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Fractional $PI^{\lambda }$ Controller for Fractional Order Linear Systems With Input Hysteresis

Necati OZDEMIR, Beyza Billur ISKENDER
In this work, single-input, single-output fractional order linear time invariant systems subject to input hysteresis, Relay and Duhem, are presented. It is assumed that the plant
is stable and fractional $PI^{\lambda }$ controller are designed with negative unity feedback to overcome the
undesirable effects of hysteresis. Tuning of the $PI^{\lambda}$ controller is demonstrated numerically by using Gr\"{u}nwald-Letnikov approach. It is shown that $PI^{\lambda }$ controller are more effective than $PI$ controller for the system subject to input Duhem hysteresis.
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