A sampled-data system such as that presented in problem (i) has a sampling period T =...
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A sampled-data system such as that presented in problem (i)
has a sampling period T =...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t)...
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...
Problem 30 (15 points) Consider the closed-loop sampled-data system in Figure 6 that uses a sample...
Problem 30 (15 points) Consider the closed-loop sampled-data system in Figure 6 that uses a sample period of 600 ms. The pulse transfer function of the continuous-time plant is Ge)- 0.04147 z-0.7408 while Ge(2) is the transfer function of a discrete-time compensator. E(Z)G.(2) Figure 6: Closed-loop sampled-data system with compensator Ge() I. (5 points) Is it possible to achieve a steady-sate error ess- 0.05 for a unit-step input r(k) = uo(k) using proportional feedback Ga(z) = K? If yes, derive...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system shown in the figure below, where the two input signals are given to be xi(t) = sinc(10t) and x2(t) = sinc(6t). ylt) z(t) LTI →2;(+) ht) Xalt) P(+) - E81-nt) a) State the sampling theorem. Be sure to include all conditions for its validity. (5 pts) b) What is the minimum frequency at which y(t) must be sampled such that it could be completely...
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a)...
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a) Locate open-loop zeros and open-loop poles. b) Construct the root-locus diagram as 0 <K <oo. Mark the portions of the real axis that belong to the root locus - Mark with K =0 the point where the root locus bra O the point where the root locus branches start and with K = oo the point where the branches end. - Find break-away and/or...
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with...
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
r[n] + K(z) D/A with ZOH G(s) A/D Here the sampling period T = 0.5 sec...
r[n] + K(z) D/A with ZOH G(s) A/D Here the sampling period T = 0.5 sec and G(s) = FT K(z) = 30 (i) Find the ZOH discrete equivalent of the system and determine if it is stable. For this problem, you are NOT allowed to use the table of z-transforms.
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...
Sketch the root locus for the unity feedback system shown in Figure P8.3 for the following...
Sketch the root locus for the unity feedback system shown in Figure P8.3 for the following transfer functions: (Section: 8.4] K(s + 2)(8 + 6) a. G(s) = 52 + 8 + 25 K( +4) b. G(S) = FIGURE PR3 152 +1) C G(s) - K(s+1) K (n1)(x + 4) For each system record all steps to sketching the root locus: 1) Identify the # of branches of the system 2) Make sure your sketch is symmetric about the real-axis...
K(z-15). Connected in the Assume a system, G[2]-z-ls, conventional negative unity, output feedbac...
Need help with this. Please show all your steps.
K(z-15). Connected in the Assume a system, G[2]-z-ls, conventional negative unity, output feedback configuration. The only adjustable parameter in the Pl controller for this problem is the gain. (a) Find the real axis line segments in the complex z-plane that belong to the Root Locus 5. and a PI controller, C[z] associated with the closed-loop poles of this system. The Root Locus is drawn for the forward gain in the system...
Control System Problem. Please do part A, B , and C. Consider the unity-feedback system with...
Control System Problem. Please do part A, B , and C.
Consider the unity-feedback system with G(s)-K(st3)(s+5)/(s+(s-7)] Sketch the root locus of this system, clearly finding any asymptotes and calculating any break-in or break-away point:s. Determine the range of gain (K) to ensure that the system is stable Draw the Nyquist diagram of this system, only considering the imaginary axis of the original RHP contour (i.e. between points A and B on the original contour). Hint: You will want to...
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...
Problem 30 (15 points) Consider the closed-loop sampled-data system in Figure 6 that uses a sample period of 600 ms. The pulse transfer function of the continuous-time plant is Ge)- 0.04147 z-0.7408 while Ge(2) is the transfer function of a discrete-time compensator. E(Z)G.(2) Figure 6: Closed-loop sampled-data system with compensator Ge() I. (5 points) Is it possible to achieve a steady-sate error ess- 0.05 for a unit-step input r(k) = uo(k) using proportional feedback Ga(z) = K? If yes, derive...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system shown in the figure below, where the two input signals are given to be xi(t) = sinc(10t) and x2(t) = sinc(6t). ylt) z(t) LTI →2;(+) ht) Xalt) P(+) - E81-nt) a) State the sampling theorem. Be sure to include all conditions for its validity. (5 pts) b) What is the minimum frequency at which y(t) must be sampled such that it could be completely...
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a) Locate open-loop zeros and open-loop poles. b) Construct the root-locus diagram as 0 <K <oo. Mark the portions of the real axis that belong to the root locus - Mark with K =0 the point where the root locus bra O the point where the root locus branches start and with K = oo the point where the branches end. - Find break-away and/or...
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
r[n] + K(z) D/A with ZOH G(s) A/D Here the sampling period T = 0.5 sec and G(s) = FT K(z) = 30 (i) Find the ZOH discrete equivalent of the system and determine if it is stable. For this problem, you are NOT allowed to use the table of z-transforms.
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...
Sketch the root locus for the unity feedback system shown in Figure P8.3 for the following transfer functions: (Section: 8.4] K(s + 2)(8 + 6) a. G(s) = 52 + 8 + 25 K( +4) b. G(S) = FIGURE PR3 152 +1) C G(s) - K(s+1) K (n1)(x + 4) For each system record all steps to sketching the root locus: 1) Identify the # of branches of the system 2) Make sure your sketch is symmetric about the real-axis...
Need help with this. Please show all your steps.
K(z-15). Connected in the Assume a system, G[2]-z-ls, conventional negative unity, output feedback configuration. The only adjustable parameter in the Pl controller for this problem is the gain. (a) Find the real axis line segments in the complex z-plane that belong to the Root Locus 5. and a PI controller, C[z] associated with the closed-loop poles of this system. The Root Locus is drawn for the forward gain in the system...
Control System Problem. Please do part A, B , and C.
Consider the unity-feedback system with G(s)-K(st3)(s+5)/(s+(s-7)] Sketch the root locus of this system, clearly finding any asymptotes and calculating any break-in or break-away point:s. Determine the range of gain (K) to ensure that the system is stable Draw the Nyquist diagram of this system, only considering the imaginary axis of the original RHP contour (i.e. between points A and B on the original contour). Hint: You will want to...
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