In this paper, a fuzzy disturbance observer and a high-gain disturbance observer based on a variable structure controller are applied to deal with imprecise multi-shaft with web materials linkage systems taking into account the variation of the moment of inertia. Specifically, a high-gain disturbance observer and an adaptive fuzzy algorithm are separately applied to estimate system uncertainties and external disturbances. The high-gain disturbance observer is designed with auxiliary variables to avoid the amplification of the measurement disturbance, and the fuzzy disturbance observer has the advantage that it does not depend on model information. The convergence properties of the tracking error are analytically proven using Lyapunov’s theory. The obtained numerical results demonstrate the validity and the adaptive performance of the proposed control law in case the system is exposed to uncertainties and disturbances. Important remarks on the design process and performance benchmarks of the two observers are also demonstrated.
In this paper, an appropriate control strategy is proposed to handle the nonlinear dynamics ofan active magnetic bearing (AMB). The goal of the control design is to drive the AMB rotor to the origin with improved transient response. In order to achieve this task, back stepping control technique with a barrier Lyapunov function are employed to keep the tracking error trajectory inside a predefined zone to avoid possible mechanical contact between rotor and stator. Besides, a speed observer is also used since information about rotor speed is not always available. The stability of the closed-loop system is proven. The effectiveness of the proposed control strategy is verified by numerical simulations.
Magnetic bearing is well-known for its advantage of reducing friction in rotary machines and is placing conventional bearings where high-speed operations and cleanliness are essential. It can be shown that the AM is a nonlinear system due to the relation between the magnetic force and current/rotor displacement. In this paper, a mathematical model of a 4-DOF AMB supported by four dual electric magnets is presented. The control objective is placed in a view of control input saturation and output limitation that are meaningful aspect in practical applications. Backstepping algorithm based control strategy is then adopted in order to achieve the high dynamic performance of the bearing. The control is designed in such a way that it takes input and output constraints into account by flexibly using hyperbolic tangent and barrier Lyapunov functions. Informative simulation studies are carried out to understand the operations of the machine and evaluate the controller quality.
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