Compensators Introduction

Cuthbert Nyack

The basic Control system is shown below where G_c(s) = K.

Designing a system in the frequency domain means adjusting K until the performance specification is satisfied. Performance specifications in the frequency domain include phase and gain margins, resonant frequency and peak, crossover frequency and bandwidth. If adjustment of K is not enough and the system variables cannot be changed then G_c(s) can be a compensator with poles and zeros. G_c(s) can be located at different points in the loop. The location in the diagram above is described as series compensation. The standard Compensators are Lead, Lag and LagLead with transfer functions illustrated below:-

The applets illustrate how the different Compensators affect the frequency domain performance specifications. When enabled some of the applets are illustrated below:-

Because of the numerical calculations used here, the numbers shown on some of the applets are only approximate.

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