Hello,
Please find the answer to the first question attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!
The answers to all questions of 1 has been printed directly on the figure.
**** Matlab Code ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% using root locus to study system characteristics
G1 = tf([1,2,1],[1 40 400 0]); % first transfer function
G2 = tf(1,[1 -2 2]); % second transfer function
G = G1*G2; % whole transfer function G = L
rlocus(G);
grid;
**** End of Code ****
Output:
1. Using the MATLAB rltool command (or rlocus and rlocfind), plot the K > 0 root...
Q1. Show analytically that the Root Locus for the unity feedback system with open loop transfer function: (a) [10 marks] K(s 4) (s + 2) is a circle, and find the centre and the radius. Determine the minimum value of the damping ratio and the corresponding value of K (b) The root locus of the open loop transfer function: [10 marks] s(s26s +15) is depicted in Figure Q1(b). Find the minimum value of gain K that will render the system...
1. a. Plot the root loci for the unity-feedback system whose feed-forward transfer function is: K G(s) = s(s? +48 + 8) If the value of K is set 8, where are the closed loop poles located? Hint: Non-dominant pole is an integer. (5 Points) b. Outline the procedure for design of a lag compensator (on the forward path) that cuts down the rise and settling times to half of the dominant second order system in 1. a. (3 Points)...
1- [a] For positive values of K, plot the root locus for a unity negative feedback control system having the following open-loop transfer function: K G(s)= (5 + 1)(8 + 4)(8 + 7) For what values of gain K does the system become unstable? Find also the value of k at which the damping ratio is 0.5 and the closed loop poles. (25%) [b] The characteristic equations of linear control systems are given below. Apply Routh-Hurwitz criterion to determine the...
1. Given a unity feedback system with the open-loop transfer function s(0.5s +1) .design a lead compensator ,0 〈 α 〈 1, such that the desired closed-loop poles at -2+2j following steps: J, by completing the (a) Find the angle deficiency from the compensator, (b)Find the zero and poles of the compensator (c) Find constant gain Kc.
1. Given a unity feedback system with the open-loop transfer function s(0.5s +1) .design a lead compensator ,0 〈 α 〈 1, such...
Sketch the root locus plot of a unity feedback system with an open loop transfer function G(s) = K / s (s+2) (s+4) Determine the value of K so that the dominant pair of complex poles of the system has a damping ratio of 0.5.
Problem 2: Given the plant G,le)+2( +3) design a PI compensator Gc(s)-K Ш such the closed-loop unity feedback system has two dominant poles at s1.2 =-1 ±j. Using Matlab ritool (or simulink), simulate your closed loop system to show that the unit-step response of the system has PO ~ 4.3%, tr 2.35 sec, and 4 ะ 4.15 sec. Compute the closed-loop poles and zeros.
Stuck on this problem, an explanation of the answer would be
very much appreciated!!
PROBLEM E3 A unity feedback system with loop transfer function G(o) is to be cascade-compensated, as shown in Figure P3 below. The closed-loop characteristic equation of the uncompensated system is given as G. (s) G(s) Cs) Figure P3. Unity feedback compensated control system block diagram. Do the following: (a) Determine the uncompensated system loop transfer function G(s). b) Sketch the root locus of the uncompensated system....
1. a. Plot the root loci for the unity-feedback system whose feed-forward transfer function is: G(s) = - s(s? + 4s + 8) If the value of K is set 8, where are the closed loop poles located? (5 Points) Hint: Non-dominant pole is an integer. b. Outline the procedure for design of a lag compensator (on the forward path) that cuts down the rise and settling times to half of the dominant second order system in 1. a. (3...
Consider a unity-feedback control system with a PI controller Gpr(s) and a plant G(s) in cascade. In particular, the plant transfer function is given as 2. G(s) = s+4, and the PI controller transfer function is of the forrm KI p and Ki are the proportional and integral controller gains, respectively where K Design numerical values for Kp and Ki such that the closed-loop control system has a step- response settling time T, 0.5 seconds with a damping ratio of...
1. Write the MATLAB commands (tf.) and zpk (...)) that yield the following trans fer functions: ii) Hy=1+1+ ii) H3-3-*+-1 (s + 1)( -2) iv) H. - 3)(8 + 4) 2. Consider the feedback system: C(0) = K * G(s) Determine the values of K, a, and b of C(s) such that the dominant-closed loop poles are located at $12 = -1 j. Use the root locus method. Provide the locations of the dominant poles. You should include the root...