Root Locus Plot

Root Locus Plot:

In the electrical drives employing closed loop control techniques, it is often necessary to investigate the effects of changing the parameters of the system on its stability. The drive motor used itself has several parameters and time constants which affect the stability of the motor itself. The controls used also introduce some time lags which may affect the system stability. It is also required sometimes to investigate the sensitivity of the drive system to para­meter variations. The feedback control used makes the system less sensitive to parameter changes. The Root Locus Plot technique is very useful in investigating

1.the stability of the system,

2.the effect of variation of parameters so that the limits of these para­meters can be determined for stable operation.

The method is particularly suitable in the design stage of the system when there is some latitude in the choice of system parameters.

The Root Locus Plot technique can be applied to determine the dynamic response of the system. This method associates itself with the transient response of the system and is particularly useful in the investigation of stability characteristics of the system. It can also be used to determine the stability boundaries of the system. Selection of suitable parameters may be made using the root locus analysis.

It is a well established fact that the condition of roots of the characteristic equation governs the transient behavior and hence the stability of the system. In the Root Locus Plot technique which is essentially a graphical procedure, the locus of the roots on the s-plane is afforded by the variation of the suitable parameters. The Root Locus Plot are drawn in the complex plane, as the roots may be real or complex.

In this technique also the open loop transfer function may be used to simplify the procedure. The plots drawn and the information obtained from these plots pertain to a closed loop system. The plots clearly illustrate the effects of variation of parameters on system stability and the nature of response. The branch of a root locus shows all the possible values of one root when a pa­rameter is varied. All the separate branches of the Root Locus Plot give the effect of variation of parameters.

The Root Locus Plot technique is essentially a time domain technique. Frequency response data can be obtained from the Root Locus Plot. Using this technique the open loop poles and zeros can be modified to satisfy the requirements to be met by closed loop poles and zeros. It may be noted here that a slight change in the pole zero configuration may cause a significant changes in the root locus configuration.