Control design for impedance model with feedback delay

In haptic and telemanipulation devices stability and transparency are contradicting requirements. Due to the network delay the control process may become unstable. In our research we consider the coupled impedance type control algorithms for force reflecting telemanipulation. There are several solutions in the control literature to handle constant time delay in feedback systems, but varying delay is still a challenge. This paper attempt to handle varying delay by a novel approach. We propose a control structure where the system with feedback delay is approximated by a non-delayed model with modified time constants. The controller is designed according to this non-delayed substitute system and the control signal is computed using its observed state vector. Tensor Product (TP) Model Transformation is utilized to make a compact polytopic representation of the observer and controller for various time delays. In this method the actual value of the feedback delay is considered as an input parameter of the TP type controller and observer. As example, a single degree of freedom impedance model with feedback delay is discussed. The results are confirmed by numerical simulation.