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Question #2 (20 pts): Transfer function of a causal system is given as s²-s-6 56 +...
3. Consider an LTI system with transfer function H(s). Pole-zero plot of H(s) is shown below....
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).
Consider an LTI system for which the system (transfer) function H(s) has a zero at s=2...
Consider an LTI system for which the system (transfer) function H(s) has a zero at s=2 and poles at s=-12, -7, -6. If the system is known to be causal and stable, choose the ROC associated with the given system function. *
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the...
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the poles and zeros b) indicate the poles and the zeros on the s-plane indicate the region of convergence (ROC) c) write the differential equation of the system. d) determine the gain of the system at dc (ie the transfer function at w=0) e) is the system described by H(s) stable? explain f) for the system described by H(s), does the Fourier transform H(jw) exist?...
4. Block Diagrams (a) Consider a causal LTI system with transfer function Show the direct-form block diagram of Hi(s) b) Consider a causal LTI system with transfer function H282+4s -6 H (s) = 2 Show...
4. Block Diagrams (a) Consider a causal LTI system with transfer function Show the direct-form block diagram of Hi(s) b) Consider a causal LTI system with transfer function H282+4s -6 H (s) = 2 Show the direct-form block diagram of Hi(s) (c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. (d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can...
4. Block Diagrams (a) Consider a causal LTI system with transfer function H(s)2 Show the direct-form block diagram of Hi(s) (b) Consider a causal LTI system with transfer function 2s2 +4s -6 H(s)- Sh...
4. Block Diagrams (a) Consider a causal LTI system with transfer function H(s)2 Show the direct-form block diagram of Hi(s) (b) Consider a causal LTI system with transfer function 2s2 +4s -6 H(s)- Show the direct-form block diagram of Hi(s) c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can draw...
5. Consider an LTI system with transfer function H(s). Pole-zero plot of H(s) is shown below....
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).
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the...
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the pole-zero plot for this system. How many possible (ROCs) are there for H(z). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to (b) Which ROC (or ROCs) correspond to a stable system? Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to the output...
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no?...
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no? c) H HG) were modified as follows. Determine the system stability as a function of parameter k, i.e, what is the minimal value of k required to keep the system stable? d) Sketch Bode the plot for T(s) including data 'k, derived from...
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...
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)...
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).
4. Block Diagrams (a) Consider a causal LTI system with transfer function Show the direct-form block diagram of Hi(s) b) Consider a causal LTI system with transfer function H282+4s -6 H (s) = 2 Show the direct-form block diagram of Hi(s) (c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. (d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can...
4. Block Diagrams (a) Consider a causal LTI system with transfer function H(s)2 Show the direct-form block diagram of Hi(s) (b) Consider a causal LTI system with transfer function 2s2 +4s -6 H(s)- Show the direct-form block diagram of Hi(s) c) Now observe that to draw a block diagram as a cascaded combination of two 1st order subsystems. d) Finally, use partial fraction expansion to express this system as a sum of individual poles and observe that you can draw...
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).
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the pole-zero plot for this system. How many possible (ROCs) are there for H(z). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to (b) Which ROC (or ROCs) correspond to a stable system? Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to the output...
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no? c) H HG) were modified as follows. Determine the system stability as a function of parameter k, i.e, what is the minimal value of k required to keep the system stable? d) Sketch Bode the plot for T(s) including data 'k, derived from...
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)...
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