Root Loci for Positive-Feedback Systems

A Hartley oscillator, a positive feedback system, maintains oscillation by feeding the output back to the input in phase, reinforcing the signal.

Positive feedback systems can be interpreted as negative feedback systems with inverted feedback signals.

The root locus in these systems includes all s-plane points where the system transfer function angle equals 360 degrees.

These systems' branches and symmetry rules mirror those in negative feedback systems.

However, the root locus exists on the real axis to the left of an even number of finite open-loop poles and/or zeros.

As the locus approaches infinity, it appears as straight lines, similar to asymptotes, with different slopes but identical intercepts on the real axis.

Negative-feedback systems with negative gain also follow these principles, forming an equivalent positive-feedback system by shifting the negative gain rightward past the pick-off point.

The root locus, left of an even count of real, finite open-loop poles and/or zeros, spans the entire positive extension of the real axis at designated intervals.

The intersections and angles are then determined to complete the sketch of the root locus.