The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey

Abstract

For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, in nonlinear control theory. The fundamental focus of this work is to enhance the wealth of this robotic benchmark and provide an overall picture of historical and current trend developments in nonlinear control theory, based on its simple structure and its rich nonlinear model. In this review, we will try to explain the high popularity of such a robotic benchmark, which is frequently used to realize experimental models, validate the efficiency of emerging control techniques and verify their implementation. We also attempt to provide details on how many standard techniques in control theory fail when tested on such a benchmark. More than 100 references in the open literature, dating back to 1960, are compiled to provide a survey of emerging ideas and challenging problems in nonlinear control theory accomplished and verified using this robotic system. Possible future trends that we can envision based on the review of this area are also presented.

Output Feedback Control With Constraints for Nonlinear Systems via Piecewise Quadratic Optimization

“…Nowadays the inverted pendulum is considering as a fundamental benchmark in nonlinear control theory [6]. Hence, for an effective verifying of control performance of proposed controller it will be an adequate controlled object.…”

Dynamics of theN-link pendulum: a fractional perspective

“…Known for their rich dynamics, pendular systems (PS) have been widely used for modelling and as benchmark systems in many areas, namely long-chain molecular physics (Mezić, 2006;Vesely, 2013), control theory (Boubaker, 2013;Kurdekar & Borkar, 2013;Larcombe, 1992), robotics (Ali, Motoi, Heerden, & Kawamura, 2013;Brisilla & Sankaranarayanan, 2015), biomechanics (Barin, 1992;Schiehlen, 2014), building structures (Housner, 1963;Zayas, Low, & Mahin, 1990), chaos and nonlinear dynamics (Gmiterko & Grossman, 2010;Hedrih, 2008;Lobas, 2005;Yu & Bi, 1998), among others (Baker & Blackburn, 2005;Jadlovská, Sarnovskỳ, Vojtek, & Vošček, 2015).…”

“…Another point of view is the analysis of the complex dynamics emerging in PS with a large number of links (Awrejcewicz et al, 2008). In all cases, the popularity of PS is due to their seminal properties, revealing phenomena ubiquitous in natural and man-made systems (Boubaker, 2013). Despite the existing models being able to deal with PS of arbitrary number of links, the lack of general tools for dynamical analysis and performance visualisation is recognised (Rivas-Cambero & SausedoSolorio, 2012).…”

Benchmarking Networked Control Systems

“…In particular, a variety of measurements has been conducted for inverted pendulums [4]- [6] (which, according to Boubaker [7], have been used since the 1950s as a control benchmark for its simple structure but nonlinear dynamics) and batch reactors [8]- [10]. All these implementations perform real-world measurements of standard NCSes to proof the validity of their contributions.…”