0.2 1. Explain the derivation of the formulae for Km'rp'rm'rfas a function of: c2, c1, cu In, etc. as explained in the lecture slides. How is this related to the tuning parameter (on? (5 marks! 2. Present your results, Simulink diagrams, and MATLAB scriptsjl4 marksl Case C: 1. What are the effects of increasing (on ? Show evidence. 13 marks[ 2. For what value of can are there sustained oscillations? ll mark] 3. What happens if can is increased beyond the point of sustained oscillation? Why? Show evidence. Is this related to the modelling of the time delay? (5 marks! [1.2. The objective of this simulation study is to examine the selection of a desired clomdloop performance in the presence of deelling errors. IEfren a rst order plus delay system with the transfer function le'' Gig} = le+1 E as shown in the lecture slides.j we rst approximated the time delay using Fade approximation, and then dem'gned PlIl controllers far this time delay system. There are three cases to he considered in the design and simulation studies. Case A. The desired closedloop bandwidth and the damping coefcient are selected as w" = [1.2. if = DEBT. With polezero cancelationy the PID controller parameters are calculated as H: = .1793; 1': = 3.0323; T5 = 1.33T5rrf = 0.5531. Case E. The desired closedhop bandwidth is increased to \".431: while .5 is unchanged. The PD] controller parameters are calculated as Kc = E1332; 1': = 7.1; T]: = 1.43; Ty = [1292. Case C. Code your own PD] controller parameter solutions by following the analytical expressions in the lecture slides. Find the desired closedloop bandwidth as,1 that will lead to sustained oscillations in the simulated output. This procedure needs to be performed by trialanderrors with the MATLAE and Simulinl-r programs you wrote. The simulation conditions for the closedloop control system are given as below. 1. Reference input signal is a step with amplitude of 3. llSho-me yeur own sampling interval t and simulation time. 2. Add input disturbance signal with amplitude ofl at halfofyour simulation time. In l'h'lATLAE, plot your reference signaL control signal and output signal far the three cases. Discuss your observations and oonclusions on the relationships between the time delay and the selected desired closedloop bandwidth