1.2 Compensator design using Bode plot

A compensator or controller is added to a system to improve its steady state as well as dynamic responses.

Nyquist plot is difficult to modify after introducing controller.

Instead Bode plot is used since two important design criteria, phase margin and gain crossover frequency are visible from the Bode plot along with gain margin.

Points to remember

• • Low frequency asymptote of the magnitude curve is indicative of one of the error constants depending on the system types.

• Specifications on the transient response can be translated into phase margin (PM), gain margin (GM), gain crossover frequency, bandwidth etc.

• Design using bode plot is simple and straight forward.

• Reconstruction of Bode plot is not a difficult task.

1.3 Phase lesd, Phase lag and Lag-lead compensators

Phase lead, phase lag and lag-lead compensators are widely used in frequency domain design.

Before going into the details of the design procedure, we must remember the following.

• • Phase lead compensation is used to improve stability margins. It increases system bandwidth thus improving the spread of the response.

• Phase lag compensation reduces the system gain at high frequencies with out reducing low frequency gain. Thus the total gain/low frequency gain can be increased which in turn will improve the steady state accuracy. High frequency noise can also be attenuated. But stability margin and bandwidth reduce.

• Using a lag lead compensator, where a lag compensator is cascaded with a lead compensator, both steady state and transient responses can be improved.

Bi-linear transformation transfers the loop transfer function in z -plane to w -plane.

Since qualitatively w -plane is similar to s -plane, design technique used in s -plane can be employed to design a controller in w -plane.

Once the design is done in w -plane, controller in z -plane can be determined by using the inverse transformation from w -plane to z -plane.

In the next two lectures we will discuss compensator design in s -plane and solve examples to design digital controllers using the same concept.