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Question# 2 Given a continuous-time control system Y (s) R(s) (s 16 2)(s + 8) ntt pole-zero mappi...
Question#1 Given the following block diagram of a continuous-time system with Ki 10 and K2=5 Rs)...
Question#1 Given the following block diagram of a continuous-time system with Ki 10 and K2=5 Rs) Yo) a) Using the forward rectangular rule equivalent discrete-time system (FRR), find the state- variable model (SVM) of the above system in matrix form. b) If the overall z-trans fer function of Y(z/R(2) is found to be 10z2 Y(z) R(2) 6622-57z+1 What discrete-time equivalent is used to reach to the above transfer function? Show work c) Using Y(z)/R(z) of part (b), if r(k)-a unit-step...
you can use matlab to solve 1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The...
you can use matlab to solve
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The appropriate sampling time d) G(z) pulse transfer function e) Continuous State Space, A, B, C, D f) Discrete State Space, A, B, C, D
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of...
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.
5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1...
5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1 - Let y(t) = s(t) represent the response of this system to a unit-step signal 0; otherwise. Assume that the Unit-Step response s(t) of this system is known to approach 1 as t o. Determine y(t) = s(t), justify your answers mathematically.
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are related by Y(s) = 2 (s+2)2 +10 a) If x(t) = u(t), find the zero-state response of the system, yzs(1). yzs() = b) Find the zero-input response of the system, yzi(t). Yzi(t) = c) Find the steady-state solution of the system, yss(t). Yss(t) =
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measur...
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
Let a be a positive real number. Consider a discrete-time echo system (called system 1) given...
Let a be a positive real number. Consider a discrete-time echo system (called system 1) given by the difference equation y[n] = v[n] + av[n – 4). Here v is the input signal and y is the output signal. A. (1 mark) Determine the systems' transfer function H1 (2). B. (1 mark) What are the pole(s) of this system? Plot the pole(s) in the complex plane. C. (2 marks) Is this system stable? Explain your answer. D. (2 marks) Determine...
Question#1 Given the following block diagram of a continuous-time system with Ki 10 and K2=5 Rs) Yo) a) Using the forward rectangular rule equivalent discrete-time system (FRR), find the state- variable model (SVM) of the above system in matrix form. b) If the overall z-trans fer function of Y(z/R(2) is found to be 10z2 Y(z) R(2) 6622-57z+1 What discrete-time equivalent is used to reach to the above transfer function? Show work c) Using Y(z)/R(z) of part (b), if r(k)-a unit-step...
you can use matlab to solve
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The appropriate sampling time d) G(z) pulse transfer function e) Continuous State Space, A, B, C, D f) Discrete State Space, A, B, C, D
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of...
5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1 - Let y(t) = s(t) represent the response of this system to a unit-step signal 0; otherwise. Assume that the Unit-Step response s(t) of this system is known to approach 1 as t o. Determine y(t) = s(t), justify your answers mathematically.
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are related by Y(s) = 2 (s+2)2 +10 a) If x(t) = u(t), find the zero-state response of the system, yzs(1). yzs() = b) Find the zero-input response of the system, yzi(t). Yzi(t) = c) Find the steady-state solution of the system, yss(t). Yss(t) =
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
Let a be a positive real number. Consider a discrete-time echo system (called system 1) given by the difference equation y[n] = v[n] + av[n – 4). Here v is the input signal and y is the output signal. A. (1 mark) Determine the systems' transfer function H1 (2). B. (1 mark) What are the pole(s) of this system? Plot the pole(s) in the complex plane. C. (2 marks) Is this system stable? Explain your answer. D. (2 marks) Determine...
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