  We study the properties of remnant function, which is a function of output
remnant versus amplitude of the input signal, of Preisach hysteresis operators.
The remnant behavior (or the leftover memory when the input reaches zero)
enables an energy-optimal application of piezoactuator systems where the
applied electrical field can be removed when the desired strain/displacement
has been attained. We show that when the underlying weight of Preisach
operators is positive, the resulting remnant curve is monotonically increasing
and accordingly a Newton and secant update laws for the iterative remnant
control are proposed that allows faster convergence to the desired remnant
value than the existing iterative remnant control algorithm in literature as
validated by numerical simulation.
