Consider the state-space model

where  are the state, input and output, respectively. The matrices  are given below

The sum of the magnitudes of the poles is __________ (round off to nearest integer).

Consider the state-space description of an LTI system with matrices

For the input, , the value of  for which the steady-state output of the system will be zero, is __________ (Round off to the nearest integer).

The state space representation of a first-order system is given as

y = x

where, x is the state variable, u is the control input and y is the controlled output. Let u =-Kx be the control law, where K is the controller gain. To place a closed-loop pole at -2, the value of K is _________.        

Consider a state-variable model of a system

where y is the output, and r is the input. The damping ratio  and the undamped natural frequency  (rad/sec) of the system are given by

Consider a system governed by the following equations

The initial conditions are such that. Let and. Which one of the following is true?

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is

.

Consider the system described by the following state space representation

 and

If u(t) is a unit step input and , the value of output y(t) at t = 1 sec (rounded off to three decimal places ) is ___________ .

Consider the following state-space representation of a linear time-invariant system.        

 and .

The value of y(t) for  is _______________.

Consider a linear time invariant system , with initial condition at t = 0. Suppose  and  are eigenvectors of  matrix A corresponding to distinct eigenvalues  and  respectively. Then the response x(t) of the system due to initial condition  is        

In the signal flow diagram given in the figure,  are possible inputs whereas  are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

The following discrete – time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variable x and y. The integration time step is h.         

For this discrete – time system, which one of the following statements is TRUE?

For the system governed by the set of equations: 

the transfer function Y(s)/U(s) is given by

The state transition matrix for the system

 is

A discrete system is represented by the difference equation

It has initial conditions. The pole locations of the system for a = 1, are

The second order dynamic system         

has the matrices P, Q and R as follows:

The system has the following controllability and observability properties.

Consider the system described by following state space equations

If u is unit step input, then the steady error of the system is

The state variable formulation of a system is given as

, , and

The system is

The state variable formulation of a system is given as

, , and

The response y (t) to a unit step input is

The state variable description of an LTI system is given by  

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

The system  with  is

A system is described by the following state and output equations

Where u(t) is the input and y(t) is the output.

The system transfer function is

A system is described by the following state and output equations

Where u(t) is the input and y(t) is the output.

The state-transition matrix of the above system is

The state space equation of a system is described by

Where x is state vector, u is input, y is output and

The transfer function G(s) of this system will be

The state space equation of a system is described by

Where x is state vector, u is input, y is output and

A unity feedback is provided to the above system G(s) to make it a closed loop system as shown in figure.

For a unit step input r(t), the steady state error In the output will be

The state equation for the current , shown in the network shown below in terms of the voltage , and the independent source V, is given by

For a system with the transfer function, the matrix A in the state space from is equal to

A state variable system

, with the initial condition and the unit step input  u(t) has

The state transition matrix

A state variable system

, with the initial condition and the unit step input u(t) has and the state transition equation

The state variable description of a linear autonomous system is X = AX, where X is the two dimensional state vector and A is the system matrix given by         

.  The roots of the characteristic equation are

A second order system starts with an initial condition of without any external input. The state transition matrix for the system is given by.  The state of the system at the end of 1 second is given by

The following equation defines a separately excited dc motor in the form of a differential equation

The above equation may be organized in the state-space form as follows

Where the P matrix is given by

The state transition matrix for the system X = AX & with initial state X(0) is

For the system, which of the following statements is true?  

For the system

with u as unit impulse and with zero initial state, the output, y, becomes

Obtain a state variable representation of the system governed by the differential equation, with the choice of state variables as

.  
Also find , given that u(t) is a unit step function and.

Given the homogeneous state-space equation

The steady state value, given the initial state value of  is

Consider the state equation

Given:

(a) Find a set of states  and  such that

(b) From , find the matrix A.

For the network of Figure, obtain the state equation in terms of capacitor voltage,and inductor current .

The state-space representation of a system is given by:

Find the Laplace transform of the state transition matrix. Find also the value of  at  if

A system is described by the state equation. The output is given by Y=CX  

Where . Transfer function G(s) of the system is :

The state equation of a linear time-invariant system is given by

(i) Find state transition
(ii) Determine the state vector for t=0 when r(t)=U(t). Assume values of states initially to be zero.

The matrix of any state-space equation for the transfer function  of the system, shown below in figure is

Consider a second order system whose state space representation is of the form

If , then system is

The transfer function for the state variable representation , , is given by