Tracking and regulation control of a two-degree-of-freedom robot arm

In this thesis, servomechanism synthesis for a two-degree-of-freedom (2-DOF) serial chain revolute-revolute joint robot arm that achieves internal stability, reference signal tracking, and torque disturbance regulation is considered. We first derive the dynamic equations of the robot arm with Euler-Lagrange method by ignoring the effects of friction. Then, using system identification methods, we derive a plant model based on data obtained from a real system through experiments. We then employ PD and PID controllers along with the gravity compensation method to stabilize the system using the passivity properties. Alternatively, we linearize the system model and examine the performance of the same controllers. A linear controller is synthesized by invoking the internal model principle and is directly applied to the nonlinear plant model. The proposed fifth order linear controllers at each channel of the robot arm suffices to achieve not only tracking of step, ramp, and sinusoidal signals at one frequency, but also regulation of step, ramp, and sinusoidal disturbances. It is shown via simulations that, even though the plant model is nonlinear, the synthesized linear controller performs better than the commonly used PID controllers.