Ch.4_Stability

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Questions and Answers

What happens if an unstable system's natural response grows without bound?

  • It does not affect the system
  • It remains constant
  • It approaches a steady state value
  • It can cause damage to the system, adjacent property, or human life (correct)

How is instability displayed in the time response plot of a physical system?

  • By transients that grow without bound (correct)
  • By the forced response only
  • By a total response that approaches a steady state value
  • By the natural response approaching zero

When is a linear, time-invariant system considered stable?

  • If the natural response neither decays nor grows but remains constant or oscillates
  • If the natural response grows without bound as time approaches infinity
  • If every bounded input yields a bounded output
  • If the natural response approaches zero as time approaches infinity (correct)

What does marginal stability imply about the natural response of a system?

<p>It neither decays nor grows but remains constant or oscillates as time approaches infinity (D)</p> Signup and view all the answers

What is the alternate definition of stability for a system?

<p>Every bounded input yields a bounded output (BIBO) (B)</p> Signup and view all the answers

Why can we control the output of a system if the steady-state response consists of only the forced response?

<p>Because the total response of a system is the sum of forced and natural responses (B)</p> Signup and view all the answers

What condition makes a system unstable?

<p>Poles in the right half-plane (A)</p> Signup and view all the answers

What kind of natural responses do poles in the left half-plane yield?

<p>Pure exponential decay (B)</p> Signup and view all the answers

How does a system with poles in the right half-plane behave?

<p>Pure exponentially increasing responses (A)</p> Signup and view all the answers

What kind of systems have closed-loop transfer functions with poles only in the left half-plane?

<p>Stable systems (B)</p> Signup and view all the answers

When is a system considered marginally stable?

<p>When it has pure sinusoidal oscillations as a natural response (B)</p> Signup and view all the answers

What is the Routh-Hurwitz criterion for stability used for?

<p>To yield stability information without finding pole coordinates (B)</p> Signup and view all the answers

What is required as the first step in the Routh-Hurwitz criterion?

<p>Generate a data table called a Routh table (B)</p> Signup and view all the answers

What kind of information does the Routh-Hurwitz criterion provide?

<h1>of poles in each section of the s-plane (B)</h1> Signup and view all the answers

What type of system has poles of multiplicity greater than 1 on the imaginary axis?

<p>Unstable systems (A)</p> Signup and view all the answers

What happens when a system has imaginary axis poles of multiplicity greater than 1?

<p>The response increases to infinity as time approaches infinity (B)</p> Signup and view all the answers

What does a pole of the input function determine?

<p>The form of the forced response (D)</p> Signup and view all the answers

What is the significance of parameter 'a' in a first-order system?

<p>Determines the time constant of the response (D)</p> Signup and view all the answers

What does a pole on the real axis generate?

<p>An exponential response (A)</p> Signup and view all the answers

What does the time constant represent in a first-order system?

<p>The time for e-at to decay to 37% of its initial value (B)</p> Signup and view all the answers

What is the function of a zero in a transfer function?

<p>Generates the form of the natural response (A)</p> Signup and view all the answers

What determines the forced response in a first-order system?

<p>Pole of the input function (C)</p> Signup and view all the answers

How is instability displayed in the time response plot of a physical system?

<p>Exponential growth in natural response (D)</p> Signup and view all the answers

What type of system can be described by a first-order system without zeros?

<p>Marginally stable system (A)</p> Signup and view all the answers

What happens when a system has poles in the right half-plane?

<p>It becomes unstable (B)</p> Signup and view all the answers

What kind of responses do poles in the left half-plane yield?

<p>Exponential decay responses (D)</p> Signup and view all the answers

What is the output response of a system composed of?

<p>The forced response and the natural response (B)</p> Signup and view all the answers

What do the poles of a transfer function represent?

<p>Values of Laplace transform variable that make the transfer function infinite (C)</p> Signup and view all the answers

What are the zeros of a transfer function?

<p>Values of Laplace transform variable that make the transfer function zero (D)</p> Signup and view all the answers

What technique enables the evaluation of the output response, but is laborious and time-consuming?

<p>Solving a differential equation (B)</p> Signup and view all the answers

What is a fast and fundamental qualitative technique for the analysis and design of control systems by inspection?

<p>Poles and zeros analysis (A)</p> Signup and view all the answers

What are the steady-state and transient responses analyzed for in a subsystem?

<p>To yield desired behavior (D)</p> Signup and view all the answers

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