??5 + 2??4 + 2??3 + 4??2 + 11?? + 10 = 0 Find the stability and number of poles on the RHP.
Problem #3 Use Routh's stability criterion to determine the stability of the following system. Also, determine the number of poles in the LHP, RHP, and on the ju-axis T(s) -
Problem 4: Given L(s) = K(8 + 1) s(s+3) (a) Use method 2 to sketch the Nyquist plot of L(s). Do not include the pole at s = 0 in the RHP contour (i.e. assume P = O unstable open-loop poles). Note: The Bode phase function is not monotonic, but you may still use method 2. (b) Using the Nyquist stability criterion, determine the range of positive K values that will result in closed-loop stability. (c) Repeat (a) and (b),...
(10 points each) Given the following unity feedback system 3. E(s) R(s) C(s) 080-00 Figure 3 Where Go) DXG+3%6+5) 2(s +2) Find stability, and how many poles are in the right half-plane, in the left half-plane, on the jw axis. a. b. Draw the root locus for the system indicating the breakaway points, the ju crossings Draw the corresponding asymptotes on the diagram, calculate number of asymptotes, center and angle of asymptotes. c. (10 points each) Given the following unity...
find the eigen space of 4a and 4c Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6. Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
EEL 4652 Control Systems 1 (Fall 2018) Homework 4 Nyquist Stability Criterion + Frequency Domain Design Problem 1: Nyquist Plots and Closed-Loop Stability A unity feedback closed-loop system has a forward transfer function of KG(s). Sketch the Nyquist plot for each of the G(s) cases listed below, and then find if the closed loop system is stable and if not - how many RHP closed loop poles there are. Find it for all the relevant ranges of K for -o0SKo,...
A =10 ſi -2 -5 4 3 11 Jo 0 1 -2 0 -4 0 0 0 0 1 3 Lo 0 0 0 0 0 ] Describe all solutions of Ax = 0. x = x2 + 4
3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4 3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4
3. Given the closed loop transfer fanction bellow find a. The range of K for stability b. The val ue of K for marginally stable system and the frequency of oscillation roots of auxiliary even polynomial to find system poles 5K (s 4) 5 s3 + 16 s2 + (12 +5 K)s + 20 K
Problem 4 Find the Present Value at Year 0. (5 points) 1-5% 8 9 10 11 12 13 14 0 1 2 3 4 $3000 5000 $7000 V $9000 $11000
4. Determine the transfer function, poles and zeros, and stability of the system represented by the following difference equation: y[n] = -1.5y[n-1] + y[n-2] + x[n] Answers:H[z]= 1/(1+(1.5z^-1) - (z^-2)); poles at z = -2, 0, 5; zeros at z=0; unstable