32 Questions
What happens if an unstable system's natural response grows without bound?
It can cause damage to the system, adjacent property, or human life
How is instability displayed in the time response plot of a physical system?
By transients that grow without bound
When is a linear, time-invariant system considered stable?
If the natural response approaches zero as time approaches infinity
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
What is the alternate definition of stability for a system?
Every bounded input yields a bounded output (BIBO)
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
What condition makes a system unstable?
Poles in the right half-plane
What kind of natural responses do poles in the left half-plane yield?
Pure exponential decay
How does a system with poles in the right half-plane behave?
Pure exponentially increasing responses
What kind of systems have closed-loop transfer functions with poles only in the left half-plane?
Stable systems
When is a system considered marginally stable?
When it has pure sinusoidal oscillations as a natural response
What is the Routh-Hurwitz criterion for stability used for?
To yield stability information without finding pole coordinates
What is required as the first step in the Routh-Hurwitz criterion?
Generate a data table called a Routh table
What kind of information does the Routh-Hurwitz criterion provide?
of poles in each section of the s-plane
What type of system has poles of multiplicity greater than 1 on the imaginary axis?
Unstable systems
What happens when a system has imaginary axis poles of multiplicity greater than 1?
The response increases to infinity as time approaches infinity
What does a pole of the input function determine?
The form of the forced response
What is the significance of parameter 'a' in a first-order system?
Determines the time constant of the response
What does a pole on the real axis generate?
An exponential response
What does the time constant represent in a first-order system?
The time for e-at to decay to 37% of its initial value
What is the function of a zero in a transfer function?
Generates the form of the natural response
What determines the forced response in a first-order system?
Pole of the input function
How is instability displayed in the time response plot of a physical system?
Exponential growth in natural response
What type of system can be described by a first-order system without zeros?
Marginally stable system
What happens when a system has poles in the right half-plane?
It becomes unstable
What kind of responses do poles in the left half-plane yield?
Exponential decay responses
What is the output response of a system composed of?
The forced response and the natural response
What do the poles of a transfer function represent?
Values of Laplace transform variable that make the transfer function infinite
What are the zeros of a transfer function?
Values of Laplace transform variable that make the transfer function zero
What technique enables the evaluation of the output response, but is laborious and time-consuming?
Solving a differential equation
What is a fast and fundamental qualitative technique for the analysis and design of control systems by inspection?
Poles and zeros analysis
What are the steady-state and transient responses analyzed for in a subsystem?
To yield desired behavior
Explore the analysis of subsystems for their transient and steady-state responses, and understand the forced response and natural response of a system. Learn about techniques like solving differential equations and taking the inverse Laplace transform to evaluate the output response.
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