An Innovative Control Design Procedure for Under-Actuated Mechanical Systems: Emphasizing Potential Energy Shaping and Structural Preservation

An Innovative Control Design Procedure for Under-Actuated Mechanical Systems: Emphasizing Potential Energy Shaping and Structural Preservation

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In this article, we propose a procedure to solve the controlled design for a class of under-actuated mechanical systems.Our proposed method can be viewed as a sub-method of the IDA-PBC Panasonic NN-CS89LB 4-in-1 Combination Steam Oven with Microwave or Controlled Lagrangian approaches, with a particular focus on shaping the potential energy.By emphasizing potential energy shaping, we can effectively tackle the bottleneck presented by the matching equation in these approaches.Moreover, our method leverages a suitable coordinate transformation that is inspired by the physics of the system, further enhancing its efficacy.Therefore, our design procedure is based on a coordinate transformation plus potential energy shaping in the new coordinates, and its Milk - Non Dairy existence and possibility of potential energy shaping can be verified via some algebraic calculations, making it constructive.

To illustrate the results, we consider the cart-pole system and a recently introduced under-actuated mechanical system named swash mass pendulum (SMP) (Salamat and Tonello, 2021).The SMP consists of a pendulum made of a rigid shaft connected to a pair of cross-shafts where two swash masses can move under the action of servo-mechanisms.