Q.1 (5 marks) The components of a robotic control system can be described by the following dynamic equations: where d0(t) de (t) +4 +100 (t) = i(t) dt dt di(t) dv(t) +2i(t) == dt dt de (t) v2(t) =Kpe(t) + K v(t) = K0(t) e(t)=r(t)v(t) dt r(t) = e(t) Desired position (reference) = Actual position (output) = Output current from an amplifier i(t) Vi(t) = Output of the position sensor V2(t) e(t) = Output voltage from PD controller = Error signal a. Perform Laplace Transform on each equation and obtain the transfer function for the first four equations (sub-systems or components), and draw a block diagram for each of the five equations. (Note: in s domain) b. Based on the transfer function for each equation, build the block diagram of the overall control system and put the transfer function of each component into the corresponding block. c. Identify and label the controller, actuator, plant and sensor on the overall block diagram. Label input and output signal for each block on the diagram.