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Developing an accurate dynamic model for an Autonomous Underwater Vehicle (AUV) is challenging due to the diverse array of forces exerted on it in an underwater environment. These forces include hydrodynamic effects such as drag, buoyancy, and added mass. Consequently, achieving precision in predicting the AUV's behavior requires a comprehensive understanding of these dynamic forces and their interplay. In our research, we have devised a linear data-driven dynamic model rooted in Koopman's theory. The cornerstone of leveraging Koopman theory lies in accurately estimating the Koopman operator. To achieve this, we employ the dynamic mode decomposition (DMD) method, which enables the generation of the Koopman operator. We have developed a Fractional Sliding Mode Control (FSMC) method to provide robustness and high tracking performance for AUV systems. The efficacy of the proposed controller has been verified through simulation results.more » « lessFree, publicly-accessible full text available September 1, 2025
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This research proposes a new fractional robust data-driven control method to control a nonlinear dynamic micro-electromechanical (MEMS) gyroscope model. The Koopman theory is used to linearize the nonlinear dynamic model of MEMS gyroscope, and the Koopman operator is obtained by using the dynamic mode decomposition (DMD) method. However, external disturbances constantly affect the MEMS gyroscope. To compensate for these perturbations, a fractional sliding mode controller (FOSMC) is applied. The FOSMC has several advantages, including high trajectory tracking performance and robustness. However, one of the drawbacks of FOSMC is generating high control inputs. To overcome this limitation, the researchers proposed a compound controller design that applies fractional proportional integral derivative (FOPID) to reduce the control efforts. The simulation results showed that the proposed compound Koopman-FOSMC and FOPID (Koopman-CFOPIDSMC) outperformed two other controllers, including FOSMC and Koopman-FOSMC, in terms of performance. Therefore, this research proposes an effective approach to control the nonlinear dynamic model of MEMS gyroscope.more » « less
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Robotic manipulators with diverse structures find widespread use in both industrial and medical applications. Therefore, designing an appropriate controller is of utmost importance when utilizing such robots. In this research, we present a robust data-driven control method for the regulation of a 2-degree-of-freedom (2-DoF) robot manipulator. The nonlinear dynamic model of the 2-DoF robot arm is linearized using Koopman theory. The data mode decomposition (DMD) method is applied to generate the Koopman operator. A fractional sliding mode control (FOSMC) is employed to govern the data-driven linearized dynamic model. We compare the performance of Koopman fractional sliding mode control (KFOSMC) with conventional proportional integral derivative (PID) control and FOSMC prior to linearization by Koopman theory. The results demonstrate that KFOSMC outperforms PID and FOSMC in terms of high tracking performance, low tracking error, and minimal control signals.
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Microelectromechanical (MEMS) gyroscopes are small devices used in different industries such as automotive and robotics systems due to their small size and low costs. The MEMS gyroscopes constantly encounter external disturbances, which introduce some mechanical and electromechanical nonlinearity in those systems. In this paper, the Koopman theory is applied to the nonlinear dynamic model of MEMS gyroscope to the linear dynamics model. Dynamic mode decomposition (DMD) is used to obtain eigenfunctions using Koopman’s theory to linearize the system. Then, a linear quadratic regulator (LQR) controller is used to control the MEMS gyroscope. The simulation results verify the performance of the proposed controller in terms of high-tracking performance.more » « less
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Abstract This research proposes a new compound fractional sliding mode control (FOSMC) and super-twisting control (FOSMC + STC) to control a microelectromechanical systems gyroscope. A new sliding mode surface has been defined to design the proposed new sliding mode controller. The main advantages of a FOSMC are its high tracking performance and robustness against external perturbation, but creating a chattering phenomenon is its main drawback. By applying a super-twisting control (STC) method with FOSMC, the chattering phenomenon is eliminated, the singularity problem is solved, and systems robustness has significantly improved. Simulation results validate the effectiveness of the proposed control approach.more » « less