In recent years, several methods of identification of the frequency response of stable processes have been developed. However, for unstable processes these methods are not applicable. In this work, a sinusoidal-signal based relay method is presented which can be used to identify several points on the Nyquist plot of an unstable process. The method is referred to as RFS (Relay Feedback with Sinusoidal input). The procedure involves injecting a mixed sinusoidal signal into the feedback loop stabilized by a standard relay. Fourier analysis techniques are then used to estimate Nyquist points corresponding to various frequencies. Information obtained from the RFS method can then be used to design robust controllers using tuning rules which consider both the minimum and maximum gains needed to stabilize the process. The methods presented in this work should help engineers involved in process control and modeling, to deal with a range of challenging unstable processes.

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