Novel controller design for plants with relay nonlinearity to reduce amplitude of sustained oscillations: Illustration with a fractional controller

•Our paper introduces a controller design formulation for plants containing relay nonlinearity.•The controller produces 'reduced' amplitude sustained oscillations in the output along-with desirable loop performance.•Describing function of nonlinearity is utilized for shaping the limit cycles and controlling the transient behavior.•The methodology is illustrated by designing a fractional PI controller.

This paper proposes a novel constrained optimization problem to design a controller for plants containing relay nonlinearity to reduce the amplitude of sustained oscillations. The controller is additionally constrained to satisfy desirable loop specifications. The proposed formulation is validated by designing a fractional PI controller for a plant with relay.