Function wbw: Finding the Bandwidth Frequency from the Damping Ratio and Peak or Settling Time

Below is the function wbw.m. This function will return the approximate bandwidth frequency of a system, given a corresponding damping ratio and rise or settling time. To employ the wbw.m function in MATLAB, enter wbw at the command line. You first will be prompted for a damping ratio. You will then be asked to enter "0" if you are using a settling time or "1" if you are using a peak time. Finally, you will be asked for the desired settling or peak time, and the bandwidth frequency will be returned. Copy the following text into a file wbw.m, and save it in the same directory as the MATLAB software, or in a directory which is contained in MATLAB's search path.

         function[] = wbw()
         DR = input('Damping Ratio?    ');
         n = 0;
         n = input('Settling Time(0) or Peak Time(1)?   ');
         if n == 0
         ts = input('Settling Time?   ');
         temp1 = sqrt((4*DR^4) - (4*DR^2) +2);
         temp2 =  1- (2*DR^2);
         temp3 = 4/(ts*DR);
         Wbw = temp3*sqrt(temp1 + temp2)
         if n ==1
         ts = input('Peak Time?   ');
         temp1 = sqrt((4*DR^4) - (4*DR^2) +2);
         temp2 =  1- (2*DR^2);
         temp3 = ts*sqrt( 1- DR^2);
         temp4 = pi/temp3;
         Wbw = temp4*sqrt(temp1 + temp2)