Posted: May 22nd, 2023
The double inverted pendulum is an age old complex system of sorts normally used as a yardstick to ascertain the efficacy of any devised method of control due to its structural simplicity. Generally, in stably controlling a double inverted pendulum, there are six input items required for the two pendulums in all the angular controls and a suitable cart control position. Studies show that there several methods that can be employed in the derivation of equations aimed at expressing the principle of double inverting. As an example, Zhong and Rock (2001) demonstrate the possibility of applying Newtonian approaches in the description of this principle. In addition, they propose the use of the Euler-Lagrange approach. This approach entails the utilization of the Euler-Lagrange equation together with the Lagrangian. Various approaches have been put forward, but in most cases the Lagrange approach is employed due to its simplicity. Unique specifications are usually put in place in the process of isolating the most suitable system requirements. Mechanical damping characteristics need to be identified and these are in turn used in choosing the most suitable approach when dealing with linear systems (Rubi and Avello 2002). The specifications of the invariable DC motors should also be stated according to Rubi and Avello (2002). The determination of the amount of noise produced during the measurement process is a key factor that has been suggested in the construction of actual systems (Katupitiya and Luong 2001).
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