PID control of second-order systems with hysteresis

The efficacy of proportional, derivative and integral (PID) control for set point regulation and disturbance rejection is investigated in a context of mechanical systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the restoring force action of the system ("hysteretic spring" effects); in the second, the hysteretic component resides (externally) in the input channel (e.g. piezo-electric actuators). In each case, robust conditions on the PID gains, explicitly formulated in terms of system data, are determined under which asymptotic tracking of constant reference signals and rejection of constant disturbance signals is guaranteed.