Problem 1: Consider the circuit diagram below containing unsteady current source, is. For this circuit, determine:
a) the number of state variables required to describe the dynamic circuit behavior,
b) list a set of state variables that could be used to determine circuit behavior,
c) determine a set of state-space equations describing circuit behavior in terms of your state variables from part b, d) state the output vector for the current flowing through capacitor ‘C’
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Problem 1: Consider the circuit diagram below containing unsteady current source, is. For this circuit, determine:...
Problem 1: Given the RLC circuit with current source as shown (assume the system is initially...
Problem 1: Given the RLC circuit with current source as shown (assume the system is initially relaxed a) (8 points) Write the state equations if the Rich Led state vector X = [i:] i Lt) 个 H y = |VC b) (7 points) Write the output equation if TVR i.e. voltage across each element. VL. c) (5 points) Using the state equations find Vr(s)/I(s)
Consider a series circuit containing a resistor of resistance R and a capacitor of capacitance C connected to a source of EMF E with negligible internal resistance.
Consider a series circuit containing a resistor of resistance R and a capacitor of capacitance C connected to a source of EMF E with negligible internal resistance. The wires are also assumed to have zero resistance. Initially, the switch is open and the capacitor discharged. (Figure 1)A Immediately after the switch is closed, what is the voltage across the capacitor?B Complete previous part(s) C Immediately after the switch is closed, what is the direction of the current in the circuit? E Eventually,...
(1) In the system shown below, the input is the ideal current source *i,' is and...
(1) In the system shown below, the input is the ideal current source *i,' is and the output is the voltage across the inductor L1I'. Derive the governing differential equations for the circuit shown below and represent them in state space form. 41-K The state variable R2 L1 R3 Vc C1
7. For the circuit shown below, choose uc, and uc, as state variables and out as...
7. For the circuit shown below, choose uc, and uc, as state variables and out as the output variable. (a) (10 points) Develop the state variable equations. Your result must be of the form = Ar+Bu, where x is the vector of state variables and u, which in this case is in, is the driver function. (Hint: it is easy to compute the currents in terms of vin, tout, and the capacitor voltages. (b) (10 points) Develop the output equation,...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1)...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
Sketch a circuit diagram with a current source Is and two parallel resistors Ri and R2....
Sketch a circuit diagram with a current source Is and two parallel resistors Ri and R2. Label the current through Ri as Ii and the current expression for the current Ii in terms of Is, RI, and R2. (C-2) Derive the mathematical expression for the current 12 in terms of Is, RI, and R2. through R2 as I2. (C-1) Derive the mathematical
1. The following two-loop circuit has a constant current source, I, across which an unknown potential...
1. The following two-loop circuit has a constant current source, I, across which an unknown potential difference, Δν, will be produced. R1 R2 R3 This circuit can still be analyzed as a linear 2 × 2 system of equations, which must be solved to determine the unknown Δν and the current, 12, that flows in the second loop with the voltage source. (a) Write down the 2 2 system of linear equations in the unknowns Δν and 12. (b) Use...
The circuit below containing a dependent current source (CCCS) is to be analyzed with mesh-current analysis....
The circuit below containing a dependent current source (CCCS) is to be analyzed with mesh-current analysis. Towards this end, three clockwise mesh currentsij, ig, and is have also been shown. It was found that mesh currents ig = 4A and is = 2 A for certain values of the circuit parameters. Then the value of the mesh currenti, is given by Mesh! 10 102 w (Mesh ? R Mesh 3 o OOOOO =-1A There is not enough information to determine...
Learning Goal: To understand the dynamics of a series R-C circuit. Consider a series circuit containing...
Learning Goal: To understand the dynamics of a series R-C circuit. Consider a series circuit containing a resistor of resistance R and a capacitor of capacitance C connected to a source of EMF ε with negligible internal resistance. The wires are also assumed to have zero resistance. Initially, the switch is open and the capacitor discharged. (Figure 1)Let us try to understand the processes that take place after the switch is closed. The charge of the capacitor, the current in...
1. Find the state equations and output equation for a parallel RL C circuit driven by...
1. Find the state equations and output equation for a parallel RL C circuit driven by a current source input; take the output to be capacitor current 2. Give examples of control and observer canonical forms
Problem 1: Given the RLC circuit with current source as shown (assume the system is initially relaxed a) (8 points) Write the state equations if the Rich Led state vector X = [i:] i Lt) 个 H y = |VC b) (7 points) Write the output equation if TVR i.e. voltage across each element. VL. c) (5 points) Using the state equations find Vr(s)/I(s)
(1) In the system shown below, the input is the ideal current source *i,' is and the output is the voltage across the inductor L1I'. Derive the governing differential equations for the circuit shown below and represent them in state space form. 41-K The state variable R2 L1 R3 Vc C1
7. For the circuit shown below, choose uc, and uc, as state variables and out as the output variable. (a) (10 points) Develop the state variable equations. Your result must be of the form = Ar+Bu, where x is the vector of state variables and u, which in this case is in, is the driver function. (Hint: it is easy to compute the currents in terms of vin, tout, and the capacitor voltages. (b) (10 points) Develop the output equation,...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
Sketch a circuit diagram with a current source Is and two parallel resistors Ri and R2. Label the current through Ri as Ii and the current expression for the current Ii in terms of Is, RI, and R2. (C-2) Derive the mathematical expression for the current 12 in terms of Is, RI, and R2. through R2 as I2. (C-1) Derive the mathematical
1. The following two-loop circuit has a constant current source, I, across which an unknown potential difference, Δν, will be produced. R1 R2 R3 This circuit can still be analyzed as a linear 2 × 2 system of equations, which must be solved to determine the unknown Δν and the current, 12, that flows in the second loop with the voltage source. (a) Write down the 2 2 system of linear equations in the unknowns Δν and 12. (b) Use...
The circuit below containing a dependent current source (CCCS) is to be analyzed with mesh-current analysis. Towards this end, three clockwise mesh currentsij, ig, and is have also been shown. It was found that mesh currents ig = 4A and is = 2 A for certain values of the circuit parameters. Then the value of the mesh currenti, is given by Mesh! 10 102 w (Mesh ? R Mesh 3 o OOOOO =-1A There is not enough information to determine...
1. Find the state equations and output equation for a parallel RL C circuit driven by a current source input; take the output to be capacitor current 2. Give examples of control and observer canonical forms
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