Article Journal of Vibration and Control 2020, Vol. 0(0) 1–11 © The Author(s) 2020 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1077546320916022 journals.sagepub.com/home/jvc Underactuated rotary inverted pendulum control using robust generalized dynamic inversion Ibrahim M Mehedi 1,2 , Uzair Ansari 2 , Abdulrahman H Bajodah 3 , Ubaid M AL-Saggaf 1,2 , Belkacem Kada 3 and Muhyaddin J Rawa 1 Abstract The article applies the robust generalized dynamic inversion control methodology to the problem of stabilizing upright equilibrium configuration of the under-actuated rotary inverted pendulum system while tracking rotary motion of the actuated arm. The proposed robust generalized dynamic inversion control law comprised equivalent and switching control parts. The equivalent control part works to enforce a virtual constraint dynamics of the controlled state variables by means of Moore– Penrose generalized inversion. The switching control part is of the sliding mode type, and it improves robustness against unmodeled system dynamics, parametric uncertainties, and external disturbances. The robust generalized dynamic inversion control design on the linearized model of the under-actuated rotary inverted pendulum is shown to guarantee semi-global asymptotically stable tracking performance. Numerous computer simulations and experiments are conducted on the Quanser rotary inverted pendulum system, revealing that the proposed algorithm has better convergence and tracking performance than conventional sliding mode and generalized dynamic inversion control strategies when both are applied separately. Keywords Robust generalized dynamic inversion, under-actuated rotary inverted pendulum, sliding mode control, Lyapunov stability, semi-global asymptotic stability 1. Introduction Rotary inverted pendulum (RotIP) belongs to a class of under-actuated system, which is considered as a bench mark test bed that has been used extensively as a proof of concept tool to validate the performance of various control algorithms (Hamza et al., 2019). The RIP system is inherently nonlinear in nature with a highly unstable equilibrium point and may get excited subject to that makes it a challenging task for control design practi- tioners to design its effective control system (Furuta et al., 1992). The RotIP system comprised an horizon- tal actuated rotary arm and an unactuated pendulum link (see Figure 1) that makes it under-actuated in the sense that only one control input is available to control the two degrees of freedom (DoFs). The major control objectives of an RotIP system that has been examined in literature are swing-up control, switching control, and stabiliza- tion and trajectory tracking control. This article deals with the latter two cases in which the pendulum link is stabilized at vertical upright position while commanding the horizontal rotary arm either to stabilize at the origin or to follow certain time-varying angular trajectory profile. To deal with stabilization and trajectory tracking control, several linear, nonlinear, and intelligent control strategies have been investigated in literature. Among linear control techniques, proportional integral derivative and linear quadratic regulator (LQR) controllers (Akhtaruzzaman and Shafie, 2010; Sainzaya et al., 2017) are used for balance 1 Department of Electrical and Computer Engineering (ECE), King Abdulaziz University, Saudi Arabia 2 Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Saudi Arabia 3 Aeronautical Engineering Department, King Abdulaziz University, Saudi Arabia Received: 25 April 2019; accepted: 5 March 2020 Corresponding author: Ibrahim M Mehedi, Department of Electrical and Computer Engineering (ECE), Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jamea, Jeddah 21589, Saudi Arabia. Email: imehedi@kau.edu.sa