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.

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Abstract-For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, for teaching and researches in control theory and robotics. This paper presents the key motivations for the use of that system and explains, in details, the main reflections on how the inverted pendulum benchmark gives an effective and efficient application. Several real experiences, virtual models and web-based remote control laboratories will be presented with emphasis on the practical design implementation of this system. A bibliographical survey of different design control approaches and trendy robotic problems will be presented through applications to the inverted pendulum system. In total, 150 references in the open literature, dating back to 1960, are compiled to provide an overall picture of historical, current and challenging developments based on the stabilization principle of the inverted pendulum.

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In this article, a fast terminal sliding mode control technique is used for robust tracking control of a nonlinear uncertain mass-spring system in the existence of external perturbation. This system is considered as a benchmark problem in the flexible joint mechanisms. The joints flexibility in the robotic systems creates one of the most significant sources of parametric uncertainties. The theory of Lyapunov stability is used for the formulation of the proposed control method, and the presence of the sliding around the switching surface is satisfied in the finite time. Simulation results as well as the experimental verifications prove the efficiency and applicability of the suggested approach in the presence of parametric uncertainty, noise, and exterior disturbance.

This paper presents an efficient and fast method for fine tuning the controller parameters of robot manipulators in constrained motion. The stability of the robotic system is proved using a Lyapunov-based impedance approach whereas the optimal design of the controller parameters are tuned, in offline, by a Particle Swarm Optimization (PSO) algorithm. For designing the PSO method, different index performances are considered in both joint and Cartesian spaces. A 3DOF manipulator constrained to a circular trajectory is finally used to validate the performances of the proposed approach. The simulation results show the stability and the performances of the proposed approach.

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A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.