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# GATE EC 2021: Control Systems Quiz 9

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Question 1

The state transition matrix of a system is given below:

Find the characteristic equation of the system.

Find the characteristic equation of the system.

Question 2

Consider the state space model of a system, as given below

The system is

The system is

Question 3

A single flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

The set of equations that correspond to this signal flow graph is

Question 4

Consider a system characterised by the non-homogenous state equation:

Where are states of the system and ‘u’ is the unit-step input function. Find the zero-input response of the system considering the initial state as is given by

Where are states of the system and ‘u’ is the unit-step input function. Find the zero-input response of the system considering the initial state as is given by

Question 5

Consider the electrical network given below.

Find the state-space representation of the system if the output is the current through the resistor.

Find the state-space representation of the system if the output is the current through the resistor.

Question 6

Transfer function of a system is given as

Find the state-space representation of the above system.

Find the state-space representation of the above system.

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Aug 23ESE & GATE EC

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