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17. For each of the dynamical systems shown below (1) find the poles and the zeros...
i. For the transfer function s+2 T(S) - 2 +9 a. find the locations of the...
i. For the transfer function s+2 T(S) - 2 +9 a. find the locations of the poles and zeros (3 marks) b. plot them on the s-plane (3 marks) c. write an expression for the general form of the step response without solving for the inverse Laplace transform (2 marks) d. State the nature of the response (2 marks)
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system d...
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system design and analysis. In this problem, we will analyze how to properly handle common poles and zeros. 2.1 Consider the following two systems System 1: G(s)~5+2 System 2: G(s) S+2 (s+1.99) (s+20) Using inverse Laplace transform, determine the step response and discuss whether you can use a first-order system to approximate the step response. 2.2 Now consider the following system G(s) = (s -1.99)...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, ho...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
Spring 2017 Name: 1. (a) Find the transfer function, Go)- v,(s),(s), for the network shown (b) Find the shown...
Spring 2017 Name: 1. (a) Find the transfer function, Go)- v,(s),(s), for the network shown (b) Find the shown below. e ramp response for the given system. (t1 fer function, G(S)-x (G)/F(S) of the translational mechanical system shown below x(t) f, 3. For each of transfer functions shown below, find the oestions of the potes ans Plot them on the 5-plane, Rnd then write an expression for de geterst form of me response without solving for the inverse Laplace tranform....
Question: A dynamical system's equations of motion are given below: du)dut) dy(t) 1 2 80-5 to0 + 6y(et+) d2x(t...
Question: A dynamical system's equations of motion are given below: du)dut) dy(t) 1 2 80-5 to0 + 6y(et+) d2x(t) dx(t) Note: initial conditions are zeros, U(s) is an impulse function and Fs) is a step function. Hint: factor nicely the denominators. For each of the dynamical system, please: (a) Compute the transfer function U(s) (b) Find the inverse Laplace transform expression for y() and x(0) (c) Compute the final value of the system. (d) Compute the initial value of the...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system zero Submit Part D-Type of Response Based on the locations af the poles and zeros, what will be the response to a unit step inpue? O Harmonic Oscillations (Marginally stable) Oscillatory motion with exponential decay tending to zero (stable O Critically damped exponential decay (stable)...
9-8 Find the Laplace transform of f(t)=54cos(100 3sin(10t)] u(t). Locate the poles and zeros of F(s).
9-8 Find the Laplace transform of f(t)=54cos(100 3sin(10t)] u(t). Locate the poles and zeros of F(s).
4. For each of the transfer functions shown below, find the locations of the poles and...
4. For each of the transfer functions shown below, find the locations of the poles and zeros, plot them on the s-plane. State the nature of each response (overdamped, underdamped, etc). G(S) =515 G(s) = (s+2)(s+7) 5(s +5) G(s) = (s +15)(s +8) 15 G(S) = 52 +85 +121 G(6) 52716 G(s) = 187332
Signals and Systems 2. The pole-zero diagram below has 2 zeros at the origin and 2...
Signals and Systems
2. The pole-zero diagram below has 2 zeros at the origin and 2 poles to represent a system A(s). Pole-Zero Map (-0.5, +1) X d Imaginary Au (-0.5, -1) X RealAxis con Is this a stable system? Explain. Write an exact simplified expression for A(s). A(s) = 3. A system has impulse response h(t)= u(t) A e' where A and B are positive constants. Write an exact simplified expression for H(S).
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (...
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
i. For the transfer function s+2 T(S) - 2 +9 a. find the locations of the poles and zeros (3 marks) b. plot them on the s-plane (3 marks) c. write an expression for the general form of the step response without solving for the inverse Laplace transform (2 marks) d. State the nature of the response (2 marks)
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system design and analysis. In this problem, we will analyze how to properly handle common poles and zeros. 2.1 Consider the following two systems System 1: G(s)~5+2 System 2: G(s) S+2 (s+1.99) (s+20) Using inverse Laplace transform, determine the step response and discuss whether you can use a first-order system to approximate the step response. 2.2 Now consider the following system G(s) = (s -1.99)...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
Spring 2017 Name: 1. (a) Find the transfer function, Go)- v,(s),(s), for the network shown (b) Find the shown below. e ramp response for the given system. (t1 fer function, G(S)-x (G)/F(S) of the translational mechanical system shown below x(t) f, 3. For each of transfer functions shown below, find the oestions of the potes ans Plot them on the 5-plane, Rnd then write an expression for de geterst form of me response without solving for the inverse Laplace tranform....
Question: A dynamical system's equations of motion are given below: du)dut) dy(t) 1 2 80-5 to0 + 6y(et+) d2x(t) dx(t) Note: initial conditions are zeros, U(s) is an impulse function and Fs) is a step function. Hint: factor nicely the denominators. For each of the dynamical system, please: (a) Compute the transfer function U(s) (b) Find the inverse Laplace transform expression for y() and x(0) (c) Compute the final value of the system. (d) Compute the initial value of the...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system zero Submit Part D-Type of Response Based on the locations af the poles and zeros, what will be the response to a unit step inpue? O Harmonic Oscillations (Marginally stable) Oscillatory motion with exponential decay tending to zero (stable O Critically damped exponential decay (stable)...
9-8 Find the Laplace transform of f(t)=54cos(100 3sin(10t)] u(t). Locate the poles and zeros of F(s).
4. For each of the transfer functions shown below, find the locations of the poles and zeros, plot them on the s-plane. State the nature of each response (overdamped, underdamped, etc). G(S) =515 G(s) = (s+2)(s+7) 5(s +5) G(s) = (s +15)(s +8) 15 G(S) = 52 +85 +121 G(6) 52716 G(s) = 187332
Signals and Systems
2. The pole-zero diagram below has 2 zeros at the origin and 2 poles to represent a system A(s). Pole-Zero Map (-0.5, +1) X d Imaginary Au (-0.5, -1) X RealAxis con Is this a stable system? Explain. Write an exact simplified expression for A(s). A(s) = 3. A system has impulse response h(t)= u(t) A e' where A and B are positive constants. Write an exact simplified expression for H(S).
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
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