Modeling and Nonlinear Control of a Single-link Flexible Joint Manipulator

In this experiment, we consider the nonlinear control of a robotic arm with joint flexibility. The specific mechanism under investigation is an attachment to rotary Quanser experimental setup. Flexibility is attained by attaching the link to the motor shaft using a pair of springs. There is some discretion in choosing the joint stiffness as there are different locations that the springs can be attached on the body as well as several spring choices. The goal of this project is to model and control the flexible joint for the case in which the arm is oriented vertically. This introduces a non-linearity into the system in the form of a sinusoid, as a result of the potential energy due to gravity. The output to be controlled is the tip angle, which is given by the sum of the motor angle θ and the joint deflection α with respect to the motor shaft. The non-linear model of the dynamics will be linearized by means of state feedback in such a way that the input-output response between the voltage applied to the motor and the tip angle becomes that of a linear system. After the system has been rendered linear by feedback, it can be controlled using any linear control system design.