(a) Implement a commented ladder logic PLC program for the control actions specified. Indicate any internal PLC locations you may use in your solution. (25 marks) (b) Explain your solution in detail, stating any assumptions you make. (5 marks) Question 4: Answerall parts (a) If the overall transfer function for motor control system in Figure Q4 (a), is 40rpm/V. What is the transfer function (T.F.) of the feedback loop (to two decimal places)? (o marks) regard to a second order control system (mass-spring-damper) subjected to a step input F, as described by the following differential equation. mdt2d2x+cdtdx+kx=F (4 marks) For the following values of m=10kg,c=2Ns/m and k=100N/m. Calculate the damping factor and comment on what this practically means? Calculate n the undamped natural frequency of a system. (4 marks) (2 marks) (c) The graph in Figure Q4 (c), shows how the output v0 of a first-order control system varies with time when subject to a step input of 2V. Estimate the first-order differential equation for the system and it's solution. (5 marks) (d) Briefly describe what 'tuning' a PID controller means. (2 marks) Determine the settings required for a PID controller which gave the process reaction curve shown in Figure Q4 (d), when the test signal was a 8% change in the control valve position. (8 marks)