4. Consider a unity (negative) feedback control system whose open-loop transfer function is given by the following. 1 G(s): s3 (s + 2) What is the steady state error of the system for input u(t) = t3 1(t)? Recall from the class lecture that steady-state error is given by the following formula. S ess = lim S-01 + G(s) U(s)

Given the following feedback system, a. Find the System type b. Find the value of the static error constants c. Find the value of K to have an steady-state error of 0.01 R(s) + E(s) C(s) K 1 s(2ドル+5s+6) S

29. The unity feedback system of Figure P7.1, where G(s) = K(s+a) s(s+ B) to Juqni ns Tol botoqxs 75 14. 9190 ST Jor Wa is to be designed to meet the following require- lo ments: The steady-state position error for a unit ramp input equals 1/10; the closed-loop poles will be located at -1 ± jl. Find K, a, and ß in order to meet Jinu onu O SIL 10 1 UST OB-DA the specifications. [Section: 7.4]

hand solution and Matlab. if its possible can any one post a command list for matlab for control?

Feedback and Control Systems Write the general form of, and determine the exact response of the capacitor voltage for the electrical network shown below. R1 = 10 kQ ww R2 = 10 ks C= 10 pF v(t)=u(t) L=200 H 0000

Consider the feedback system. It is known that G(s) has one unstable zero and one unstable pole. On the G(s)-plane -1+j0 point is encircled one time in the clockwise direction as s moves in the clockwise direction on the Nyquist path. What can be said about the closed-loop system? a. Stable O b. C. e. Of. G(s) Has 1 unstable pole Od. Has 2 unstable poles and 1 stable zero Has 1 unstable pole and 1 unstable zero Has 2 unstable poles and 2 unstable zeros Has 2 unstable poles and 1 ustable zero None g.

The control system G(s) = Kp / s (s+2) (s+6) has a unity feedback a. Kp is variable, discuss stability by using Routh Hurwitz method. Mark the poles ofthe system on root-locus curve below. b. When Kp = 26.7 , roots of the characteristic equation becomes s1= -0.6-1.89i, s2= -0.6+1.89i and s3= -6.8. Are you happy about this case? How do you evaluate,why ? c. How the root locus and step response would be effected by adding a controller Gc= Kp ( s + 0.5)2/ s . Give a comment about the addition of Gc on root locus andon step response.

- 6. The unity feedback system shown in Figure P9.1 with K(s+6) G(s) (s+2)(s + 3)(s + 5) is operating with a dominant-pole damping ratio of 0.707. Design a PD controller so that the settling time is reduced by a factor of 2. Compare the transient and steady-state performance of the uncompensated and compensated systems. Describe any problems with your design. [Section: 9.3]

8nn

5. Consider following feedback system. R(s) + 100 S+4 +1 Find the steady-state error for (i) step input and (ii) ramp input.

The unity feedback system with open loop transfer function G(s) K S2 is to be designed to have closed loop poles at -2.4 + j4.16. If the compensator's zero is placed at -1, do the following: a) Find the compensator pole b) Find the system gain c) Find the location of the third pole. d) Evaluate the steady-state error characteristic. e) Plot the step response of the compensated system

Control

For the open-loop system G(s) = 3/s^2 + 2s - 3 assume there is a feedback with a proportional gain, K. And sketch a locus of closed-loop rootsverse K. What is the minimum value of K to achievea stable system?