Problem 4: The block diagram of a positioning control system is shown in Fig. 4. In consistent units, the values of the fixed parameters are T-0.1 , J-0.01 , Ki = 10. D(s) C(s) R(s)- 1+Ts JS Fig. 4 a) Determine how the values of K and K, affect the steady-state error, where the error is defined as e(t)-r(t)-c(t). for the following cases: 1) D(s) -0, R(s) is a unit step input. 2) D(s)-0, R(s) is a unit ramp input. 3) R(s)=0, D(s) is a unit step disturbance. b) Set K-0.01. Find the smallest steady-state error that you can actually get by varying K when R(s)-0 and D(s) is a unit step disturbance. From the transient response standpoint, would you operate the system with this value of K Explain c) Assume that it is desired to operate this system with K as selected in part (b). Find the value of K, so that the complex roots of the characteristic equation will have a real part of -2.5. Find these three roots. Hint: The characteristic equation for this third order system can be written as