GATE ECE
Control Systems
State Space Analysis
Previous Years Questions

## Marks 1

Consider the state space realization $$\left[ {\matrix{ {\mathop x\limits^ \bullet } & {\left( t \right)} \cr {\mathop x\limits^ \bullet... Consider the system$${{dx} \over {dt}} = Ax + Bu$$with$${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\...
A linear system is equivalently represented by two sets of state equations. $$\mathop x\limits^ \bullet = \,\,{\rm A}X\,\, + BU$$ and $$\mathop W\li... The transfer function Y(s)/U(s) of a system described by the state equations$$\mathop x\limits^ \bullet $$(t) = -2x(t)+2u(t) y(t) = 0.5x(t) is ... The system mode described by the state equations$$$X = \left( {\matrix{ 0 & 1 \cr 2 & { - 3} \cr } } \right)x + \left( {\matrix{ ... ## Marks 2 The state equation and the output equation of a control system are given below: $$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr... A second order LTI system is described by the following state equation.$$$\eqalign{ & {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \righ...
A second-order linear time-invariant system is described by the following state equations \eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_... A network is described by the state model as\eqalign{ & {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u, \cr & \mathop {{x_2}}... The state variable representation of a system is given as \eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 ... The state transition matrix\phi \left( t \right)$$of a system$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}...
The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = ... An unforced linear time invariant (LTI) system is represented by$$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\... Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is... Consider the state space model of a system, as given below The system is... The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations The state transition m... The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations The state-variable equ... The state variable description of an LTI system is given by where y is the output and u is 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 stat... 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... A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is... Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$ If the initial sta... Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$ If the initial sta... The state space representation of a separately excited DC servo motor dynamics is given as $$\left[ {\matrix{ {{{d\omega } \over {dt}}} \cr {... A linear system is described by the following state equation$$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),...
The state variable equations of a system are: $${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u$$$$${\mathop x\limits^ \bullet _2} = 2{x... If A =$$\left[ {\matrix{ { - 2} & 2 \cr 1 & { - 3} \cr } } \right],$$then sin At is Given A$$ = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$the state transition matrix eAt is given by... The zero, input response of a system given by the state space equation$$$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \over {\mathop {{x_2}}\limits^ ...
For the system described by the state equation $$\mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & ... A certain linear time invariant system has the state and the output equations given below$$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } ... A linear time-invariant system is described by the state variable model $$\left[ {\matrix{ {{{\mathop x\limits^ \bullet }_1}} \cr {{{\mathop... A linear second order single input continuous-time system is described by the following set of differential equations$$$\eqalign{ & \mathop {{...

## Marks 5

The block diagram of a linear time invariant system is given in Figure is (a) Write down the state variable equations for the system in matrix form...
A certain linear, time-invariant system has the state and output representation shown below: \eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}... For the circuit shown in the figure, choose state variables as{x_{1,}}{x_{2,}}{x_3}$$to be$${i_{L1}}\left( t \right),{v_{c2}}\left( t \right),{...
Obtain a state space representation in diagonal form for the following system \${{{d^3}y} \over {d{t^3}}} + 6{{{d^2}y} \over {d{t^2}}} + 11{{dy} \ove...

## Marks 10

A system is characterized by the following state-space equations: a) Find the transfer function of the system b) Compute the state-transition matrix/...
EXAM MAP
Joint Entrance Examination