Design of first order controllers for a flexible robot arm with time delay

In an earlier work, Gündeş et al. (2007), stabilizing PID controllers for a class of unstable plants with time delays (I/O delays) are obtained. By utilizing this approach and methods given in Özbay and Gündeş (2007, 2014) we aim to investigate appropriate PI, PD and PID controllers by finding the maximum allowable boundaries for each controller parameter. A model of a flexible robot arm which includes a time delay and an integrator is considered as an application example. It is aimed to find the optimal coefficients for the derivative and integral gains such that the designs achieve a set of performance and robustness objectives. Stability and robustness properties of the closed-loop system are also investigated. Specifically, for PD controller design, optimal derivative action gain is determined under various performance objectives. For PI controller design, optimal P (proportional) and D (derivative) gains are determined to achieve the least fragile integral action gain. Moreover, system performance is compared with other PID designs considering different types of control objectives.