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
4. Determine the transfer function, poles and zeros, and stability of the system represented by the...
For the following systems, find the transfer function using MATLAB. Also, determine the poles and zeros of each transfer. You should be able to use some combination of the following MATLAB functions: 'ss2tf( )', 'ss( )', 'tf( )', 'pole( )', "zero( )', and 'roots() 100 ).y) = [0_1)|) 2 a. |x2(t)] -10 [x1 (t lx20 21 b. + 01 x1 (t) 0 x2(t) 1 u(t), y(t): ol]x3(t)] [(t)] x2(t) 3(t) [x1 (t)] [o 0 1x2(t) [x3(t)] -4 -2 0 2...
Compute the poles and zeros of each of the filters given in problem 4. Which filters are stable? 4a) H(z) = 1/1 + z-3 4b) H(z) = (1+3z-1+2z-2)/(1-z-1) *I understand that a system is stable if all poles are strictly inside the unit circle, and unstable if any are outside the unit circle. If a pole is ON the unit circle or the boundary of the unit circle like 1 or -1, would that make it stable or unstable? *I...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system zero Submit Part D-Type of Response Based on the locations af the poles and zeros, what will be the response to a unit step inpue? O Harmonic Oscillations (Marginally stable) Oscillatory motion with exponential decay tending to zero (stable O Critically damped exponential decay (stable)...
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and the zeros on the s-plane (4) Is this system stable or unstable? Why or why not? (5) Estimate the system's response (not knowing the type of the input) 210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and...
obtain to the transfer function of the system (Theoretically & Practically). a) Poles = -1, and -2. Zeros = there isn't zeros. Gain =2 b) Ples = -1,-3, and -4 . Zeros = -2 and -5. Gain = 1 (Control System)
QUESTION ONE (a) Determine the stability of the system whose overall transfer function is given below; 2s +5 55 +1.554 +253 +4s+55 +10 If the system is found unstable, how many roots has it has with positive real parts? (b) Determine the stability of a closed-loop control system whose characteristics equation is; ss +54 +253 +252 +11S + 10 = 0 (20 marks)
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (8-0) is 1, that is, a. Note that H (θ)-H(z)IFeje and H(θ)18-0-1 is equivalent to H(z)IF1-1 b. Plot the pole-zero diagram. c. Plot the magnitude response |H(6) d. Plot the phase response H(6) e. Find yin) as a function of x(n), x(n-1), x(n-2), x(n-3),x(n-4), x(n-5),x(n-6),x(n-7)
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles and zeros. We are interested in a system whose transfer function G(z) has the same poles and zeros as H(z) but doubled (meaning that each pole of H(z) is a double pole of G(z), and same for the zeros). How should we choose g[n]? g[n]=h[n]+h[n] (addition) g[n]=h[n].h[n] (multiplication) g[n]=h[n]th[n] (convolution) None of the above
(1) When a polynomial for the numerator of a transfer function is represented by the vector [1 3 0j in Matlab, what is the polynomial (in )? Ss35 (2) What is the final value of a response which is given b1612 (o)- (0)-3(0)3 ()undefined (3) Determine the damping ratio of the system described by)235 )1(b) 2.5 (c)5 (d) 10 (e) 25 (f) something else (4) (True or alse) The system with the following characteristic equation is stable. (5) Marginally stable...
Determine poles and zeros of transfer function H(S) = 2(3-3) 52 +55+6 Zero: -3; Poles: -2 and -3 Zero: 2; Poles: -2 and 3 Zero: 0; Poles: 2 and -3 Zero: 3; Poles: -2 and -3