Using the riocus function, obtain the root locus for the following transfer function shown in Figure 1 when 0 < k < ∞ and G(s) is defined as the following:
G(s) = (s5+4s4+ 6s3+8s2+6s+4)/( s6+2 s5+2s4+s3+s2+10 -1)
1. Comment on the stability of the system as k varies.
Consider the feedback system shown in Figure 2 above. There are three potential controllers for your system:
• Gc (s) = K (proportional controller)
• Gc (s) = K/s (integral controller)
• Gc (s) = K(1+1/s) (proportional, integral (PI) controller)
The design specifications are T(s) ≤ 10 seconds P.O. ≤ 10% for a unit step input.
1. For the proportional controller, sketch the root locus using MATLAB with 0 < K < ∞. Determine the range of K which results in stability. Determine the value of K, K/s, and K(1+1/s) so that the design specifications are satisfied
2. Co-plot the unit step responses for the closed-loop systems with each controller designed.
3. Compare and contrast the three controllers, concentrating on the steady-state errors and transient performance.
4. Recommend a controller and justify your choice.
The solution is provided in the attached files. The MATLAB script is also included in the zip file.
BMdoc5_1.m is for ...
The solution examines control system comparisons. Three different controllers are compared and contracted concentration on the steady-state errors and transient performance.