Find the state equations choosing lambda (flux) as the electrical state
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Find the state equations choosing lambda (flux) as the electrical state
problem 1: the magnetic core shown in the figure has the following parameters ELECTRICAL ENGINEERING DEPARTMENT...
problem 1: the magnetic core shown in the figure has the
following parameters
ELECTRICAL ENGINEERING DEPARTMENT CALIFORNIA POLYTECHNIC STATE UNIVERSITY EE 255 Assignment #3 Problem 1: The magnetic core shown in the figure has the following parameters: 1 = 10 cm , A = 2.5 cm, N = 100 turns, u = 5000, andf = 60 Hz. For a current of I() = 5 cos(01) A, determine: (a) Flux in the core, (b) Flux linkage, (c) Inductance (L-0.157 H), and...
Consider the magnetic system in Figure 1 h? Figure1 When x = 0, there's no airgap...
Consider the magnetic system in Figure 1 h? Figure1 When x = 0, there's no airgap between two parts of this system. The area of cross-section is m Assume x = 3t where t is the time. The total length of the whole iron magnetic loop (excluding airgap) is 9 m. Given dp-3000 , 40-4? × 10-7 H/m, and number of turns N = 20 Answer the following questions: (i) Calculate the reluctance the magnetizing path as a function of...
Or (B) The following is the electrical equivalent model of a fluid system. Find the state...
Or (B) The following is the electrical equivalent model of a fluid system. Find the state equations and the matrices A and B of the model X' AX + BU. Extra Credit for (B): Find the matrices C and D in the output equation Y = CX + DU when the output is just Pout indicated in the figure. f- てw OUT
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindri...
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindrical magnetic core of permeability μ μ0Hm The cylindrical core, extending along the z-axis, has radius α n turns per unit length, current I per turn Magnetic material of μ (a) If the solenoid is considered as infinite in length, it can be shown that the magnetic field, expressed in cylindrical coordinates, is: r> a Apply Ampere's law, using the rectangular path...
8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c. Determine the eq...
8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c. Determine the equations governing λ and x. d. Determine u°()given x(0)-0 and x(1) I
8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c....
Problem 4 (50 pts): Consider the electrical circuit represented in figure, with R = 102, C...
Problem 4 (50 pts): Consider the electrical circuit represented in figure, with R = 102, C = 1 F and L=1 H. Assume V (t) as input and i(t) as output E ER V.(t) a) (5 pts) Determine the differential equation of the system b) (5 pts) Find the transfer function of the system c) (20 pts) Write the symbolic expressions of magnitude and phase of the transfer function d) (20 pts) Determine the expression of steady-state response of the...
Problem 1) Derive differential equations governing the given fluid system for the system and present them...
Problem 1) Derive differential equations governing the given fluid system for the system and present them in state space form. The density of the fluid is p. The fluid exiting the tank with capacitance C3, flows through a resistor R4 and then a long pipe of length L with an inertance I State vector X-[h h, h, h, q input vector u={qil qi2 qǐ3)" Output Vector Y (42 i2 41 92 h3 C. 93 Rs 3 You may solve the...
the system of equations describing the operation of the ci find the numerical values of the...
the system of equations describing the operation of the ci find the numerical values of the electrical currents if R,-1 Ω, R2-2 Ω, R,-452, R,-7 Ω, Q-3 Electrical DC circuit is given in Fig, 3. Please: i) Use Kirchhoff's laws and derive rcuit; ii) Solve the system from i) and Ri R2 R3 R4 V2
A) For the schematic above find the state-space equations that define this system. B) Using the...
A) For the schematic above find the state-space equations that
define this system.
B) Using the controllability rank test determine if this system
is controllable.
C) Using the observability rank test determine if this system is
observable.
1. Controllability and Observability L = 100 m R1 = 10 Ohms Mm R2 = 100 Ohms R4 = 100 Ohms ( = 100 microfarads ult) 1V R3 = 100 Ohms R5 = 100 Ohms Xı = i(t) y = valt) vi(t) =...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin ...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin to find the input u that minimizes dt a. Determine the state function of Pontryagin H. b. Find the optimal input and H c. Find the matrix A that will yield the governing equations x1 ai If xi (0) : 0.x2(0) = O and xi (1) = İ. x 2(1) =0 determine the govem equations for λǐ(0) and λ2(0) in terms of the elements...
problem 1: the magnetic core shown in the figure has the
following parameters
ELECTRICAL ENGINEERING DEPARTMENT CALIFORNIA POLYTECHNIC STATE UNIVERSITY EE 255 Assignment #3 Problem 1: The magnetic core shown in the figure has the following parameters: 1 = 10 cm , A = 2.5 cm, N = 100 turns, u = 5000, andf = 60 Hz. For a current of I() = 5 cos(01) A, determine: (a) Flux in the core, (b) Flux linkage, (c) Inductance (L-0.157 H), and...
Consider the magnetic system in Figure 1 h? Figure1 When x = 0, there's no airgap between two parts of this system. The area of cross-section is m Assume x = 3t where t is the time. The total length of the whole iron magnetic loop (excluding airgap) is 9 m. Given dp-3000 , 40-4? × 10-7 H/m, and number of turns N = 20 Answer the following questions: (i) Calculate the reluctance the magnetizing path as a function of...
Or (B) The following is the electrical equivalent model of a fluid system. Find the state equations and the matrices A and B of the model X' AX + BU. Extra Credit for (B): Find the matrices C and D in the output equation Y = CX + DU when the output is just Pout indicated in the figure. f- てw OUT
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindrical magnetic core of permeability μ μ0Hm The cylindrical core, extending along the z-axis, has radius α n turns per unit length, current I per turn Magnetic material of μ (a) If the solenoid is considered as infinite in length, it can be shown that the magnetic field, expressed in cylindrical coordinates, is: r> a Apply Ampere's law, using the rectangular path...
8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c. Determine the equations governing λ and x. d. Determine u°()given x(0)-0 and x(1) I
8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c....
Problem 4 (50 pts): Consider the electrical circuit represented in figure, with R = 102, C = 1 F and L=1 H. Assume V (t) as input and i(t) as output E ER V.(t) a) (5 pts) Determine the differential equation of the system b) (5 pts) Find the transfer function of the system c) (20 pts) Write the symbolic expressions of magnitude and phase of the transfer function d) (20 pts) Determine the expression of steady-state response of the...
Problem 1) Derive differential equations governing the given fluid system for the system and present them in state space form. The density of the fluid is p. The fluid exiting the tank with capacitance C3, flows through a resistor R4 and then a long pipe of length L with an inertance I State vector X-[h h, h, h, q input vector u={qil qi2 qǐ3)" Output Vector Y (42 i2 41 92 h3 C. 93 Rs 3 You may solve the...
the system of equations describing the operation of the ci find the numerical values of the electrical currents if R,-1 Ω, R2-2 Ω, R,-452, R,-7 Ω, Q-3 Electrical DC circuit is given in Fig, 3. Please: i) Use Kirchhoff's laws and derive rcuit; ii) Solve the system from i) and Ri R2 R3 R4 V2
A) For the schematic above find the state-space equations that
define this system.
B) Using the controllability rank test determine if this system
is controllable.
C) Using the observability rank test determine if this system is
observable.
1. Controllability and Observability L = 100 m R1 = 10 Ohms Mm R2 = 100 Ohms R4 = 100 Ohms ( = 100 microfarads ult) 1V R3 = 100 Ohms R5 = 100 Ohms Xı = i(t) y = valt) vi(t) =...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin to find the input u that minimizes dt a. Determine the state function of Pontryagin H. b. Find the optimal input and H c. Find the matrix A that will yield the governing equations x1 ai If xi (0) : 0.x2(0) = O and xi (1) = İ. x 2(1) =0 determine the govem equations for λǐ(0) and λ2(0) in terms of the elements...
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