Dominant Mode Design of Third-Order Linear Control Systems: Part 1

Abstract

The method of design involves three steps:

Choose a closed loop system with the aid of contour plots of the performance criteria.

Obtain the poles of the open loop inferred by the chosen system.

Provide a synthesised transfer function which will correct the actual open loop to the form given by (2).

This paper deals with (1) and provides the contour plots for:

Time to 90% and to cross over.

Time to within 1%.

Overshoot and undershoot.

Maximum rate.

Velocity error constant.

Bandwidth.

Phase and gain margin.

These are plotted against c and k where c is the ratio of real pole abscissa to the real part of the dominant complex poles and k is the ratio of the imaginary to the real part of the complex poles. A preferred region is defined which will be suitable for many industrial applications.