State-Space Representation in Network Analysis

Classical approach

Limited applicability

Rapidly provide stability and transient response information

<p>State-space approach</p> Signup and view all the answers

<p>Nonlinear systems with backlash and saturation</p> Signup and view all the answers

<p>Limited applicability</p> Signup and view all the answers

<p>Classical approach</p> Signup and view all the answers

<p>To model systems for digital simulation</p> Signup and view all the answers

<p>The number of variables</p> Signup and view all the answers

<p>To find all other system variables</p> Signup and view all the answers

<p>It can be used for a wide range of systems</p> Signup and view all the answers

<p>It is not as intuitive as the classical approach</p> Signup and view all the answers

<p>You will not be able to solve for all other system variables.</p> Signup and view all the answers

<p>Physical variables of a system and decoupled variables.</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>The dimension of the system matrix is increased unnecessarily.</p> Signup and view all the answers

<p>It can be used for the simulation of physical systems on the digital computer.</p> Signup and view all the answers

<p>A set of state variables where each subsequent state variable is defined to be the derivative of the previous state variable.</p> Signup and view all the answers

<p>A unique representation of a system that depends on the choice of state variables</p> Signup and view all the answers

<p>A sum of variables where each variable is multiplied by a constant</p> Signup and view all the answers

<p>The order of the differential equation describing the system</p> Signup and view all the answers

<p>The values of the state variables cannot be expressed as linear combinations of each other</p> Signup and view all the answers

<p>It becomes impossible to write particular output equations</p> Signup and view all the answers

<p>The order of the denominator of the transfer function</p> Signup and view all the answers

<p>$x_1 = y, x_2 = \dot{y}, x_3 = \ddot{y}, ..., x_n = \dot{y}^{n-1}$</p> Signup and view all the answers

<p>$y = Cx + Du$</p> Signup and view all the answers

<p>$C(sI - A)^{-1}B + D$</p> Signup and view all the answers

<p>$sX(s) = AX(s) + BU(s)$</p> Signup and view all the answers

<p>Choose the output, y(t), and its (n-1) derivatives as the state variables.</p> Signup and view all the answers

<p>$y = C(sI - A)^{-1}Bu + Du$</p> Signup and view all the answers

<p>Classical approach</p> Signup and view all the answers

<p>They provide stability and transient response information</p> Signup and view all the answers

<p>It can only be applied to linear, time-invariant systems</p> Signup and view all the answers

<p>It is a unified method for modeling a wide range of systems</p> Signup and view all the answers

<p>Nonlinear systems with backlash, saturation, and dead zone</p> Signup and view all the answers

<p>It relates the input to the output of the system</p> Signup and view all the answers

<p>It provides a unified method for modeling a wide range of systems.</p> Signup and view all the answers

<p>To represent the relationship between the input and output variables.</p> Signup and view all the answers

<p>Two</p> Signup and view all the answers

<p>The system's output cannot be determined.</p> Signup and view all the answers

<p>It is not as intuitive as the classical approach.</p> Signup and view all the answers

<p>The number of derivative terms in the differential equation.</p> Signup and view all the answers

<p>The number of simultaneous, first-order differential equations</p> Signup and view all the answers

<p>To calculate the system's output</p> Signup and view all the answers

<p>It can handle multiple-input, multiple-output systems</p> Signup and view all the answers

<p>They provide a more intuitive understanding of system behavior</p> Signup and view all the answers

<p>It may result in a large number of state variables</p> Signup and view all the answers

<p>The order of the differential equation</p> Signup and view all the answers

<p>To simplify the writing of state equations</p> Signup and view all the answers

<p>When they are not required to solve for any other variables</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>It increases the size of the system matrix unnecessarily</p> Signup and view all the answers

<p>It allows for the simulation of non-linear systems</p> Signup and view all the answers

<p>To represent the output variables in terms of the state variables</p> Signup and view all the answers

<p>Cross-multiplying and taking the inverse Laplace transform</p> Signup and view all the answers

<p>$Y(s) = C(sI - A)^{-1}B$</p> Signup and view all the answers

<p>$C(sI - A)^{-1}B + D0$</p> Signup and view all the answers

<p>To relate the output vector to the state vector</p> Signup and view all the answers

<p>It provides a unified method for modeling, analyzing, and designing systems</p> Signup and view all the answers

<p>Choosing the output and its derivatives as state variables</p> Signup and view all the answers