Select the transfer function that best matches the pole-zero diagram shown here: 25 0 -25 -100...
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...
5. The diagram function Ha) oco.s on the let shows the pole-zero plot of the transfer a DT LTI systen Assume that the pole is at a dista the from theorigin and that the zero not at the origin is a origin. a) Write a mathematical expressio n for the tr the impulse response of the sy from t , inction of the system. b) Obtain assuming that it is UNSTABLE (15 pts.)
5. Consider an LTI system with transfer function H(s). Pole-zero plot of H(s) is shown below. Im (a) How many ROCs can be considered for this system? (b) Assume system is causal. Find ROC of H(S) (c) Assume y(t) is system output with step unit as input. Given lim y(t) = 5 , 00 Find H(s).
3. Consider an LTI system with transfer function H(s). Pole-zero plot of H(s) is shown below. Im O--- Re (a) How many ROCs can be considered for this system? (b) Assume system is causal. Find ROC of H(S) (c) Assume y(t) is system output with step unit as input. Given lim yết) = 5 , Find H(s). (d) (optional) Find y(2) (y(t) for t = 2).
The pole-zero diagram of a system is given below. The DC gain of the system is 15(1- Im(zI 1기 -0 0. (i) Sketch the approximate magnitude response of the system i) Determine the transfer function Ha), of the systenm (ii) Sketch the Direct Form I and Direct Form II implementations of this system The pole-zero diagram of a system is given below. The DC gain of the system is 15(1- Im(zI 1기 -0 0. (i) Sketch the approximate magnitude response...
2. Consider the pole-zero plot of a transfer function H(s) given in Figure P14.2. (a) If the dc gain is -10, find HG). (b) Compute the impulse response. (c) Compute the step response. CHECK: Your answer to (b) should be the derivative of your answer to (c), since the delta function is the derivative of the step function. (d) If the input is 10 ), find the pos- itive number a such that the response does not have a term...
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...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t) r*(t ZOH Process zero-order hold, and the process are given by 2s +1 Go(s) =--s G(s) = There parameter a is some real number, and T is the sampling time. (a) (15 points) Determine the discrete-time transfer function G(z). 4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y...
Question #2 ( 25 points) C(s) a) Reduce the block diagram shown in Figure 1 to a single transfer function T(s) =R) using the append and connect commands in MATLAB. pts b) Using Simulink simulate the transfer obtained in a) for a step input. c) Obtain the state-space representation of T(s). [10 [5 pts [10 pts] C(s) Ris 50 s+I 2 Figure 1 -Irt Question #2 ( 25 points) C(s) a) Reduce the block diagram shown in Figure 1 to...
t Im Re (0 3 1) Find the equivalent transfer function H (s). Remark: Since you're only given the pole-zero plot (with no information about the actual circuit that governs H(s), your answer for H(s) will contain an undetermined coefficient M zero factors pole factors RLAA P1 t Im Re (0 3 1) Find the equivalent transfer function H (s). Remark: Since you're only given the pole-zero plot (with no information about the actual circuit that governs H(s), your answer...