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Optimal sign inverting control for multiple time-delayed systems

In this paper, we present a controversial control concept, Sign Inverting Control (SIC), for systems with multiple time delays. The main motivation for SIC is to provide added robustness capability of a system against delay variations. A nominal control law is formulated for non-delayed case and SIC suggests the sign inversion in these nominal control gains, which is a paradoxical proposition, in order to enlarge the stable operating regions in the domain of the delays. SIC functions with one critical premise that, the union of two control schemes, i.e., nominal and SIC, produces a larger stable region than each of its components does. The selection of an ideal nominal control law for a successful SIC strategy invites some compromising scenarios. Thus an optimization procedure is followed. To achieve this, we propose a systematic procedure starting with an LQR (Linear Quadratic Regulator)-based controller. Then, a 1-D parametric optimization is performed using a scaling factor on the control gain. The proposed optimal SIC procedure is effectively implemented on a single-axis manipulator setup.