(Solved): The \( \mathrm{P} \) (proportional) controller equation is given as follows. \[ u(t)=\left\{\begin ...

The \( \mathrm{P} \) (proportional) controller equation is given as follows. \[ u(t)=\left\{\begin{array}{cc} u_{\max } & e \geq e_{0} \\ u_{0}+K e(t) & -e_{0} \leq e(t) \leq e_{0} \\ u_{\min } & e<-e_{0} \end{array}\right. \] (a) What is the function of the term \( u_{0} \) ? (b) Explain how this function can be automated in a feedback control framework. [5 m