Nonlinear Position Control Using Only Position Feedback under Position Errors and Yaw Constraints for Air Bearing Planar Motors

Abstract

In this paper, we propose a nonlinear position control using only position feedback to guarantee the tolerances for position tracking errors and yaw. In the proposed method, both mechanical and electrical dynamics are considered. The proposed method consists of the nonlinear position controller and nonlinear observer. The nonlinear position controller is designed by a backstepping procedure using the barrier Lyapunov function to satisfy the constraints of position error and yaw. The nonlinear observer is developed to estimate full state using only position feedback. The stability of the closed-loop system is proven using Lyapunov and input-to-state stabilities. Consequently, the proposed method satisfies the constraints of position error and yaw using only position feedback for the planar motor.

Lyapunov-Based Controller Using Nonlinear Observer for Planar Motors

“…Theorem 2. According to the current tracking error dynamics (7), the voltage inputs of the planar motor with the integral terms of the current tracking errors are defined as follows:…”

“…Therefore, in order to improve the position tracking performance of microstepping, a feedback controller, considering the electrical dynamics, is required to guarantee the convergence of the phase currents to the desired phase currents of the electrical dynamics in planar motors. Therefore, various studies have been developed to enhance the current tracking performance of planar motors [1,[6][7][8]. A robust adaptive control with consideration of electrical dynamics is required to achieve the desired position performances [1].…”

“…Since it is important to have the information of measured signals such as the position and current to linearize nonlinear dynamics, this can be obtained by implementing various sensors such as an encoder and a resolver; current feedback can be measured via sensing resistors. However, it is actually difficult to measure all state variables for Therefore, various studies have been developed to enhance the current tracking performance of planar motors [1,[6][7][8]. A robust adaptive control with consideration of electrical dynamics is required to achieve the desired position performances [1].…”

“…A current controller with linear techniques based on nonlinear cascade control algorithms was proposed to enhance the transient response in the position control [6]. A nonlinear position control scheme using only position feedback under position tracking errors and yaw constraints was proposed to guarantee the tolerances for position tracking errors and yaw [7]. A linear parameter varying H ∞ control based on an augmented nonlinear observer was proposed to enhance both the position tracking performance and yaw regulation performance [8].…”

Barrier Lyapunov Function-Based Adaptive Back-Stepping Control for Electronic Throttle Control System

“…An asymmetric BLF controller and an asymmetric time varying BLF controller are designed respectively for the problem of slip rate constraint in the ABS system in [28,29]. A nonlinear position controller is designed in [30] by a backstepping procedure using the barrier Lyapunov function to satisfy the constraints of position error and yaw. In [31], in order to deal with robust stabilization and output constraints of the system, a novel tan-type BLF and a power integrator technique have been proposed.…”