O'Reilly logo

Advanced Modern Control System Theory and Design by Stanley M. Shinners

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

APPENDIX B

CHARACTERISTIC RESPONSES OF SECOND-ORDER CONTROL SYSTEMS

The purpose of this appendix is to describe the transient response of a typical feedback control system which is referred to many times in this book. We consider a very common configuration in which a two-phase ac servomotor is enclosed by a simple unity feedback loop. Figure 4.1 illustrates the block diagram of this second-order system. For purposes of simplicity, the gain of the amplifier driving the motor is assumed to be unity.

The closed-loop transfer function of this system is given by

images

By defining the undamped natural frequency ωn and the dimensionless damping ratio ζ as

images

images

Figure B.1 Second-order feedback system containing a two-phase ac servomotor.

Eq. (B.1) can be rewritten as

images

The parameters ωn and ζ are very important for characterizing a system's response. Note from Eq. (B.3) that ωn turns out to be the radian frequency of oscillation when ζ = 0. As ζ increases from 0, the oscillation decays exponentially and becomes more damped. When ζ 1, an oscillation does not occur.

We assume that the initial conditions ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required