Analysis of effects of differential gain on dynamic stability of digital force control

The paper presents an analytical investigation of the dynamics of digital force control. A one degree-of-freedom (DoF) mechanical system with low viscous damping is subjected to proportional–derivative (PD) force control. Analytical results are presented in the form of stability charts in the parameter space of sampling time, control gains and mechanical parameters. Simple closed form results include the largest stable proportional gain and the least steady state force error that provide synthesis of mechanical and control system parameter influences for the design of digital force control. Also, a novel analytical explanation is given why even the properly filtered force derivative signal is rarely used in practice, and why the occurring vibrations have frequencies one range smaller than that of the sampling frequency of the digital control.