Domain analysis

The manner in whieh a dynamie system responds to an input, expressed as a funetion of time, is ealled the time response. The theoretieal evaluation of this response is said to be undertaken in the time domain, and is referred to as time domain analysis. It is possible to eompute the time response of a system if the following is known ... 

Frequeney domain analysis is eoneerned with the ealeulation or measurement of the steady-state system output when responding to a eonstant amplitude, variable frequeney sinusoidal input. Steady-state errors, in terms of amplitude and phase relate direetly to the dynamie eharaeteristies, i.e. the transfer funetion, of the system. 

The Nichols chart shown in Figure 6.26 is a rectangular plot of open-loop phase on the x-axis against open-loop modulus (dB) on the jr-axis. M and N contours are superimposed so that open-loop and closed-loop frequency response characteristics can be evaluated simultaneously. Like the Bode diagram, the effect of increasing the open-loop gain constant K is to move the open-loop frequency response locus in the y-direction. The Nichols chart is one of the most useful tools in frequency domain analysis. 

This tutorial introduees the reader to time domain analysis using MATLAB. It uses eommands from the Control System Toolbox. A list of the eommands ean be found using... 

With frequency-domain analysis, the average spectmm for a machine-train signature can be obtained. Recurring peaks can be normalized to present an accurate representation of the machine-train condition. Figure 43.20 illustrates a simplified relationship between the two methods (i.e., time-domain and frequency-domain). 

The real advantage of frequency-domain analysis is the ability to normalize each vibration component so that a complex machine-train spectrum can be divided into discrete components. This ability simplifies isolation and analysis of mechanical degradation within the machine-train. 

In addition, it should be noted that frequency-domain analysis can be used to determine the phase relationships for harmonic vibration components in a typical machine-train spectrum. Frequency-domain normalizes any or all running speeds, where time-domain analysis is limited to true running speed. 

Reciprocating Limitations of the frequency-domain analysis prevent total analysis of reciprocating compressors. It is limited to the evaluation of the rotary forces generated by the main crankshaft. Therefore, time-domain and phase analysis are required for complete diagnostics. 

Even as we speak of time-domain analysis, we invariably still work with Laplace transform. Time-domain and Laplace-domain are inseparable in classical control. 

From the last example, we may see why the primary mathematical tools in modem control are based on linear system theories and time domain analysis. Part of the confusion in learning these more advanced techniques is that the umbilical cord to Laplace transform is not entirely severed, and we need to appreciate the link between the two approaches. On the bright side, if we can convert a state space model to transfer function form, we can still make use of classical control techniques. A couple of examples in Chapter 9 will illustrate how classical and state space techniques can work together. 

Dorf, R. C., Time-Domain Analysis and Design of Control Systems, Addison-Wesley, Reading, Massachusetts, 1964. 

Redford, G. I. and Clegg, R. M. (2005). Polar plot representation for frequency-domain analysis of fluorescence lifetimes. J. Fluoresc. 15, 805-15. 

Forde, T. and Hanley, Q. S. (2006). Spectrally resolved frequency domain analysis of multi-fluorophore systems undergoing energy transfer. Appl. Spectrosc. 60, 1442-52. 

Reyes-Cruz, G., Hu, J., Goldsmith, P. K., Steinbach, P. J., and Spiegel, A. M. (2001) Human Ca2+ receptor extracellular domain. Analysis of function of lobe I loop deletion mutants../. Biol. Chem. 276, 32145-32151. 

LAPLACE-DOMAIN ANALYSIS OF CONVENTIONAL FEEDBACK CONTIOL SYSTEMS 345... 

LAPIACE-DOMAIN ANALYSIS OF CONVEtmONAL FEEDBACK CONTROL SYSTEMS... 

I.APLACE-DOMAIN ANALYSIS OF CONVF.NTIONAL FEEDBACK CONTROL SYSTEMS 357... 

LAPLACE-DOMAIN ANALYSIS OF ADVANCED CONTROL SYSTEMS 377... 

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