A system has overall transfer function \(T\left( s \right)=\frac{G\left( s \right)}{1+G\left( s \right)H\left( s \right)}\)
The expression for the peak time tp can be obtained by equating to zero, the derivative of:
1
input r(t) with respect to time.
2
the convolution of r(t) and L-1[T(s)] with respect to time.
3
\(\frac{C\left( s \right)}{R\left( s \right)}\) with respect to the time where C(s) is the system response.
4
δ(t) T(p) with respect to time, where δ(t) is the impulse response.