Question

Consider a process with transfer function $G_{p} = 2e^{−s} / (5s+1)².$ A first-order plus dead time (FOPDT) model is to be fitted to the unit step process reaction curve (PRC) by applying the maximum slope method. Let $τ_{m}$ and $θ_{m}$ denote the time constant and dead time, respectively, of the fitted FOPDT model. The value of $τ_{m}/θ_{m}$ is ____ (rounded off to 2 decimal places). Given (as shown in the figure): for G $= 1/(τs+1)²,$ the unit step output response y(t) $= 1−(1+t/τ)e^{−t/τ},$ dy(t)/dt $= (t/τ²)e^{−t/τ},$ and $d²y(t)/dt² = (1/τ²)(1−t/τ)e^{−t/τ}.$

Official answer: 5.6 to 5.7