Complex Root Limits in PID-Controlled Systems: An Approach Using D-Decomposition

This thesis develops a new approach to the design of Proportional Integral Derivative (PID) controllers, solving an open problem in identifying feasible pole placement for controlled systems that allows for optimization of transient time-domain characteristics such as damping ratio and response oscillation. It also offers an alternative to previously developed methods for reducing overshoot and settling time of the step response. The method relies on the novel application of previously developed techniques. Fundamentally, the method uses a variant of Neimark’s D-Decomposition technique to place all closed-loop poles of a system in a specified region of the complex plane