Test: The State Variable Analysis - 3
20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: The State Variable Analysis - 3
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The state-space representation for a system is
The transfer function Y(s) /U(s) is
Substituting the values,
Determine the state-space representation for the transfer function given in question. Choose the state variable as follows
Q. 
(s3 + a2s2 + a1s + a0)C(s) = b0R(s)
Taking the inverse Laplace transform assuming zero initial conditions
Determine the state-space representation for the transfer function given in question. Choose the state variable as follows
Q. 
Fourth order hence four state variable
A state-space representation of a system is given by
The time response of this system will be
Consider the system shown in fig.
The controllability matrix is
Consider the system shown in fig.
The observability matrix is
Consider the system shown in fig.
The system is
det CM = 0. Hence system is not controllable. det OM = 1. Hence system is observable.
Consider the system shown in fig.
Q. The controllability matrix for this system is
Consider the system shown in fig.
The observability matrix is
Consider the system shown in fig.
Q. The system is
Since the determinant is not zero, the 3 x 3 matrix is nonsingular and system is controllable
The rank of OM is 3. Hence system is observable.
A state flow graph is shown in fig.
Q.The state and output equation for this system is
A state flow graph is shown in fig.
The system is
det OM = 0. Thus system is not observable
det CM = -1. Thus system is controllable.
Consider the network shown in fig. The state-space representation for this network is
vc and iL are state variable.
Hence equation are 
For the network shown in fig. The output is
iR(t). The state space representation is
Hence v1 and i3 are state variable.
Consider the network shown in fig. This system may be represented in state space representation 
Q. The state variable may be
Energy storage elements are capacitor and inductor. vC and iL are available in differential form and linearly independent. Hence vC and iL are suitable for state-variable.
Consider the network shown in fig. This system may be represented in state space representation
Q. If state variable are chosen as in previous question, then the matrix A is
.....(i)
.....(ii)
Solving equation (i) and (ii)
Consider the network shown in fig. This system may be represented in state space representation
Q. The matrix B is
Consider the network shown in fig.
Q. The state variable may be
There are three energy storage elements, hence 3 variable. i2 ,i4 and vo are available in differentiated form hence these are state variable.
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22 docs|274 tests
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22 docs|274 tests
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