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LQR and looptune were compared in terms of transient and steady-state performance, and robustness to uncertainty using a 4-DOF robotic arm. For this purpose, three different full state feedback control architectures were developed. The feedback gain for the first control system was computed using LQR. In comparison, SFG-SISO PI and SFG-MIMO PI controllers were synthesized by looptune. The SFG-SISO PI and SFG-MIMO PI controllers were also compared in terms of trajectory tracking. The value of the state feedback gain calculated using LQR was used as an initial value by looptune. Despite expending a large amount of control effort, the LQR was unable to eliminate steady-state error. Moreover, it was found to lack robustness against increasing mass variation. The SFG-SISO PI controller delivered a slightly slow response by considerably reducing its control effort. It also eliminated the steady-state error while showing robustness to uncertainty. For a slight decrease in control effort, the response of SFG-MIMO PI controller was slowest. However, it still showed robustness to uncertainty. Therefore, from an overall perspective, the SFG-SISO PI controller fares as the best controller, validates the superiority of looptune over LQR and affirms the potential of looptune for future control system applications. In this research, we have proposed a Type-I (position control) system for a rigid robotic arm. The proposed methodology may be extended to include velocity or acceleration control. This can prove highly useful in the context of robotic automation processes such as welding, painting, packaging, pick and drop etc. In addition, it has been assumed that all of the states are measurable. Practically, one or more of the states may not be measurable, necessitating the requirement of an observer. Consequently, the performance of a Linear Quadratic Gaussian (LQG) (or other observer based controllers) may be compared against looptune synthesized observer based controllers. Likewise, looptune synthesized controllers can also be compared against adaptive or intelligent controllers discussed in Section 1. The performance or robustness of looptune can also be compared against manually tuned and controllers. Finally, the performance of looptune can be evaluated for flexible robotic manipulator models. In summary, there are multiple directions in which the methodology applied in this paper can be explored or further improved. Summarize the above in few words.
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The research compared the performance of LQR and looptune controllers for a 4-DOF robotic arm. Three control architectures were developed: LQR, SFG-SISO PI, and SFG-MIMO PI. LQR had poor steady-state error elimination and lacked robustness to increasing mass variation. SFG-SISO PI had slightly slower response but effectively eliminated steady-state error and showed robustness. SFG-MIMO PI had the slowest response but also demonstrated robustness. Overall, SFG-SISO PI was considered the best controller, highlighting the superiority of looptune over LQR. The proposed methodology can be extended to include velocity or acceleration control and can be applied in various robotic automation processes. Future research can explore the use of observers, compare looptune with other controllers, and evaluate its performance in flexible robotic manipulators.

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