This paper presents the virtual design of a four-arm Delta parallel robot for potential applications in the food industry, specifically for the automated preparation of fast foods. Kinematic and dynamic models were developed based on the morphology of this type of robot. Cutting-edge and previously unexplored control strategies for these types of manipulators are then designed and implemented based on Fuzzy PD and Fuzzy PID configurations. Several performance indicators, such as the Integral Square Error (ISE), Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE), were used to conduct a performance comparison of the control techniques, considering type-1 and interval type-2 fuzzy sets. In all the analyzed scenarios, the fuzzy controllers correspond to the Takagi–Sugeno–Kang model using linear functions of the inputs in the outputs. Among the main contributions of this work is the development of a detailed dynamic model of the robot in Simscape, incorporating realistic aspects that are often overlooked during analytical modeling. To ensure more accurate results, the rejection of external disturbances is thoroughly analyzed in simulations, considering elements such as time delays and control signal saturations. The results demonstrate the veracity of the proposed design for a four-arm Delta robot, both in models and in the Simscape/Simulink implementation. In the trajectory tracking task and external disturbance rejection, the superiority of the Fuzzy PID controller with interval type-2 fuzzy sets over fuzzy controllers with PD structure and over type-1 fuzzy sets is evidenced.