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Root Locus Design

A common technique for meeting design criteria is root locus design. This approach involves iterating on a design by manipulating the compensator gain, poles, and zeros in the root locus diagram.

The root locus diagram shows the trajectories of the closed-loop poles of a feedback system as a single system parameter varies over a continuous range of values. Typically, the root locus method is used to tune the loop gain of a SISO control system by specifying a feedback gain the closed-loop pole locations.

Consider, for example, the tracking loop

where is the plant, is the sensor dynamics, and is a scalar gain to be adjusted. The closed-loop poles are the roots of

The root locus technique consists of plotting the closed-loop pole trajectories in the complex plane as varies. You can use this plot to identify the gain value associated with a desired set of closed-loop poles.

The DC motor design example focused on the Bode diagram feature of the SISO Design Tool. Each of the design options available on the Bode diagram side of the tool have a counterpart on the root locus side. To demonstrate these techniques, this example presents an electrohydraulic servomechanism.

The SISO Design Tool's root locus and Bode diagram design tools provide complementary perspectives on the same design issues; each perspective offers insight into the design process. Since the SISO Design Tool displays both root locus and Bode diagrams, you can also choose to combine elements of both perspectives in making your design decisions.


  Adding a Prefilter Example: Electrohydraulic Servomechanism