A three-dimensional cam for generating a function of two variables is shown in Figure P12.12(a). Both $x$ and $\theta$ may be controlled using a position control system $[19]$. The control of $x$ may be achieved with a DC motor and position feedback of the form shown in Figure P12.12(b), with the DC motor and load represented by
$$
G(s)=\frac{K}{s(s+p)(s+4)},
$$
where $1 \leq K \leq 3$ and $1 \leq p \leq 3$. Normally $K=2.5$ and $p=2$. Design an ITAE system with a PID controller so that the peak time response to a step input is less than 3 seconds for the worst-case performance.