TABLE OF CONTENTS 12 1 To apply frequency-response transfer functions to determine response of linear systems to sinusoidal or other periodic inputs.
12 2 To construct (analytically and/or with MATLAB) and to interpret magnitude and phase characteristics (Bode diagrams) of system frequency response.
12 3 To construct (analytically and/or with MATLAB) and to interpret polar plots of frequency response (Nyquist diagrams).
12 4 To develop, manipulate, and simplify transfer function block diagrams of complex systems made up of many subsystems.
The response of linear systems to sinusoidal inputs forms the basis of an extensive body of theory dealing with the modeling and analysis of dynamic systems. This theory was developed first in the field of communications (telephone and radio) and later became extended and then widely used in the design and development of automatic control systems. The theory is useful not only in determining the sinusoidal response of a system but also in specifying performance requirements (as in sound-system components or in a radar-tracking system), in finding the responses to other periodic inputs (square wave, sawtooth wave, etc.), [1] and for predicting the stability of feedback control systems (amplifiers, regulators, and automatic controllers). A graphical portrayal of the input and output sinusoids of a typical linear system is provided in Fig. 12.1.
[1] See Appendix 1 for a review of the Fourier series and its use in describing a periodic time function...
