LPV H∞ Control with an Augmented Nonlinear Observer for Sawyer Motors
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Department of Electrical Engineering, Chonnam National University, Gwangju 61186, Korea
2
Department of Energy System Engineering, Chung-Ang University, Seoul 06974, Korea
3
School of Energy System Engineering, Chung-Ang University, Soeul 06974, Korea
*
Authors to whom correspondence should be addressed.
Academic Editor: Jen-Chih Yao
Mathematics 2022, 10(1), 18; https://doi.org/10.3390/math10010018
Received: 12 November 2021
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Revised: 13 December 2021
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Accepted: 19 December 2021
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Published: 21 December 2021
This study presents LPV H∞ control with an augmented nonlinear observer (ANOB) to improve both the position and yaw tracking errors for Sawyer motors. The proposed control method consists of the forces and torque modulation scheme, an ANOB, and a Lyapunov-based current controller with the LPV H∞ state feedback controller to guarantee the stability of tracking error dynamics. The ANOB is designed to estimate all the state variables including the position, velocity, current, and disturbance using only position feedback. We propose a vertex expansion technique to solve the influence of the convex interpolation parameters in the LPV system on the tracking error performance. To be robust against disturbance, a state feedback controller with the LPV gain scheduling is determined by applying the H∞ control in the linear-matrix-inequality (LMI) technique. The closed-loop stability is proved through the Lyapunov theory. The effectiveness of the proposed control method is evaluated through simulation results and compared with the conventional proportional-integral-derivative (PID) control method to verify both the improved tracking error performance and a suitable disturbance rejection.
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Keywords:
Sawyer motors; linear parameter varying (LPV) system; disturbance observer; augmented observer; linear matrix inequality (LMI); H∞ control
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MDPI and ACS Style
Su, K.H.; Byeon, K.; Kim, W.; Lee, Y. LPV H∞ Control with an Augmented Nonlinear Observer for Sawyer Motors. Mathematics 2022, 10, 18. https://doi.org/10.3390/math10010018
AMA Style
Su KH, Byeon K, Kim W, Lee Y. LPV H∞ Control with an Augmented Nonlinear Observer for Sawyer Motors. Mathematics. 2022; 10(1):18. https://doi.org/10.3390/math10010018
Chicago/Turabian StyleSu, Khac Huan, Kwankyun Byeon, Wonhee Kim, and Youngwoo Lee. 2022. "LPV H∞ Control with an Augmented Nonlinear Observer for Sawyer Motors" Mathematics 10, no. 1: 18. https://doi.org/10.3390/math10010018
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