help $1.$ A robotic arm and camera have been used in a robot fruit picker as shown in FIGURE Q$1.$ The camera is used as unity feedback to close the loop to a microcomputer, which controls the arm. Microcomputer imaging takes the difference of the actual and desired positions of the gripper and generates error. This error is multiplied by an amplifier with gain of $\backslash ($ K $\backslash ).$ The process may be represented by the transfer function $\backslash ($ G$($s$)=\backslash$frac$\{10\}\{$s$(\backslash$tau s$+1)\}\backslash ),$ where $\backslash ($ r$=0\mathrm{.}001\backslash$mathrm$\{$~s$\}\backslash ).$

FIGURE Q$1$

a$.$ Describe the robot fruit picker control system using an appropriate block diagram.

$[5$ marks$]$

b$.$ Determine the closed loop transfer function from the input to the output.

$[5$ marks$]$

c$.$ Evaluate the steady$-$state position error for a unit step change in the desired input.

$[5$ marks$]$

d$.$ Propose the value of $\backslash ($ K $\backslash )$ to yield a $\backslash (10\backslash \%\backslash )$ overshoot in the transient response.

$[5$ marks$]$

e$.$ Discuss the effect of varying the gain $\backslash ($ K $\backslash )$ to the transient and steady state response of the system.