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Stabilization of Benchmark Under-actuated Systems via Saturated Controls

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  • Control Theory and Applications
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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.

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Authors and Affiliations

  1. School of Automation, Central South University, Changsha, 410083, China

    Jun Liu, Huawen Ye & Xianting Qi

  2. Hunan College of Electrical and Mechanical Technology, Changsha, 410151, China

    Jun Liu

Authors
  1. Jun Liu
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  2. Huawen Ye
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  3. Xianting Qi
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Correspondence to Huawen Ye.

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This work was supported in part by the National Natural Science Foundation of China under grant no. 61374024, and the Hunan Provincial Natural Science Foundation of China (2020JJ4755).

Jun Liu received his B.S. degree in automation and an M.S. degree in control theory and control engineering from China University of Geosciences, Wuhan, China, in 2007 and 2010, respectively. He is currently pursuing a Ph.D. degree in control science and engineering from Central South University, Changsha, China. His current research interests include uncertain nonlinear systems and saturated control systems.

Huawen Ye received his Ph.D. degree in control science and engineering from Northwestern Polytechnical University, Xi’an, China, in 2002. He is currently a professor at the School of Automation, Central South University. His research interests include nonlinear control systems and networked control systems.

Xianting Qi received her B.S. degree from the Department of Automation from Wuhan University of Technology (WHUT), Wuhan, China, in 2018, and an M.S. degree in control engineering from Central South University (CSU), Changsha, China, in 2021. Her current research interests include nonlinear control.

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Liu, J., Ye, H. & Qi, X. Stabilization of Benchmark Under-actuated Systems via Saturated Controls. Int. J. Control Autom. Syst. 20, 3524–3539 (2022). https://doi.org/10.1007/s12555-021-0583-1

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  • DOI: https://doi.org/10.1007/s12555-021-0583-1

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