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Question 3 (10 pts): Consider the closed-loop system pictured below, with two inputs: the reference input z (ideally, to be tracked by output y) and a "disturbance" input d. (Note the mi...
pleas show all work thank you Disturbance D(s) Reference Control Output Input Error Input t US) Y(s) Plant Given the above closed loop block diagram: Let aundl s) KK (a) Show that the above system wil...
pleas show all work thank you
Disturbance D(s) Reference Control Output Input Error Input t US) Y(s) Plant Given the above closed loop block diagram: Let aundl s) KK (a) Show that the above system will have zero steady state error for step reference input (when D(s)-0) as well as for step disturbance input (when R(s)-0). (b) LetJ B K1 and Kp0, what about the stability of the closed loop system?
Disturbance D(s) Reference Control Output Input Error Input t...
please show steps 4. (25 points) Laplace and LCCDE Systems Consider an LTI system with input-output...
please show steps
4. (25 points) Laplace and LCCDE Systems Consider an LTI system with input-output relation described by the LCCDE: -2y(t) - y0) + 3x(t) + deco (O) = (a) (5 pts) Find the transfer function H(s) and write it in factored form. (b) (5 pt) Sketch the ROC corresponding to H(s) if it is known the system is causal. Mark the poles and zeros. (c) (5 pts) Sketch the ROC corresponding to H(s) if it is known the...
4. Consider the block diagram shown below where D(s) is a step disturbance input. D(s) Controller...
4. Consider the block diagram shown below where D(s) is a step disturbance input. D(s) Controller Plant R(s) + E(s) C(s) G2(s) Ideally you want your controller design to reject a step disturbance input at D(s). This means that in the steady state for D(s)-1, the value of Y(s) is unchanged (a) Ignoring the input R(s), what is the transfer function器in terms of Gi(s) and G2(s)? (b) For G1(s)Ks 2) and G2(s)0419 what is the steady state error resulting from...
Problem 1 Open-loop tersus Closed-loop control: Consider a first-order system Σ' with inputs (d,u) and output...
Problem 1 Open-loop tersus Closed-loop control: Consider a first-order system Σ' with inputs (d,u) and output y, governed by Z(t) y(t) ar(t1+hd(t)+5a1(t), cr(t) = = (a) Assume Σ is table (ie, a < 0). For Σ, what is the steady-state gain fron u to y (assuming d 0)? What is the steady-state gain from d to y (assuming t. 0)? These are the open-loop steady-state gains. Call these SSGy and SSGgby respectively (b) Σ is controlled by a "proportional" controller...
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a first order system with transfer function 2 Is the closed-loop system stable? Obtain the asymptotic val...
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a first order system with transfer function 2 Is the closed-loop system stable? Obtain the asymptotic value of the error e when z and d are steps, respectively z au and d-Au, with α and β positive constants. Justify your steps.
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a...
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design...
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
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).
a = 3 signals and systems 1) [10 pts. Let a system be defined as ta...
a = 3
signals and systems
1) [10 pts. Let a system be defined as ta y(t) x(31 - 2a)dt 2a Is this system b) No b) No b) No vii) memoryless? a) Yes viii) Linear? a) Yes ix) Time invariant? a) Yes x) Causal? a) Yes xi) BIBO stable? a) Yes 2) [5 pts. What is the impulse response h(t)? 3) [10 pts.] Let a signal in s domain b) No b) No 2 Y(S) Sa What is the...
Problem 2 (50 pts): Consider the unity-feedback system: R(2) E(z) Y(2) K G(2) 2 G(2) =...
Problem 2 (50 pts): Consider the unity-feedback system: R(2) E(z) Y(2) K G(2) 2 G(2) = is the transfer-function of the plant and zero-order hold. (2 – 1)(z – 0.2) a) (5 points) Find the closed-loop transfer-function Hyr(2). b) (5 points) Find the characteristic polynomial. c) (20 points) Determine the range of K for closed-loop stability.
A closed-loop control system has Gc(s) = 10, G(s) = (s+50)/(s^2+60s+500), and H(s) = 1. a)...
A closed-loop control system has Gc(s) = 10, G(s) = (s+50)/(s^2+60s+500), and H(s) = 1. a) Find the transfer function Y(s)/R(s). b) Plot the pole-zero map of the transfer function. c) Find the response y(t) to a unit step input. d) Find the steady-state (final) value of the output.
pleas show all work thank you
Disturbance D(s) Reference Control Output Input Error Input t US) Y(s) Plant Given the above closed loop block diagram: Let aundl s) KK (a) Show that the above system will have zero steady state error for step reference input (when D(s)-0) as well as for step disturbance input (when R(s)-0). (b) LetJ B K1 and Kp0, what about the stability of the closed loop system?
Disturbance D(s) Reference Control Output Input Error Input t...
please show steps
4. (25 points) Laplace and LCCDE Systems Consider an LTI system with input-output relation described by the LCCDE: -2y(t) - y0) + 3x(t) + deco (O) = (a) (5 pts) Find the transfer function H(s) and write it in factored form. (b) (5 pt) Sketch the ROC corresponding to H(s) if it is known the system is causal. Mark the poles and zeros. (c) (5 pts) Sketch the ROC corresponding to H(s) if it is known the...
4. Consider the block diagram shown below where D(s) is a step disturbance input. D(s) Controller Plant R(s) + E(s) C(s) G2(s) Ideally you want your controller design to reject a step disturbance input at D(s). This means that in the steady state for D(s)-1, the value of Y(s) is unchanged (a) Ignoring the input R(s), what is the transfer function器in terms of Gi(s) and G2(s)? (b) For G1(s)Ks 2) and G2(s)0419 what is the steady state error resulting from...
Problem 1 Open-loop tersus Closed-loop control: Consider a first-order system Σ' with inputs (d,u) and output y, governed by Z(t) y(t) ar(t1+hd(t)+5a1(t), cr(t) = = (a) Assume Σ is table (ie, a < 0). For Σ, what is the steady-state gain fron u to y (assuming d 0)? What is the steady-state gain from d to y (assuming t. 0)? These are the open-loop steady-state gains. Call these SSGy and SSGgby respectively (b) Σ is controlled by a "proportional" controller...
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a first order system with transfer function 2 Is the closed-loop system stable? Obtain the asymptotic value of the error e when z and d are steps, respectively z au and d-Au, with α and β positive constants. Justify your steps.
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a...
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
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).
a = 3
signals and systems
1) [10 pts. Let a system be defined as ta y(t) x(31 - 2a)dt 2a Is this system b) No b) No b) No vii) memoryless? a) Yes viii) Linear? a) Yes ix) Time invariant? a) Yes x) Causal? a) Yes xi) BIBO stable? a) Yes 2) [5 pts. What is the impulse response h(t)? 3) [10 pts.] Let a signal in s domain b) No b) No 2 Y(S) Sa What is the...
Problem 2 (50 pts): Consider the unity-feedback system: R(2) E(z) Y(2) K G(2) 2 G(2) = is the transfer-function of the plant and zero-order hold. (2 – 1)(z – 0.2) a) (5 points) Find the closed-loop transfer-function Hyr(2). b) (5 points) Find the characteristic polynomial. c) (20 points) Determine the range of K for closed-loop stability.
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