Applications of the Block Backstepping Algorithm on 2-DOF Underactuated Mechanical Systems: Some Case Studies
Before dealing with the actual content of this chapter, the authors would like to refer the definition of engineering from Merriam-Webster dictionary. It defines engineering as “the application of science and mathematics by which the properties of matter
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Applications of the Block Backstepping Algorithm on 2-DOF Underactuated Mechanical Systems: Some Case Studies
Abstract Before dealing with the actual content of this chapter, the authors would like to refer the definition of engineering from Merriam-Webster dictionary. It defines engineering as “the application of science and mathematics by which the properties of matter and the sources of energy in nature are made useful to people.” Indeed, engineers should deal with the practical problem instead of spending time in analyzing theoretical issues. In order to make the book compatible as well as a primed one for engineering readers, applications of the proposed control law on different members of underactuated mechanical system (UMS) family have been presented in a systematic manner. Several important UMSs such as acrobot, pendubot, Translational oscillator and rotational actuator (TORA), Furuta pendulum, Inertia wheel pendulum (IWP), inverted pendulum, single dimensional overhead crane fall under the category of two degrees of freedom UMSs. Quite often 2-DOF systems are being used as a standard laboratory test bed to gain physical insight of the complicated real-time systems [37, 38]. In addition, several higher order nonlinear systems can be represented as a cascade combination of 2-DOF systems. Keeping in view the immense importance of 2-DOF underactuated mechanical systems, this chapter presents systematic formulations of the proposed control algorithm on seven different 2-DOF systems. For the sake of better comprehensibility, at first, the system with most simple construction (having simple Lagrangian dynamic model) has been selected for demonstrating application of the proposed control law on an UMS. Thereafter, based on the constructional complexity of the other family members of the same class (i.e., 2-DOF underactuated mechanical systems) one after another system has been selected for the aforesaid purpose. Prime objective of this chapter is to ensure the fact that regardless of configuration of the concerned UMS, proposed control law is versatile enough to offer a satisfactory stabilizing performance for any kind of 2-DOF underactuated mechanical systems. Authors are very much confident with the fact that lucid treatment of this chapter would be able to convince the readers to implement the control law on different 2-DOF underactuated mechanical systems. Since the Inertia wheel
Electronic supplementary material The online version of this article (doi:10.1007/978-98110-1956-2_4) contains supplementary material, which is available to authorized users. © Springer Science+Business Media Singapore 2017 S. Rudra et al., Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems, DOI 10.1007/978-981-10-1956-2_4
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4 Applications of the Block Backstepping Algorithm on 2-DOF …
pendulum (IWP) possesses a comparatively simple dynamic model, at the onset, a comprehensive description of the application of proposed control law on an IWP is presented in Sect. 4.1 for better
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