of such systems is not an easy task since there is a moving boundary as the time-dependent cable length is not prescribed and has to be determined as a part of the solution.A set of coupled highly non-linear hybrid partial differential and ordinary differential equations of motion are derived by using Hamilton’s principle and the variation approach. An accurate model, where the time dependent spatial domain was considered as dependent variable, resulted in a reasonable and accurate system representation. It should be noted that previous publications in the field considered the spatial variable as an independent variable.The continuous time dependent flexible cable crane system is discretized by using two methods namely; a modified Galerkin method (MGM) and a variable domain finite element method (MFEM). In the modified Galerkin method, the shape function is time dependent as it is function of the time-dependent cable length. In the variable domain finite element method, the number of elements is fixed while the size of the element changes with time. It can be concluded from results of the thesis that each method has its own merits and drawbacks. It is known the the MFEM is more general as regarding time-dependent domain and the consideration of the payload at the tip of the cable is straight forward. This is not the case for MGM where a different set of mode functions should be assumed to be able to deal with the payload. Also, the MGM depends crtically on the boundary conditions and, as a result, modal functions may not be available in closed form.On the other hand, the choice of the interpolation function has a significant effect on the accuracy of the MFEM solution. Moreover, the MFEM generates a large dimensional system which requires a very large computational time as compared to the MGM. In MGM discertization, a finite number of modes is sufficient to practically represent the vibration of the cable and saves a lote of computational time. The simulation results clearly shows that the MGM performance is better than that of the MFEM in the sense of having less computational time, more accurate control and faster speed of reponse.The two models developed by using the above mentioned methods are simulated by using simple PD controller for both the trolley and the cable motions. The results show a reasonably good interpretation of the qualitative feature of the coupled system. A fuzzy logic scheme is also proposed to control the motion of the underlying overhead crane system. The analysis is based on the developed overhead crane models that include transverse cable vibration, trolley motion and payload hoisting /lowering. The considered model is simulated under the effect of three fuzzy logic controllers to control the trolley motion, payload oscillation and cable hoisting/lowering motion. Separate controllers are used for each motion since simple rules can be developed for each controller when its action is considered independently. Such rules are based on observation of the dynamics of the corresponding sub-system. The output of the first two controllers, trolley controller and payload swing controller, are combined and used as the commanded force to the trolley. The simulation results illustrated the effectiveness of performance of the proposed fuzzy control strategy.As regarding the control schemes applied in the thesis, the simulation results show that: The fuzzy controller reached the steady state of both the trolley and payload vertical positions faster and with negligible errors than the PD controller. The control forces required for the fuzzy controller is much less than those required for the PD controoler. This is desirable since it leads to less power consumption and high operating speed of the deriving motors. The fuzzy controller has no overshoot in the trolley and the payload displacement responses compared to the PD controller which has reverse trolley motion “óvershoot”. This obviously makes the PD control scheme not practical for controlling overhead cranes as compared to fuzzy control. Both control schemes need optimization techniques to applied to improve their performance. The gains of the PD controller need optimization to get the best convergence results, and, the fuzzy controller needs optimization for the membership functions. The fuzzy system is robust with respect to the crane parameters. On the other hand, the PD control system performance depends on the system parameter such as, payload, trolley mass, the cable density and length.It is, therfore, can be generally concluded that the fuzzy controller has superior performance and gives better results in controlling the undelying overhead crane.The contribution of the present work can thus be summarized as follow:1. A generalized model of an overhead crane with time dependent flexible cable whose length is time dependent is developed for the first time.2. A model considering the time dependent spatial domain as dependent variable gave more accurate system representation as compared to models with independent spatial domain.3. A modified Galerkin method and a variable domain modified finite element method are used to discretize the distributed system of the considered overhead crane.4. Set point PD controller is developed to control the overhead crane motion and payload swing and also to give experience knowledge for the fuzzy logic controller.5. Three fuzzy logic controllers have been applied, since simple rules can be proposed for each controller when its action is considered independently.RECOMMENDATIONS FOR FUTURE WORKThe present work addresses the complicated problem of modeling and control of overhead crane with time-dependent flexible cable. Several points have been addressed and several assumptions have been relaxed as discussed in the thesies. Some points relate to the current problem have, however, not discussed and are considered possible subjects for future research. These points can be summarized as follows:1. The consideration of the transverse cable vibration in two dimensions as a result of trolley motion in two dimensions.2. The effect of the flexibility of guiding rails of the trolley and the crane structure.3. Dynamic stability analysis.4. The problem of optimizing the parameters of the membership functions of the controller’s variables. The performance of the fuzzy logic controller is generally dependent on the fuzzy inference rules. Different optimization technique can be used to develop certain imposed characters for choosing the fuzzy rules as: Lyapunove stability, genetic algorithms, sliding modes and neural network.
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