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.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.61P

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