Sinusoidal dither in a relay feedback system

This paper examines the effect of a sinusoidal dither in a relay feedback system. The use of dither in achieving signal stabilization and quenching of limit cycles is well known in nonlinear systems. The effect of dithering is a similar to that of forced oscillations where the external signal causes oscillations of the same frequency to occur in the system. This paper shows that FO of higher frequencies will produce a lower amplitude and achieve a reduction in the amplitude of oscillations for dither periods below a certain value, T_f*. This idea is used to design a sinusoidal dither signal which results in reduced oscillation amplitudes. Analytical expressions for T_f* are obtained for first and second order plants. For higher order systems, the Tsypkin Loci is used to identify T_f*. Simulation studies are presented to illustrate the results.