- R S C S G S Q4 Given The Unity Feedback System Shown In Figure 2 Where K G S S 1 8 3 15 Do The Following 1 (92.45 KiB) Viewed 44 times
R(s) C(s) G(s) Q4: Given the unity feedback system shown in Figure 2 where K G(s) (s + 1)(8 + 3)(+ 15) Do the following: 1- Sketch the root locus by hand. 2- Find the range of K for stability and the John Wiley & Sons Inc. frequency of oscillation when marginally Figure 2 stable. 3- Find the closed loop poles when the gain K equals 13.5. 4- For K = 13.5, can the system be approximated as a second order system? 5. If you answer Yes to part 4, find the following when K = 13.5 a. peak time (Tp) b. settling time (Ts) c. percent overshoot (%OS) 6- For K = 13.5, state the system type and find the static error constants Kp, K, and K, Q5: For the feedback control system defined in Q4 do the following 1- Design a PD controller for the system to reduce the original system's settling time by a factor of 4 while continuing to operate the system with same %OS when K =13.5. 2- Design a PI controller to drive the steady state error to zero while minimizing the impact on transient. Evaluate your design via MATLAB simulation. 3- Design a PD controller to make the system (with the PI controller in stepl) stable for all values of gain K.