As we mentioned before, we can relate bandwidth frequency to closed-loop natural frequency and damping ratio. Thus, we can relate bandwidth frequency to damping ratio and rise or settling time with the following equations.

Settling Time

In order to make our life easier, we usually plot these equations instead of plugging in the values:

Rise Time

Again, we usually look at the graph instead of plugging in the values.

Matlab Code

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)
	end
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)
	end

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8/27/96 BRN