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Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfe...
Problem #4 [15 Points] Given -1001 00-1」 11 0 1 00 (a) Find the impulse response...
Problem #4 [15 Points] Given -1001 00-1」 11 0 1 00 (a) Find the impulse response h(t) and the transfer function matrix H(s). Which modes are present in h(t)? What are the poles of H(s)? b) Is the system asymptotically stable? Is it BIBO stable? Explain. (c) ls it possible to determine a linear state feedback control law u = Fr+r so that all closed loop eigenvalues are at -1? If yes, find such F
Problem 3. The input and the output of a stable and causal LTI system are related...
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Problem 1: (15 points) Determine if the following statements are True or False and briefly describe...
Problem 1: (15 points) Determine if the following statements are True or False and briefly describe the reasons for your answers. (2 points for the correct answer of True or False, and 3 points for the correct reasoning.) (a) The Laplace transform of an LTI system's zero-input response is always equal to the system's transfer function, H(s). (b) The transfer function of an LTI system is H(s) = e. Then, it can be concluded that the system is BIBO stable....
. (15 points) An unstable system can be stabilized by using negative feedback with a gain...
. (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)...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps...
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps arriving to your answer. p(-)x(1-)a L(2- r)x(1)dr-L*-1)x(1)dr (10 points) y(t) a. b. (10 points) y(t) -00 4. (10 points) An LTI system has the impulse response: h(t) = 4e-0.75(-1)[u(t + 4) - u(t - 10)]. this system Causal or Non-Causal? You must justify your answer. A correct answer with no justification worth only 4 points Is
3. For following input/output system relationships, determine the...
(please explain your answers). for the following transfer function, a) determine if the associated system is...
(please explain your answers). for the following transfer
function,
a) determine if the associated system is BIBO stable
b) if BIBO stable systems in question a). For these systems,
determine the steady state output Yss(t) given
- an input u(t) = 2step(t) → Yss(t) = lim t→+∞ (y(t)) = constant
value
-an input u(t) = 3 sin(t) → Yss(t) = sin function
c) if non BIBO stable systems in question a). For these systems,
find a bounded input that makes...
signal and system 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 d...
signal and system
8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a)...
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
Problem #4 [15 Points] Given -1001 00-1」 11 0 1 00 (a) Find the impulse response h(t) and the transfer function matrix H(s). Which modes are present in h(t)? What are the poles of H(s)? b) Is the system asymptotically stable? Is it BIBO stable? Explain. (c) ls it possible to determine a linear state feedback control law u = Fr+r so that all closed loop eigenvalues are at -1? If yes, find such F
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Problem 1: (15 points) Determine if the following statements are True or False and briefly describe the reasons for your answers. (2 points for the correct answer of True or False, and 3 points for the correct reasoning.) (a) The Laplace transform of an LTI system's zero-input response is always equal to the system's transfer function, H(s). (b) The transfer function of an LTI system is H(s) = e. Then, it can be concluded that the system is BIBO stable....
. (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)...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps arriving to your answer. p(-)x(1-)a L(2- r)x(1)dr-L*-1)x(1)dr (10 points) y(t) a. b. (10 points) y(t) -00 4. (10 points) An LTI system has the impulse response: h(t) = 4e-0.75(-1)[u(t + 4) - u(t - 10)]. this system Causal or Non-Causal? You must justify your answer. A correct answer with no justification worth only 4 points Is
3. For following input/output system relationships, determine the...
(please explain your answers). for the following transfer
function,
a) determine if the associated system is BIBO stable
b) if BIBO stable systems in question a). For these systems,
determine the steady state output Yss(t) given
- an input u(t) = 2step(t) → Yss(t) = lim t→+∞ (y(t)) = constant
value
-an input u(t) = 3 sin(t) → Yss(t) = sin function
c) if non BIBO stable systems in question a). For these systems,
find a bounded input that makes...
signal and system
8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
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