Experimental control of a ‎f‎lexible ‎l‎ink ‎by ‎the ‎method ‎of‎ ‎Controlled Lagrangian

The Controlled Lagrangian method is a branch of energy shaping methods that is designed to control underactuated mechanical systems. The method employs the mechanical energy (kinetic energy plus potential energy) of an artificial Lagrangian system, that generates similar equations of motion to the original underactuated system, as the Lyapunov function. This paper presents an application of the Controlled Lagrangian method to control an underactuated flexible link, and the results of a theoretical study through simulations confirmed by the results from an experimental setup. It is shown that the method’s performance is acceptable from a practical point of view as well as theoretical perspective. The simulations and the experimental results are presented in the sequel tovalidate the theoretical studies. The effect of changing controller gains on the designed controller performance is studied in more detail under the terms of the system’s mechanical energy. Moreover, gain tuning is also performed to attain high quality performance in the experimental study by the aid of their influence in the system’s nergy.Comparison of the proposed method with the partial feedback linearization method shows the degree of robustness of the proposed method. The simplicity of the gain tuning shows that the method can be implemented conveniently to control mechanical systems