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Stabilization of Benchmark Under-actuated Systems via Saturated Controls

Jun Liu, Huawen Ye*, and Xianting Qi
International Journal of Control, Automation, and Systems, vol. 20, no. 11, pp.3524-3539, 2022

Abstract : In this paper, we present controllers to stabilize benchmark under-actuated systems such as inertia wheel pendulum (IWP), cart-pole, cart-pendulum, overhead crane, VTOL aircraft, ball-and-beam, translational oscillations with a rotational actuator (TORA), and active magnetic bearing (AMB). The mentioned systems are transformed into the feedforward systems subject to uncertain gains, the nested-saturation controllers in an almost unified form are then designed. Due to the analysis mechanism of saturation reduction (checking the time-derivatives of boundary surfaces), the bounds of uncertain gains can always be determined in small domains. In turn, there is no need to treat in advance certain subsystems, and the fully-saturated controllers (rather than partially-saturated ones) can be taken as global stabilizers. Moreover, the explicit inequality conditions can always be summarized. In addition, for the relatively complicated systems such as the overhead crane system, a non-strict upper-triangular subsystem of the ball-and-beam system as well as the TORA system, special technical strategies are developed to treat the linear perturbation, the non-strict upper-triangular structure and an oscillator.

Keyword : Saturated control, stabilization, uncertain nonlinear systems, under-actuated system.

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