The thesis deals with mathematical modelling, simulation and control design for a gantry crane with a weight attached to a winch with a rope. The system is based on the experimental device Amira PS600 on which we performed experiments for the thesis.
The initial section, which is devoted to modelling and simulation, involves a theoretical derivation of the differential equation describing the mathematical model. The Lagrange method was applied to derive differential equations. Using the Matlab-Simulink software we constructed the schema of the mathematical model. The schema helped us run the simulation and record the responses of the mathematical model which were then compared to the responses of the real device. The model's structure and parameters regarding friction had to be changed to better describe the dynamics of the real device. The modified mathematical model thus provides a good description of the dynamics.
Fuzzy logic was applied in the design of the closed-loop system. The Fuzzy Logic Toolbox, which is a part of the Matlab-Simuling software, was used for developing two fuzzy controllers. One of them controlled the position of the cart, while the other controlled the length of the rope. Both controllers were designed by defining the membership functions of input and output variables and the rules that make up the fuzzy inference system connecting the input and output variables.
Having set the fuzzy controllers, we conducted a practical experiment of closed-loop control of the system, assessed the quality of control over cart movement and rope length, and presented the results and findings of the experiment. The fuzzy controllers ensure adequate control performance of cart position and rope length.