Sampling Delay and Backlash in Balancing Systems

A mechanical model of a digital balancing system is constructed and its stability analysis is presented. This model considers experimental problems like backlash and sampling delay. The conditions of existence of stable stationary and periodic solutions are determined for the case of the system without delay. Phase diagrams and bifurcation diagrams are revealed after simulations and bifurcation analysis. Adding sampling delay to the system, the stability conditions are changed and above a critical value of the delay, the balancing is impossible. The stability conditions and the stability chart are determined again and the critical sampling delay is calculated versus the parameters describing the system.