The circuit shown in Figure 3 consists of an inductor L, a capacitor C, and a resistor R. The input is the source voltage Vs(t) and the output is the voltage Vo across the resistor Ro. Vs(t) R Figure 3 Using IL and Vc as the state variables, Construct a complete state-space model for the system shown in figure 3. Specifically, express system equations in the vector-matrix form: i = Ax+ Bu y = Cx+Du in the usual notation, where 'x' is the state vector, 'u' is the input vector, and 'y' is the output vector, and determine all the elements of the four matrices A, B, C, and D in terms of the circuit parameters R, Ro, L, and C.

The circuit shown in Figure 3 consists of an inductor L, a capacitor C, and a resistor R. The input is the source voltage Vs(t) and the output is the voltage Vo across the resistor Ro. Vs(t) R Figure 3 Using IL and Vc as the state variables, Construct a complete state-space model for the system shown in figure 3. Specifically, express system equations in the vector-matrix form: i = Ax+ Bu y = Cx+Du in the usual notation, where 'x' is the state vector, 'u' is the input vector, and 'y' is the output vector, and determine all the elements of the four matrices A, B, C, and D in terms of the circuit parameters R, Ro, L, and C.

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 6.59P

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