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The statespace representation for a system is
The transfer function Y(s) /U(s) is
Substituting the values,
Determine the statespace representation for the transfer function given in question. Choose the state variable as follows
Q.
(s^{3} + a_{2}s^{2} + a_{1}s + a_{0})C(s) = b_{0}R(s)
Taking the inverse Laplace transform assuming zero initial conditions
Determine the statespace representation for the transfer function given in question. Choose the state variable as follows
Q.
Fourth order hence four state variable
A statespace 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 C_{M} = 0. Hence system is not controllable. det O_{M }= 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 O_{M} 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 O_{M} = 0. Thus system is not observable
det C_{M} = 1. Thus system is controllable.
Consider the network shown in fig. The statespace representation for this network is
v_{c} and i_{L} are state variable.
Hence equation are
For the network shown in fig. The output is
i_{R}(t). The state space representation is
Hence v_{1} and i_{3} 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. v_{C }and i_{L} are available in differential form and linearly independent. Hence v_{C }and i_{L} are suitable for statevariable.
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. i_{2} ,i_{4} and v_{o} are available in differentiated form hence these are state variable.
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