The feedback system includes a PI controller defined as:
Gc(s) = 2 × (1 + 1 / (5s))
and a process transfer function:
Gp(s) = 5 / (2s² + 3s + 1)
with actuator gain Ga = 0.01 and sensor gain Gs = 20. The closed-loop transfer function becomes:
Gcl(s) = [Gc(s) × Gp(s) × Ga] / [1 + Gc(s) × Gp(s) × Ga × Gs]
To get the step response, compute:
Y(s) = Gcl(s) × (1 / s)
Then apply inverse Laplace transform:
y(t) = L⁻¹{Y(s)}
If the plotted response looks too small, the issue is likely the low actuator gain; you can either increase Ga or adjust the plot’s Y-axis range to make the response more visible.