# Design, Simulation, and Comparison of Advanced Control Strategies for a 3-Degree-of-Freedom Robot
###### Abstract
In the future, it is planned to implement both control strategies on a real robotic platform. It is also proposed to investigate the performance of control when the robotic arm is subject to disturbances and uncertainties, as well as an application-oriented study to explore practical avenues for research. In [12], the authors present a redundant planar manipulator with six degrees of freedom (6-DoF) that features an innovative structural configuration including rotary and prismatic joints, to which three control strategies are applied for monitoring and regulating the joint trajectory tracking problem of the robot under variable loads. The selected control laws were MPC and fuzzy logic controller (FLC), subsequently comparing them with the classical Proportional-Integral-Derivative (PID) controller. The simulation models the behavior of the redundant planar manipulator in a virtual environment prior to its physical construction in order to conduct performance tests of its controllers and anticipate possible damages/failures in the system mechanics before implementing control strategies on a real robot. The effectiveness of these three control strategies is validated through qualitative comparisons (trajectory tracking performance graphs) and quantitative comparisons (the performance indicator of the Common Mode Rejection Ratio (CMRR) and joint error indices, such as the Residual Mean Square (RMS), the Residual Standard Deviation (RSD), and the Index of Agreement (IA)). It has been demonstrated that the conventional PID controller performs well in linear systems; however, it is challenging to tune the controller parameters, as most industrial plants are represented by complex dynamic systems of higher order that do not include linearities or time delays. FLC control has been one of the most successful intelligent control techniques, and its main advantage is that it does not depend on the dynamics of the robotic manipulator. Furthermore, the fuzzy controller enhances the system's performance by minimizing disturbances and uncertainties. The MPC technique has also become a powerful tool for controlling both linear and nonlinear systems. In recent decades, the trajectory tracking problem has been widely investigated with the aim of reducing the tracking error to zero, where robotic manipulators often suffer from various uncertainties, such as unstructured dynamics, external disturbances, unknown load variations, and nonlinear friction, which degrade the system's performance. Moreover, the adaptive control strategy is mentioned, which requires a constant unknown parameter; this condition is only met if the load of a robotic manipulator is fixed, which does not occur in practice, as a robotic manipulator often needs to pick up and drop specific loads repeatedly, leading to jumps in the values of the robot's unknown parameters. Regarding the results obtained, it can be mentioned that the PID controller is feasible in redundant robots; however, its performance was not good when the applied variable load exhibited linear characteristics. By adopting the fuzzy method, the uncertainties and disturbances of the system were managed, and control of disturbance attenuation was achieved. It is also indicated that the control signal from the FLC was smooth and did not present significant instabilities during the transient regime, except at the moment when the robot's joints exited their inertia. When applying variable loads to the robot, its recovery was adequate, as it did not exhibit overshoots or jerky movements in its joints compared to the PID controllers and the MPC-based controller; it was confirmed that the obtained RMS/RSD values were close to zero and those of the IA were close to one when using the FLC. Moreover, the high CMRR values of the FLC demonstrated that the compensation performed by these controllers, when variable loads were applied, was much more effective than that of the PID and MPC-based controllers.