Abstract
The inverted pendulum system has great potential for various engineering applications, and its stabilization is challenging because of its unstable characteristic. The well-known Kapitza’s pendulum adopts the parametrically excited oscillation to stabilize itself, which generally requires a complex controller. In this paper, self-sustained oscillation is utilized to stabilize an inverted pendulum, which is made of a V-shaped, optically responsive liquid crystal elastomer (LCE) bar under steady illumination. Based on the well-established dynamic LCE model, a theoretical model of the LCE inverted pendulum is formulated, and numerical calculations show that it always develops into the unstable static state or the self-stabilized oscillation state. The mechanism of the self-stabilized oscillation originates from the reversal of the gravity moment of the inverted pendulum accompanied with its own movement. The critical condition for triggering self-stabilized oscillation is fully investigated, and the effects of the system parameters on the stability of the inverted pendulum are explored. The self-stabilized inverted pendulum does not need an additional controller and offers new designs of self-stabilized inverted pendulum systems for potential applications in robotics, military industry, aerospace, and other fields.
Highlights
The pendulum in an inverted position is a multivariate, high-order, nonlinear, strong coupling, and natural unstable system (Nivedita and Soumitro, (2020); Gonzalez and Rossiter, (2020))
For θ0 ≤ 1.5°, the inverted pendulum oscillates under steady illumination and the amplitude does not change as the value of θ0 increases, whereas for θ0 > 1.5°, the liquid crystal elastomer (LCE) bar eventually evolves into static at θ 180°
Based on the well-established dynamic LCE model, the nonlinear dynamic theory of the LCE inverted pendulum under steady illumination is formulated, and numerical calculation shows that the inverted pendulum system always evolves into the static state or the selfstabilized oscillation state
Summary
The pendulum in an inverted position is a multivariate, high-order, nonlinear, strong coupling, and natural unstable system (Nivedita and Soumitro, (2020); Gonzalez and Rossiter, (2020)). Based on different stimuli-responsive materials and structures, different feedback mechanisms are proposed to realize energy compensation, such as a coupling mechanism between chemical reaction (Lahikainen et al, 2018) and large deformation (Cheng et al, 2019), a self-shading mechanism (Serak et al, 2010), and a coupling mechanism in a droplet evaporation multiprocess (Chakrabarti et al, 2020) These mechanisms originate from the nonlinear coupling of multiple processes for implementing feedback. Based on a light-fueled, self-excited oscillation, we propose a new self-stabilized inverted pendulum system in this paper It is made up of a V-shaped LCE bar and can autonomously rotate around its pivot under steady illumination.
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