Second Order Transfer Function. Decomposing the system function into a cascade of a simple pole a zero and a second order transfer function. Equation1 is the standard form or transfer function of second order control system and equating its denominator to zero gives s2 2xi omega ns omega n2 02 equation2 called the characteristic equation of second order control system.
I if ζ1 we have overdamped response and two different real poles. Second order transfer functions 2002 b. Its analysis allows to recapitulate the information gathered about analog filter design and serves as a good starting point for the realization of chain of second order sections filters.
First order processes second order processes order of the process is the degree of the characteristic denominator polynomial the relative order is the difference between the degree of the denominator polynomial and the degree of the numerator polynomial.
The roots s 1 and s 2 are real. Equation1 is the standard form or transfer function of second order control system and equating its denominator to zero gives s2 2xi omega ns omega n2 02 equation2 called the characteristic equation of second order control system. Fraccsrsfracomegan2s2omegan2 rightarrow csleft fracomegan2s2omegan2 right rs. For the second order system function evaluate and show on the bode plot the peak value and peak frequency ωr.