Frequency Response Characteristics
MATLAB has a powerful GUI tool, called LTI Viewer, for obtaining both the time and frequency response characteristics of a given Linear Time Invariant system. The basic features of this GUI tool and its use for time response analysis have already been given in MATLAB Module 5. The use of LTI Viewer for frequency response analysis is similar.
The frequency response parameters can also be obtained from the plots generated by the commands nyquist, bode, and nichols. Right-clicking away from the curves generated by these commands brings up a menu. From the menu, various frequency-response characteristics can be selected.
Important measures of performance of control systems are the resonance peak Mr , the resonance frequency , the bandwidth of the closed-loop frequency response, phase margin , gain margin GM , gain crossover frequency , and phase crossover frequency .
We observed in module 8 that the measures of performance of a closed-loop system can be obtained from the Bode plots of its open-loop transfer function. In this module, we will use Nichols chart that gives closed-loop performance measures from the open-loop frequency response. However, this technique is applicable only for unity feedback systems. For non-unity feedback systems, we construct the closed-loop frequency response and therefrom obtain the measures of performance.
Non-unity Feedback Systems
Unity Feedback Systems on Nichols Chart