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15 pts) For the following transfer functions. explain why the responses will be stable (or unstable)...
3. Determine whether the LTIC systems with the following transfer functions are BIBO stable and explain why or why not. = 2 + (8+1)(8+2) (a) Ĥ2(s) 82 +55+6 (b) A3 (8) (5-1+j5)(3-1-15) (c) Î(8) = (6+2)5+4) (d) Â14(8) 1,2716 (e) Âg(s)
A Calculator is allowed. Question 7: The following transfer function is unstable. H(s) = ! Explain why the function is unstable. Plot any existing poles and zeros on the complex (s-domain) plane. Find a feedback method (P,D, or Ior any summative combination of P, D, or I) to make the system stable. Prove it is stable mathematically.
Q4. 1 2 3 G 10 pts. Use MATLAB and plot the step response of the following systems G3 2s+1 figure. Gy on the same 2s+1 2s+1 Explain the similarities (at least 1) and differences (at least 1) between these responses. E_ figure. G, G 3 10 pts. Use MATLAB and plot the impulse response of the following systems Explain the similarities and differences between these responses. on the same 25+1 10 pts. Find the time constant (Te), pole(s), DC...
Show all your work II of the following transfer functions. Also function represents a stable system. (5+2)(5-5) a. (s+4)(s2 +65)(s2+25) s(s+4)(s+7) b. (5-1)(s+7)(s+9) (S-2)(+3)(s2+16) (83+652-125)(s+1)(s2+4s+4) (2) Draw the frequency response for the following transfer functions: 10 (5+105)(s+107) a. (s+104)(s+108)
2. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the pole-zero plot of the transfer function. b) Show all possible ROC's associated with this transfer function. c) Obtain the impulse response h(t) associated with each ROC of the transfer function. d) Which one (if any) of the impulse responses of part c) is stable? 2. The transfer function of a CT LTI system is given by H(s) (s2...
Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5) (s+4) (s2+6s)(s2 +16) s(s+4)(s+7) (s+2) (s+3) (s2+9) (s2+4s2+13s) (s-1)(s2+10s+34) C. (22 Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5) (s+4) (s2+6s)(s2 +16)...
For each of the following transfer functions, plot the pole-zero pattern, draw curves of M(a) versus ω and θ(a) versus ω, and comment briefly on your results. For the function in part (c), include the numerical values for ω- 9.9, 10.0, and 10.1 rad/s. 2 H(s)= s2+2s +1 a. 2s2 H (s) = 0.25+100 C. For each of the following transfer functions, plot the pole-zero pattern, draw curves of M(a) versus ω and θ(a) versus ω, and comment briefly on...
1. There are 8 pole-zero graphs of system transfer functions in Figure E-1. Answer the following questions about their frequency responses, impulse responses and step responses. Frequency response: (a) Which have a phase approaching zero at very high frequencies? (b) Which have a phase that is discontinuous at zero frequency? (c) Which have a magnitude approaching zero at high frequencies? Step response: (a) Which have a step response that is non-zero in the limit to? (b) Which have a step...
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
Sketch the approximate Bode magnitude and phase plots for the following transfer functions by hand. a. G(s) b. G(s)- 200 (s2 +2s)(0.1s +1) s+1 s2 +2s +100