GATE Questions & Answers of State variable model and solution of state equation of LTI systems

What is the Weightage of State variable model and solution of state equation of LTI systems in GATE Exam?

Total 11 Questions have been asked from State variable model and solution of state equation of LTI systems topic of Control Systems subject in previous GATE papers. Average marks 1.91.

The state diagram of a system is shown below. A system is described by the state-variable equations

X=AX+Bu;     y=CX+Du   

The State-variable equations of the system shown in the figure above are

The state diagram of a system is shown below. A system is described by the state-variable equations

X=AX+Bu;     y=CX+Du   

The state transition matrix e A t of the system shown in the figure above is

The state variable description of an LTI system is given by

x1.x2.x3.= 0a1000a2a300 x1x2x3+001u

y=100x1x2x3

where y is the output and u is the input. The system is controllable for

The block diagram of a system with one input u and two outputs y1 and y2 is given below.

A state space model of the above system in terms of the state vector x and the output vector y=y1y2T is

The signal flow graph of a system is shown below.

The state variable representation of the system can be

The signal flow graph of a system is shown below.

The transfer function of the system is

Consider the system dxdt=Ax+Bu with A=1001 and B=pq where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?

A single flow graph of a system is given below

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

The state space representation of a separately excited DC servo motor dynamics is given as

dωdtdiadt=-11-1-10ωia+010u

where ω is the speed of the motor, ia is the armature current and u is the arnature voltage. The transfer function ωsUs of the motor is

Consider a linear system whose state space representation is x·t=Axt. If the initial state vector of the system is x0=1-2, then system response is xt=e-2t-2e-2t. If the initial vector of the system changes to x0=1-1, then the system responce becomes xt=e-t-e-t.

The eigenvalue and eigenvector pairs λi,vi for the system are

Consider a linear system whose state space representation is x·t=Axt. If the initial state vector of the system is x0=1-2, then system response is xt=e-2t-2e-2t. If the initial vector of the system changes to x0=1-1, then the system responce becomes xt=e-t-e-t.

The system matrix A is