Abstract:
This thesis focuses on the output regulation of control-affine time-invariant non-minimum phase nonlinear systems, specifically regarding the output tracking of time-varying signals in the presence of system uncertainty. Much of the published output regulation theory for this class of system faces significant barriers to practical application. The more practical approaches, which are not limited by these same barriers, have seen limited application to practical systems within the literature. Three such approaches – the kth-order approximate output regulator, the kth-order robust output regulator, and the stable system centre based sliding mode control approach – are herein applied to two case studies in order to both provide additional examples of their application to physically meaningful systems and to gain further insight into the strengths and weaknesses of each approach in regard to practical application e.g. when facing various forms of system uncertainty. Furthermore, a novel "approximate stable system centre" approach was developed and shown to provide improved tracking performance over the standard stable system centre approach under certain conditions. The two case studies considered are the spherical inverted pendulum, which is a more complex system compared to the standard SISO inverted pendulum on a cart commonly used a benchmark nonlinear system, and the two-wheeled balancing robot, which serves as a direct practical application in the area of mobile robotics. Simulations were conducted for the 2D position control of the spherical inverted pendulum and the 2D forward and yaw speed control of the two-wheeled robot in the presence of parametric and unstructured uncertainty. Measurement noise and delay was additionally considered in the two-wheeled robot simulations. Experimental testing was also conducted for the straight-line position control of the two-wheeled robot. Overall, the kth-order robust output regulator provided the most accurate steady state tracking under most conditions considered, but suffered from poor transient response. The kth-order approximate output regulator gave the fastest transient response, but only provided acceptable steady state performance under low levels of uncertainty. The approximate stable system centre approach provided a well-balanced performance under most conditions, but was the most sensitive to the presence of system delays due to use of the sliding mode controller.