$Q_2,(10$ marks$)$: Fuzzy System Design.

A ONE JOINT CONTROL method of $($xyz$)3$D path following robotic system in $3$D space is shown below. Convert the $($Gain Block only$)$ control law into an Intelligent Block to act as a full PID Fuzzy Control, while using the error, integrated error, and rate of error as inputs $($i$.$e$.$ three inputs$)$ and single output.

Design the full PID controller law according to your thinking on how the PID is working.

Write the fuzzy FIS rules $($four rules$).$

For a chosen inputs, show how the output is computed by hand via fuzzification, inference, and defuzzification. $($Show your FIS hand calculations$).$