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20e 82 amd M(M) is a three-state Problem I: Given the nonlinear system, in which G(s)amd N(M) is a three-state relay...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Dev...
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Develop a state space model for this transfer function, in the standard form y=Cx + Du (b) Suppose that zero input is applied, such that u 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how...
The M/M/m/m Server Loss System: Consider the queuing system given by the following state- transition diagram. Each arri...
The M/M/m/m Server Loss System: Consider the queuing system
given by the following state- transition diagram.
Each arriving customer is given a private server, but there is a
maximum of m servers available. If a customer arrives when all m
servers are busy, the customer is denied service and is turned
away. The arrival rate is Poisson with parameter λ and the service
rate is kμ with 1 ≤ k ≤ m as shown. Use the results obtained in Set...
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V...
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V(r)2r2. The particle is in the I-0 state. Noting that all eigenfunetions must be finite everywhere, find the ground-state radial wave-function R() and the ground-state energy. You do not have to nor oscillator is g (x) = C x exp(-8x2), where C and B are constants) harmonic malize the solution....
Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable pa...
Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable parameter pl(s) Dal(sKp+ g) Assuming W-0, find the transfer function Y(s)/R(s) h) Assuming R-0, find the transfer function Y(s)/W(s) i) What is the type of the system (with respect to steady-state error)? j) What is the steady-state error when rt)u(t) (unit-step) and w(t)-0 k) What is the s.s. error when r(t) t u(t) and w(t)-0 ) Assume r(t)-0, what is the...
Consider the system. (1) M →1.0) M +0.1 kg, B=0.2 N-s/m Mv(1) + By(t) = 1,01)...
Consider the system. (1) M →1.0) M +0.1 kg, B=0.2 N-s/m Mv(1) + By(t) = 1,01) Consider a system described by the following differential equation: 0.1"WX2 +0.2v(t) = .0), where y(t) and 4.0) are the output and the input of the system. dt (la) Convert the above differential equation into the form of the typical first-order dynamic system: + ) = ), and explain the physical meaning of the two parameters 7 and v.. (5%) dv(1) (1b) According to the...
Problem 6 State space representation of motor - driven cart with inverted pendulum You are given...
Problem 6 State space representation of motor - driven cart with inverted pendulum You are given that the cart carrying the inverted pendulum shown in the figure below is driven by an electric motor powering one pair of wheels so that the whole cart, pendulum and all, becomes the load on the motor. z is the cart position, M is its mass, θ is the pendulum angle with respect to the vertical, I its length, and m its mass. The...
Exercise 12.2 In Example 12.1b, find the optimal strategy and the op- timal value when the urn contains three red and four blue balls S. Example 12.1b An urn initially has n red and m blue balls. At...
Exercise 12.2 In Example 12.1b, find the optimal strategy and the op- timal value when the urn contains three red and four blue balls S. Example 12.1b An urn initially has n red and m blue balls. At each stage the player may randomly choose a ball from the urn; if the ball is red, then 1 is earned, and if it is blue, then 1 is lost. The chosen ball is discarded. At any time the player can decide...
Mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s)...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Develop a state space model for this transfer function, in the standard form y=Cx + Du (b) Suppose that zero input is applied, such that u 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how...
The M/M/m/m Server Loss System: Consider the queuing system
given by the following state- transition diagram.
Each arriving customer is given a private server, but there is a
maximum of m servers available. If a customer arrives when all m
servers are busy, the customer is denied service and is turned
away. The arrival rate is Poisson with parameter λ and the service
rate is kμ with 1 ≤ k ≤ m as shown. Use the results obtained in Set...
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V(r)2r2. The particle is in the I-0 state. Noting that all eigenfunetions must be finite everywhere, find the ground-state radial wave-function R() and the ground-state energy. You do not have to nor oscillator is g (x) = C x exp(-8x2), where C and B are constants) harmonic malize the solution....
Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable parameter pl(s) Dal(sKp+ g) Assuming W-0, find the transfer function Y(s)/R(s) h) Assuming R-0, find the transfer function Y(s)/W(s) i) What is the type of the system (with respect to steady-state error)? j) What is the steady-state error when rt)u(t) (unit-step) and w(t)-0 k) What is the s.s. error when r(t) t u(t) and w(t)-0 ) Assume r(t)-0, what is the...
Consider the system. (1) M →1.0) M +0.1 kg, B=0.2 N-s/m Mv(1) + By(t) = 1,01) Consider a system described by the following differential equation: 0.1"WX2 +0.2v(t) = .0), where y(t) and 4.0) are the output and the input of the system. dt (la) Convert the above differential equation into the form of the typical first-order dynamic system: + ) = ), and explain the physical meaning of the two parameters 7 and v.. (5%) dv(1) (1b) According to the...
Problem 6 State space representation of motor - driven cart with inverted pendulum You are given that the cart carrying the inverted pendulum shown in the figure below is driven by an electric motor powering one pair of wheels so that the whole cart, pendulum and all, becomes the load on the motor. z is the cart position, M is its mass, θ is the pendulum angle with respect to the vertical, I its length, and m its mass. The...
Exercise 12.2 In Example 12.1b, find the optimal strategy and the op- timal value when the urn contains three red and four blue balls S. Example 12.1b An urn initially has n red and m blue balls. At each stage the player may randomly choose a ball from the urn; if the ball is red, then 1 is earned, and if it is blue, then 1 is lost. The chosen ball is discarded. At any time the player can decide...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
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