Page 549 - Mechanical Engineers' Handbook (Volume 2)

540 Control System Performance Modification

Figure 35 Closed-loop frequency response specifications.

Transient specifications are typically based on a step input response. By specifying the
rise time, overshoot, and settling time, the response is confined to within the shaded region
of Fig. 34. It is then assumed that a system whose step response satisfies these constraints
will have an acceptable transient response to any kind of input.
In the frequency domain the bandwidth and the resonant peak of the closed-loop fre-
quency response are measures roughly corresponding to rise time and overshoot, respectively.
Specification of these parameters constrains the magnitude of the closed-loop frequency
response to the region shown in Fig. 35. An alternative way of constraining the transient
response by frequency-domain criteria is to stipulate the smallest acceptable gain and phase
margins.
Often used compensators are the so-called three-term controllers (PID) and lag and lead
compensators. These controller or compensator designs are discussed later. They are often
done on a trial-and-error basis and can be designed in the s-domain or the z-domain de-
pending on the type of application. Continuous-time or s-domain compensators can often be
converted to equivalent z-domain compensators by techniques such as pole–zero maps, hold
equivalence, and Butterworth pole configurations. 4

REFERENCES

1. B. C. Kuo, Automatic Control Systems, Prentice-Hall, Englewood Cliffs, NJ, 1982.
2. K. Ogata, Modern Control Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1970.
3. G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, Addison-
Wesley, Reading, MA, 1986.
4. G. F. Franklin and J. D. Powell, Digital Control of Dynamic Systems, Addison-Wesley, Reading, MA,
1980.

BIBLIOGRAPHY
Bode, H. W., Network Analysis and Feedback Amplifier Design, Van Nostrand, New York, 1945.
Chestnut, H., and R. W. Mayer, Servomechanisms and Regulating Systems Design, 2nd ed., Vol. 1, Wiley,
New York, 1959.
D’Azzo, J. J., and C. H. Houpis, Linear Control System Analysis and Design, McGraw-Hill, New York,
1988.
Distefano, J. J., III, A. R. Stubberud, and I. J. Williams, Feedback and Control Systems (Schaum’s
Outline Series), Schaum Publishing, New York, 1967.
Doebelin, E. O., Control System Principles and Design, Wiley, New York, 1985.