Method for determination of interaction between a two-wheeled self-balancing vehicle and its rider

Calculation of the critical delay for the double inverted pendulum

“…Stabilization of an inverted pendulum with delayed feedback is a benchmark problem in control engineering literature [2,28,26,33] as well as in understanding human balancing and human motor control [18,21,20,23]. As a matter of fact, many control concepts are often implemented in simple inverted pendulum systems, see, e.g., [22,12,26,11]. As mentioned in the Introduction, stabilization by a delayed state feedback is not possible if the delay is larger than a critical value [30].…”

“…If ω = 0 then (10) gives b 0 = −a 0 , which is a so-called real root boundary [1]. If ω > 0, then ( 10) and (11) give the parametric curve…”

“…Stabilization of an inverted pendulum with delayed feedback is a benchmark problem in the control engineering literature (Atay, 1999;Qin et al, 2014;Sieber and Krauskopf, 2005;Xu et al, 2017) as well as in understanding human balancing and human motor control (Maurer and Peterka, 2005;Milton and Insperger 2019;Milton et al, 2009;Morasso et al, 2019). As a matter of fact, many control concepts are often implemented in simple inverted pendulum systems, for example Ciezkowski (2016), Habib et al (2017), Molnar and Insperger (2016) and Qin et al (2014). As mentioned in the Introduction, stabilization by a delayed state feedback is not possible if the delay is larger than a critical value (Stepan, 2009).…”