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Signals and system & Consider the causal L.TI system whose system function is specified as +7s + 12 H)+Ds +2) De...
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...
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...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 +...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 + 3y(t) = x(t). Draw a block digram representation for S. Then, convert this differential equation into an integral equation, and draw a corresponding block diagram representation. dt
2. Consider the causal LTI system in which the input x(t) and output y(t) are related...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related through the following block diagram respresentation: x(t) y(t) + 1/s # 7 -5 1/s 10 6 a. Find the system function. (2.5 points). b. Determine the differential equation relating y(t) and x(t). (2.5 points). c. Show that this system can be realized as a cascade interconnection of four first order subsystems. Give the system function for each subsystem, and sketch the block diagram of...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference equation for the system specified by H(z) b) Assuming the system is causal, determine the impulse response hln]. c) Is it possible to find an h[n] that is stable? If not, explain why. If it is possible, determine h[n] for this case.
(2) (10 points) Consider a causal LTI system which its zero-pole plot of H(z) is shown...
(2) (10 points) Consider a causal LTI system which its zero-pole plot of H(z) is shown in Fig. 1 2. Suppose it is known that lim h[n]= 1) Determine the h[n] of the system. 2) Determine the difference equation of this system. jim (z) 3) Draw the the Block Diagram of this system. -1/3 Re (z) 2 Fig. 2
3. Block diagram consist of functions performed by each component of a system and flow of signals meanwhile, signal...
3. Block diagram consist of functions performed by each component of a system and flow of signals meanwhile, signal flow graph consists of branches which represents the systems and nodes which represents the signals For the block diagram shown in Figure 5, determine the relationship between the output variable C(s) and the input variable R(s) by analyzing the system's variables. (a) (12 marks) Gil GloC V(s) Figure 5 (b) Consider a simple first-order system G(s). Find the time constant and...
Problem 5: (20=10+5+5 points) Consider a causal system with the following transfer function (the z-transform) 2...
Problem 5: (20=10+5+5 points) Consider a causal system with the following transfer function (the z-transform) 2 +42-2 H2) = 1 - 52-1 +6 1-52-1 +62- 2 2 < 121 <3. (a) Find the inverse z-transform of H(2). (b) Find the difference equation with input-output relation for this system. (c) Draw the diagram of realization (in form II) for this system.
Question 2 20 Marks Consider the transfer function, (6-1)(8-2) (82 7s 12)(s +13) G(s) = 1....
Question 2 20 Marks Consider the transfer function, (6-1)(8-2) (82 7s 12)(s +13) G(s) = 1. Using direct synthesis, synthesize a biproper controller with integral action for this process The desired complementary sensitivity function is given by: (T(s)d- where r is a positive integer to be specified in the design, η1 and η2 are constants to be assigned. 2. What will be the dominant feature of the closed-loop response of the output to a step change in the set-point? Justify...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine:...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine: (i) The system function representation; (ii) the difference-equation representation (Note: this is just terminology that refers to expressing the input and output time-domain signals in the form of an equation. E.g., what we did when we went over the equations for block diagrams); (iii) The pole-zero plot, sketched by hand; and (iv) the output y(n) if the input is x(n) = (0.25)n u(n) [10...
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...
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...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 + 3y(t) = x(t). Draw a block digram representation for S. Then, convert this differential equation into an integral equation, and draw a corresponding block diagram representation. dt
2. Consider the causal LTI system in which the input x(t) and output y(t) are related through the following block diagram respresentation: x(t) y(t) + 1/s # 7 -5 1/s 10 6 a. Find the system function. (2.5 points). b. Determine the differential equation relating y(t) and x(t). (2.5 points). c. Show that this system can be realized as a cascade interconnection of four first order subsystems. Give the system function for each subsystem, and sketch the block diagram of...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference equation for the system specified by H(z) b) Assuming the system is causal, determine the impulse response hln]. c) Is it possible to find an h[n] that is stable? If not, explain why. If it is possible, determine h[n] for this case.
(2) (10 points) Consider a causal LTI system which its zero-pole plot of H(z) is shown in Fig. 1 2. Suppose it is known that lim h[n]= 1) Determine the h[n] of the system. 2) Determine the difference equation of this system. jim (z) 3) Draw the the Block Diagram of this system. -1/3 Re (z) 2 Fig. 2
3. Block diagram consist of functions performed by each component of a system and flow of signals meanwhile, signal flow graph consists of branches which represents the systems and nodes which represents the signals For the block diagram shown in Figure 5, determine the relationship between the output variable C(s) and the input variable R(s) by analyzing the system's variables. (a) (12 marks) Gil GloC V(s) Figure 5 (b) Consider a simple first-order system G(s). Find the time constant and...
Problem 5: (20=10+5+5 points) Consider a causal system with the following transfer function (the z-transform) 2 +42-2 H2) = 1 - 52-1 +6 1-52-1 +62- 2 2 < 121 <3. (a) Find the inverse z-transform of H(2). (b) Find the difference equation with input-output relation for this system. (c) Draw the diagram of realization (in form II) for this system.
Question 2 20 Marks Consider the transfer function, (6-1)(8-2) (82 7s 12)(s +13) G(s) = 1. Using direct synthesis, synthesize a biproper controller with integral action for this process The desired complementary sensitivity function is given by: (T(s)d- where r is a positive integer to be specified in the design, η1 and η2 are constants to be assigned. 2. What will be the dominant feature of the closed-loop response of the output to a step change in the set-point? Justify...
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