Stability analysis for dynamic control on contact with soft interface in continuous-discrete time system

We analyze the stability of dynamic control on contact with a soft interface, the viscoelastic material between a manipulating finger and manipulated object. First, we model a dynamic control system on contact with a soft interface. The system is described in continuous-discrete time. Second, we formulate the dynamics using the modified z-transform in the continuous-discrete time system for feedback and feedforward control. Thus, we show that the stability of the system depends on viscoelasticity of the soft interface for feedback control. In particular, we point out that, in critical stability, the relationship between material viscosity and sampling time is not monotonous. Next, we analyze this phenomenon by the root locus method. Finally, we compare the stability analysis by the modified z-transform, simulations based on the Runge-Kutta method, and a regular z-transform. Thus, we demonstrate that the relationship is specific to the continuous-discrete time system.