(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. Question 4: Answer all parts (a) If the overall transfer function for motor control system in Figure Q4 (a), is 40 rpm/V. What is the transfer function (T.F.) of the feedback loop (to two decimal places)? Ampiler-Relay TF 20 H? m Figure Q4 (a) Mator T.F.35 rpm/V (5 marks) Explain what you understand by the terms 'damping' and 'damping ratio (5)' with regard to a second order control system (mass-spring-damper) subjected to a step input F, as described by the following differential equation. dx dt dx -+c+lxxx = F dt (5 marks) Calculate wn the undamped natural frequency of a system. (4 marks) Y For the following values of m= 10 kg, c = 2Ns/m and k = 100 N/m. Calculate the damping factor and comment on what this practically means? (4 marks) (2 marks) The graph in Figure Q4 (c), shows how the output vo 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. Output v. (Voila) Measure signal % 52963 2.5 15 D.S 6 0 0.5 (5 marks) 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) t Control Mode P PI PID 15 3 Time (s) Figure Q4 (c) 200 49 400 800 600 1000 Time from start of test signal (seo) Ti Kp P/RL 0.9P/RL 3.33L 1.2P/RL 2L Figure Q4 (d) TD 0.5L