design a driveline speed controller

You are to design a driveline speed controller for a four cylinder SI engine. Assume that there are flexibilities in the drive shaft (axle) and the clutch. Using the state space model equations for such a driveline model (equations 7.84 - 7.86), derive the transfer function between crankshaft speed (output) and engine torque (input). Assume that J1 = 0.13; J2 = 0.07; J3 = 0.25;kc =5;kd =2.0;dc =1,dd =0.9;d2 =1.0;d3 =0.7,l=0.02;it =1.5;andif =3.Theunits of all parameters can be assumed to be in SI units. You may use the ss2tf function in MATLAB to obtain the transfer function.

For the open loop transfer function obtained above, plot the root locus using MATLAB function. What are the stability limits for the transfer function? Note your observations.