Root Locus-methode

Consider a cruise control system in a car designed to maintain a set speed automatically. The control system measures the vehicle's speed and fine-tunes the accelerator.

The root locus method aids in understanding how the cruise control system behavior varies when there are changes, like going uphill, downhill, or strong wind resistance.

A block diagram can represent this system. The transfer function for this system can be given with the quadratic formula applied to its denominator to determine pole locations for different gas pedal forces.

As pedal force varies, one system pole moves right, the other left. They converge at a point, then diverge into the complex plane, altering the system's closed-loop poles.

The root locus shows the impact of the pedal force variation on the system response: overdamped at low forces, critically damped at a specific force, and underdamped at high forces.

Since the root locus never crosses into the right half-plane, the system remains stable, irrespective of the pedal force.

Root locus analysis proves valuable for analyzing and designing systems higher than second order.