Flatness based Control of under-actuated flexible link system

A flexible rod is a combination of continuous points. Each point has its degree of freedom in space, which means that the rod has an infinite degree of freedom. An infinite number of inputs would be needed to control this rod. However, if we are interested in controlling only the end of the rod then it can be achieved by controlling the other end in the same way as an angler controls the fish rods. For the study purpose, we discretize the rod into n rigid link connected through the revolute joints having torsional springs. For a considerable number of links, this setup will mimic the nature of the continuous flexible rod. The ‘n’ joints in the system, in general, will need n actuators and sensors to achieve the desired state. However, using the concept of differential flatness we can control this under actuated system. The required force and torque inputs is expressed in terms of flat outputs. Exploiting this property, the trajectory of the rod end is controlled.