Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Design and Implementation of a Furuta Pendulum Device for Benchmarking Non-Linear Control Methods

Furuta pendulum is an academic benchmark example for evaluating non-linear control algorithms. The main aim of this dissertation is to study this physical system, showing its dynamic model and several strategies for its control. An assortment of swing-up and upright control approaches is reported with its design and simulations. Besides, this document describes the project development which is being done at the FabLab of the Obuda University, whose objective is to design and manufacture a demonstration device that is capable to test and display various control strategies. Requirements and specications of the design, used tools and future work are described. The dissertation is structured in eight different chapters: (1) History of the Furuta pendulum, describing the origin of this system; (2) State-of-the-art in non-linear control, giving a background for the different control strategies; (3) Dynamic model of the Furuta pendulum; (4) Swing-up by energy control, based on the work of Astrom and Furuta; (5) Stabilizing local control, via full state feedback; (6) Hybrid control, which sums up the previous approaches; (7) Development project, which describes the work realized in the FabLab and (8) Conclusion, discussing the knowledge extracted from the development of this thesis

Multi-mode control based on HSIC for double pendulum robot

Double pendulum robot has four equilibrium points: Down-Down, Down-Up, Up-Down, and Up-Up. Define the transfer control from one equilibrium point to another equilibrium point as acrobatic action of DPR, and there are total of 20 acrobatic actions. This paper proposes the multi-mode control algorithm based on Human Simulated Intelligent Control theory for the realization process of those acrobatic actions, which has the structure of multi sub-controllers and multi control modes. As an example, the acrobatic action from Down-Up to Up-Down is realized in simulation and real-time experiments, and the results demonstrate the effectiveness of the proposed algorithm