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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)...
5. The diagram function Ha) oco.s on the let shows the pole-zero plot of the transfer...
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.)
For all problems -given a transfer function G(s) sketch the magnitude and phase characteristics in the...
For all problems -given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s-jw and writing the TF using DC-gain KO and time-constants i. Arange break-points (poles, zeros or on for complex-conjugate poles) in ascending order ii Based on the term Ko(ju)Fk, determine: initial slope of the magnitude-response asymptote for low frequencies as F k 20 dB/dec (e.g....
2. Consider the pole-zero plot of a transfer function H(s) given in Figure P14.2. (a) If...
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...
please help answer all the question and dont skip. Thank you! 1. Sketch the pole-zero diagram...
please help answer all the question and dont skip. Thank
you!
1. Sketch the pole-zero diagram for the following transfer function. Ensure you label the axes and the pole-zero locations. Assume a > b > 0. TF(s) = (s + a) s(s+b) 2. If the time constant of the lowest frequency pole in a system is 1 second, after approx- imately what period of time following turn-on could the system be considered to be in steady-state conditions? 3. The PID...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero plot for this system How many possible regions of convergence (ROCs) are there for H(). 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...
Consider the transfer function of a DC motor given by G(s) = 1 / s(s+2) 3. Consider the transfer function of a DC motor...
Consider the transfer function of a DC motor given by G(s) = 1 /
s(s+2)
3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response...
Given the transfer function 4. G(s)H(s) - (s + 8) (s +6s + 13) (a) Sketch the root locus plot using Matlab. (b) Estimate the system gain when the damping ratio is 7 0.707 (c) Add a simple pole, (s...
Given the transfer function 4. G(s)H(s) - (s + 8) (s +6s + 13) (a) Sketch the root locus plot using Matlab. (b) Estimate the system gain when the damping ratio is 7 0.707 (c) Add a simple pole, (s 2), to G (s)H (s) and examine the resulting root locus (d) Add a simple zero, (s +2), to G(s)H(s) and examine the resulting root locus
Given the transfer function 4. G(s)H(s) - (s + 8) (s +6s + 13)...
Problem (4): Sketch the root locus plot for a system, whose transfer function are given by 10 K (s2 +3 s+7) the complex poles. G(s) (s +3) i) Determine the joo -axis crossing, breakaway point and the...
Problem (4): Sketch the root locus plot for a system, whose transfer function are given by 10 K (s2 +3 s+7) the complex poles. G(s) (s +3) i) Determine the joo -axis crossing, breakaway point and the angle of departure from (i) Determine the value of the gain for which the closed loop system will have a pole at (-10)
Problem (4): Sketch the root locus plot for a system, whose transfer function are given by 10 K (s2 +3...
For the given system above, determine the gain K that will give the system desired response below: Settling time of 5 seconds Peak time of 0.5 seconds The given plant has a transfer function of: Gp...
For the given system above, determine the gain K that will give
the system desired response below:
Settling time of 5 seconds
Peak time of 0.5 seconds
The given plant has a transfer function of: Gp = (s + 4)/( (s +
1)*(s + 3) )
The controller has a transfer function of: Gc =
(s+27.75)/s
QUESTION 2 10 points Save Answer Y(S) R(s) Gc(s) Gp(s) For the given system above, determine the gain K that will give the system...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] –...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
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.)
For all problems -given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s-jw and writing the TF using DC-gain KO and time-constants i. Arange break-points (poles, zeros or on for complex-conjugate poles) in ascending order ii Based on the term Ko(ju)Fk, determine: initial slope of the magnitude-response asymptote for low frequencies as F k 20 dB/dec (e.g....
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...
please help answer all the question and dont skip. Thank
you!
1. Sketch the pole-zero diagram for the following transfer function. Ensure you label the axes and the pole-zero locations. Assume a > b > 0. TF(s) = (s + a) s(s+b) 2. If the time constant of the lowest frequency pole in a system is 1 second, after approx- imately what period of time following turn-on could the system be considered to be in steady-state conditions? 3. The PID...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero plot for this system How many possible regions of convergence (ROCs) are there for H(). 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...
Consider the transfer function of a DC motor given by G(s) = 1 /
s(s+2)
3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response...
Given the transfer function 4. G(s)H(s) - (s + 8) (s +6s + 13) (a) Sketch the root locus plot using Matlab. (b) Estimate the system gain when the damping ratio is 7 0.707 (c) Add a simple pole, (s 2), to G (s)H (s) and examine the resulting root locus (d) Add a simple zero, (s +2), to G(s)H(s) and examine the resulting root locus
Given the transfer function 4. G(s)H(s) - (s + 8) (s +6s + 13)...
Problem (4): Sketch the root locus plot for a system, whose transfer function are given by 10 K (s2 +3 s+7) the complex poles. G(s) (s +3) i) Determine the joo -axis crossing, breakaway point and the angle of departure from (i) Determine the value of the gain for which the closed loop system will have a pole at (-10)
Problem (4): Sketch the root locus plot for a system, whose transfer function are given by 10 K (s2 +3...
For the given system above, determine the gain K that will give
the system desired response below:
Settling time of 5 seconds
Peak time of 0.5 seconds
The given plant has a transfer function of: Gp = (s + 4)/( (s +
1)*(s + 3) )
The controller has a transfer function of: Gc =
(s+27.75)/s
QUESTION 2 10 points Save Answer Y(S) R(s) Gc(s) Gp(s) For the given system above, determine the gain K that will give the system...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
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