Digital controlling of piecewise linear systems

A mechanical model of a digital balancing system is constructed and its stability analysis is presented. This model describes practical problems like backlash and sampling delay. Stationary and periodic solutions are determined numerically for the case of the system without sampling. The existence and stability of periodic solutions are checked analytically. Adding sampling delay to the system, the stability conditions change and above a critical value of the delay, the balancing is impossible. The stability chart is determined again, and stable motions are identified.