Ch.4_Stability

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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?

It neither decays nor grows but remains constant or oscillates as time approaches infinity Signup and view all the answers

What is the alternate definition of stability for a system?

Every bounded input yields a bounded output (BIBO) 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?

Because the total response of a system is the sum of forced and natural responses Signup and view all the answers

What condition makes a system unstable?

Poles in the right half-plane Signup and view all the answers

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

Pure exponential decay Signup and view all the answers

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

Pure exponentially increasing responses Signup and view all the answers

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

Stable systems Signup and view all the answers

When is a system considered marginally stable?

When it has pure sinusoidal oscillations as a natural response Signup and view all the answers

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

To yield stability information without finding pole coordinates Signup and view all the answers

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

Generate a data table called a Routh table 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</h1> Signup and view all the answers

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

Unstable systems Signup and view all the answers

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

The response increases to infinity as time approaches infinity Signup and view all the answers

What does a pole of the input function determine?

The form of the forced response Signup and view all the answers

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

Determines the time constant of the response Signup and view all the answers

What does a pole on the real axis generate?

An exponential response Signup and view all the answers

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

The time for e-at to decay to 37% of its initial value Signup and view all the answers

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

Generates the form of the natural response Signup and view all the answers

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

Pole of the input function Signup and view all the answers

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

Exponential growth in natural response Signup and view all the answers

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

Marginally stable system Signup and view all the answers

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

It becomes unstable Signup and view all the answers

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

Exponential decay responses Signup and view all the answers

What is the output response of a system composed of?

The forced response and the natural response Signup and view all the answers

What do the poles of a transfer function represent?

Values of Laplace transform variable that make the transfer function infinite Signup and view all the answers

What are the zeros of a transfer function?

Values of Laplace transform variable that make the transfer function zero Signup and view all the answers

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

Solving a differential equation Signup and view all the answers

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

Poles and zeros analysis Signup and view all the answers

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

To yield desired behavior Signup and view all the answers

Ch.4_Stability

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Questions and Answers

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

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

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

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

What is the alternate definition of stability for a system?

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

What condition makes a system unstable?

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

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

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

When is a system considered marginally stable?

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

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

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

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

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

What does a pole of the input function determine?

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

What does a pole on the real axis generate?

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

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

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

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

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

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

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

What is the output response of a system composed of?

What do the poles of a transfer function represent?

What are the zeros of a transfer function?

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

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

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

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