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Non-Differentially Flat Systems
Published in Hebertt Sira-Ramírez, Sunil K. Agrawal, Differentially Flat Systems, 2018
Hebertt Sira-Ramírez, Sunil K. Agrawal
In the seminal paper by Fliess et al. [15] an interesting high frequency control plus averaging method is proposed for the systematic “flatenning” of kinematic models of underactuated mechanical systems which are not differentially flat. Here we present a case study example of application of the method to the popular Furuta pendulum, or rotational pendulum (See Furuta [24]).
Robust stabilisation of rotary inverted pendulum using intelligently optimised nonlinear self-adaptive dual fractional-order PD controllers
Published in International Journal of Systems Science, 2019
Omer Saleem, Khalid Mahmood-ul-Hasan
The Rotary-Inverted-Pendulum (RotPend) is an inherently unstable nonlinear dynamical system that requires an active control scheme to vertically stabilise itself (Boubaker & Iriarte, 2017; Sukontanakarn & Parnichkun, 2009). The RotPend system is commonly referred to as the ‘Furuta Pendulum’ in the open literature (Mandić, Lazarević, & Šekara, 2016). It is an ideal platform for the validation of advanced control algorithms for real-life applications such as stabilisation of air-crafts, rockets, missiles, and self-balancing robots (Alt, Hartung, & Svaricek, 2011; Kumar & Jerome, 2013). The attitude stabilisation of RotPend majorly constitutes the swing-up control, balancing control, and position control (Mathew, Rao, & Sivakumaran, 2013).
A speed regulator for a force-driven cart-pole system
Published in International Journal of Systems Science, 2022
Jesús Sandoval, Rafael Kelly, Víctor Santibáñez
In this section, we present an approach to design speed regulators for a class of underactuated mechanical systems possessing at least one nonactuated joint. Such a class of mechanism is assumed to have a constant inertia matrix and a potential energy function depending only of the nonactuated joints. Furthermore, the actuated joints do not possess displacement stop limits. In the life world, laboratory mechanisms with the latter feature (actuated joints without hard stop displacement limits) are the so-called inertia wheel pendulum and Furuta pendulum.
Periodic motion planning and control for underactuated mechanical systems
Published in International Journal of Control, 2018
Zeguo Wang, Leonid B. Freidovich, Honghua Zhang
Some control methods could be implemented to generate periodic motions. Variable structure control along with describing function method is used for the periodic motion of a Furuta pendulum (Aguilar, Boiko, Fridman, & Iriarte, 2009). An energy-based control is given for the oscillation generation of Furuta pendulum as well ( Freidovich, Shiriaev, Gordillo, Gomez-Estern, & Aracil, 2009). Furthermore, Shiriaev, Robertsson, Perram, and Sandberg (2006) gives a periodic motion planning method through virtual holonomic constraints. This method could be applied to all mechanical systems with underactuation degree one. It is applied in many applications, e.g. helicopter (Meza-Sánchez, Aguilar, Shiriaev, Freidovich, & Orlov, 2011), Furuta pendulum (Shiriaev, Freidovich, Robertsson, Johansson, & Sandberg, 2007), Pendubot (Freidovich, Robertsson, Shiriaev, & Johansson, 2008), inertial wheel pendulum (Freidovich et al., 2009), and bicycle (Consolini & Maggiore, 2013). As for a higher underactuation degree system, to the best of our knowledge only Shiriaev, Freidovich, and Spong (2014) give a more general method using dynamic reduction via an appropriate projection. However, it requires that the reduced dynamics satisfy the Euler–Lagrange equation, which is not trivial. De Luca and Oriolo (2000) give a motion planning method using feedback linearisation for a three-link robot. For a more general system, Sangwan and Agrawal (2009) shows the differential flatness of a biped robot and then plans the motion using flatness outputs. It avoids the difficulty of finding feasible motion, which has to satisfy passive dynamics equations (Rouchon, Fliess, Lévine, & Martin, 1993), but to find appropriate flatness outputs is still a challenging work. In addition, La Hera, Shiriaev, Freidovich, Mettin, and Gusev (2013) present a motion planning method based on numerical optimisation and virtual holonomic constraints for a three-link biped robot with underactuation degree two. However, the optimisation procedure might fail to find a periodic motion since the search procedure is quite sensitive on the initial guess, which is difficult to obtain.