TAILIEUCHUNG - Mechanical Engineering Handbook - Ep2

The frequency response of a fixed linear system is typically represented graphically, using one of three types of frequency response plots. A polar plot is simply a plot of the vector H in the complex plane, where Re is the abscissa and Im is the ordinate. A logarithmic plot or Bode diagram consists of two displays. | STATE-VARIABLE METHODS 829 Frequency Response Plots The frequency response of a fixed linear system is typically represented graphically using one of three types of frequency response plots. A polar plot is simply a plot of the vector H j u in the complex plane where Re w is the abscissa and Im ft is the ordinate. A logarithmic plot or Bode diagram consists of two displays 1 the magnitude ratio in decibels Mdb where Afdb ft 20 log Af u versus log ft and 2 the phase angle in degrees X versus log a . Bode diagrams for normalized first- and second-order systems are given in Fig. . Bode diagrams for higher-order systems are obtained by adding these first- and second-order terms appropriately scaled. A Nichols diagram can be obtained by cross plotting the Bode magnitude and phase diagrams eliminating log a . Polar plots and Bode and Nichols diagrams for common transfer functions are given in Table . Frequency Response Performance Measures Frequency response plots show that dynamic systems tend to behave like filters passing or even amplifying certain ranges of input frequencies while blocking or attenuating other frequency ranges. The range of frequencies for which the amplitude ratio is no less than 3 db of its maximum value is called the bandwidth of the system. The bandwidth is defined by upper and lower cutoff frequencies ac or by ứ 0 and an upper cutoff frequency if M ũ is the maximum amplitude ratio. Although the choice of down 3 db used to define the cutoff frequencies is somewhat arbitrary the bandwidth is usually taken to be a measure of the range of frequencies for which a significant portion of the input is felt in the system output. The bandwidth is also taken to be a measure of the system speed of response since attenuation of inputs in the higher-frequency ranges generally results from the inability of the system to follow rapid changes in amplitude. Thus a narrow bandwidth generally indicates a sluggish system response. Response to General .

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