The steady state gain and the time constant seconds

A formal laboratory report is not required. There is no need for an introduction and methodology section. Your answers must be organised into the question parts below. Figures (including SIMULINK diagrams) must be captioned and numbered (e.g. Fig. 1 Open-loop Model); and the discussion in part (d) should be of a formal scientific nature.

The marking scheme is based on these instructions so do not ignore or forget them!

(a) Construct a SIMULINK diagram of the above model. Plot the response to a step input in engine power from zero to 0.6 units, with the step occurring after 5 s and assuming zero initial conditions. Submit the SIMULINK diagram and a fully annotated graph of the response. Also, write down the calculation showing the expected value of the speed at steady state (and check that your answer is correct from the graph). (4 marks)

Now use yourSIMULINK diagram to investigate how changing the value of the time constant and steady state gain changes the response. This may be useful information for answering part (d) below and for the end of year examinations. However, do not submit these results (they will not be marked).

Now use yourSIMULINK diagram to investigate how changing the value of the integral gain changes the response. This may be useful information for answering part (d). However, do not submit these results (they will not be marked).

(d) Use a trial and error approach, and yourSIMULINK diagrams from part (b) and part (c), to find suitable values of the integral and proportional control gains that best address the cruise–control problem. Submit two fully annotated graphs, i.e. showing the best proportional control response and best integral control response, quoting the value of the control gain you have chosen in the figure caption. Here, ‘best’ is a qualitative judgement that you should make and justify. State whether the proportional or integral controller is your preferred option for the final design, and explain how this design successfully addresses the cruise–control problem.