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Given is the parallel connected RLC network as depicted in the figure below. L R 1)I(t) iz(1) The controllable current source I(t) is the system input. The current ig(t) flowing through a resistive load is the system output. The constant system parameters ar the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory. For the following, the parameter values R=10, L=0.01, C=0.1 are assumed. b) For the above RLC network, assume a closed-loop system with the feedback gain K. Calculate the optimal value of the K-gain so that the closed-loop system has the maximal possible natural frequency (i.e. max ) and is critically damped (i.e. =1) at the same time.

Given is the parallel connected RLC network as depicted in the figure below. L R 1)I(t) iz(1) The controllable current source I(t) is the system input. The current ig(t) flowing through a resistive load is the system output. The constant system parameters ar the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory. For the following, the parameter values R=10, L=0.01, C=0.1 are assumed. b) For the above RLC network, assume a closed-loop system with the feedback gain K. Calculate the optimal value of the K-gain so that the closed-loop system has the maximal possible natural frequency (i.e. max ) and is critically damped (i.e. =1) at the same time.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Given is the parallel connected RLC network as depicted in the figure below. L C R (↑)I(1) ↑ )I(1) The controllable current source I(t) is the system input. The current ig(t) flowing through a resistive load is the system output. The constant system parameters are the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory. For the following, the parameter values R=10, L=0.01, C=0.1 are assumed. b) For the above RLC network, assume a closed-loop system with the feedback gain K. Calculate the optimal value of the K-gain so that the closed-loop system has the maximal possible natural frequency (i.e. max @n) and is critically damped (i.e. =1) at the same time.
Transcribed Image Text:Given is the parallel connected RLC network as depicted in the figure below. L C R (↑)I(1) ↑ )I(1) The controllable current source I(t) is the system input. The current ig(t) flowing through a resistive load is the system output. The constant system parameters are the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory. For the following, the parameter values R=10, L=0.01, C=0.1 are assumed. b) For the above RLC network, assume a closed-loop system with the feedback gain K. Calculate the optimal value of the K-gain so that the closed-loop system has the maximal possible natural frequency (i.e. max @n) and is critically damped (i.e. =1) at the same time.
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