Abstract
This paper presents a novel algorithm for the design and analysis of an adaptive backstepping controller (ABC) for a microgyroscope. Firstly, Lagrange–Maxwell electromechanical equations are established to derive the dynamic model of a z-axis microgyroscope. Secondly, a nonlinear controller as a backstepping design approach is introduced and deployed in order to drive the trajectory tracking errors to converge to zero with asymptotic stability. Meanwhile, an adaptive estimator is developed and implemented with the backstepping controller to update the value of the parameter estimates in the Lyapunov framework in real-time. In addition, the unknown system parameters including the angular velocity may be estimated online if the persistent excitation (PE) requirement is met. A robust compensator is incorporated in the adaptive backstepping algorithm to suppress the parameter variations and external disturbances. Finally, simulation studies are conducted to prove the validity of the proposed ABC scheme with guaranteed asymptotic stability and excellent tracking performance, as well as consistent parameter estimates in the presence of model uncertainties and disturbances.
Highlights
As primary information sensors, microgyroscopes have a large potential for several types of applications in navigation, control, and guidance systems
Fabrication imperfections in microgyroscopes always generate some coupling between oscillation modes
The conventional controller for a microgyroscope is to force the drive mode into a known oscillatory motion and detect the Coriolis effect coupling along the orthogonal sense mode, which provides the information about the applied angular velocity
Summary
Microgyroscopes have a large potential for several types of applications in navigation, control, and guidance systems. The conventional controllers are immanently sensitive to some typical types of fabrication imperfections, such as the cross-damping term, which produces zero-rate output To solve these problems, advanced control schemes such as adaptive controller [2,3,4,5], sliding mode controller [6], compound robust controller [7], adaptive neural controller [8,9,10], and adaptive fuzzy controller [11,12,13] have been applied to microgyroscopes. The Lyapunov-based adaptive controller is obtained to guarantee the asymptotic stability of the closed-loop system and the consistent parameter estimates, including the external angular velocity if the persistent excitation (PE) condition is satisfied. A robust term is incorporated in the adaptive backstepping algorithm to suppress the lumped disturbances
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