ABSTRACT
The frequency-response [1,2] method of analysis and design (frequency-domain analysis [FDA]) is a powerful technique for the comprehensive study of a system by conventional methods. Performance requirements can be readily expressed in terms of the frequency response as an alternative to the s plane analysis using the root locus. Since noise, which is always present in any system, can result in poor overall performance, the frequency-response characteristics of a system permit evaluation of the effect of noise. The design of a passband for the system response may result in excluding the noise and therefore improving the system performance as long as the dynamic tracking performance specifications are met. The frequency response is also useful in situations for which the transfer functions of some or all of the components in a system are unknown. The frequency response can be determined experimentally for these situations, and an approximate expression for the transfer function can be obtained from the graphical plot of the experimental data. The frequency-response method is also a very powerful method for analyzing and designing a robust multiple-input multiple-output (MIMO) [3] system with structured uncertain plant parameters. In this chapter, two graphical representations of transfer functions are presented: the logarithmic plot and the polar plot. These plots are used to develop the Nyquist stability criterion [1,4-6] and the closed-loop design procedures. The plots are also readily obtained by use of computer-aided design (CAD) packages like MATLAB®. The closed-loop feedback response M( jω) is obtained as a function of the open-loop transfer function G( jω). Design methods for adjusting the open-loop gain are developed and demonstrated. They are based on the polar plot of G( jω) and the Nicholas plot. Both methods achieve a peak value Mm and a resonant frequency ωm of the closed-loop frequency response. A correlation between these frequency-response characteristics and the time response is developed.
