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TAS > Chapter 2 > Flashcards

Chapter 2 Flashcards

1
Q

What is the difference between a model and a simulation?

A
  • A model represents a physical system
  • A simulation is the repeated solving of a model in order to produce the behavior of the modeled system
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2
Q

Why do we simulate?

A
  • Identify and compare feasibility of design systems
  • Obtain insight into behavior of a system
  • Simulator development
  • Understand how a system will behave in different situations
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3
Q

What is control development and what are some examples?

A

It determines what inputs are needed to obtain a desired output

  • Gain Tuning
  • Preliminary Testing
  • Model-based control
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4
Q

What are some simulation verification Techniques?

A
  • Model in the Loop
  • Simulation in the Loop
  • Process in the Loop
  • Hardware in the Loop
  • Physical System Tests
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5
Q

What is model in the loop testing?

A

It tests if the controller logic works

  • Testing on simulated system model
  • Record and save IO behavior of model
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6
Q

What is Process in the Loop testing?

A
  • Put controller code on embedded processor and run closed loop simulation on simulation plant
  • Determine if processor is able to run the developed controller logic
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7
Q

What is Hardware in the Loop testing?

A
  • For testing behavior that cannot be captured in simulation
  • Run simulation model on real time system with real physical connections to embedded processor
  • Check for problems in IO interfaces
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8
Q

What is a time invariant system?

A

Response signal does not change with time

Does not matter when in time an input is applied

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9
Q

What is an ordinary differential Equation?

A
  • Depends on just one independent variable
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10
Q

What is a Partial Differential Equation?

A

Depends on more than one variables

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11
Q

What is the formula for the Laplace Transform?

A

F(s) = \int_{0}^{\infty} f(t)e^{-st} dt

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12
Q

What is the transfer function?

A

Ratio of Laplace transform of output to Laplace transform of input when initial conditions are assumed to be zero

  • Relates input and output with an algebraic expression
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13
Q

What are the limitations of the transfer function?

A
  • Only works for linear time-invariant system
  • Only single input output systems
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14
Q

What is mathematical representation of transfer function?

A

Y(s)/ U(s) = (2s+3)/(s+1)(s+4)

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15
Q

What are the poles of a transfer function?

A

Values of s for which G(s) approaches infinity

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16
Q

What are zeros of a transfer function?

A

Values of s for which G(s) approaches 0

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17
Q

What is the gain of a transfer function?

A

Steady state value of G(s), s=0

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18
Q

n

A
19
Q

What is a state space system?

A
  • A representation of the dynamics of an nth order system as a set of first-order differential state equations
  • State-space models describe temporal change (first-order time derivative) of the state variables as a function of current state variables and current inputs
20
Q

What is the notation used for the state space system ?

A

/dot{x} = f(x,u), y = h(x,u)

x: state vector, describes current state completely. Components of x are state variables.

u: input vector, contains the input variables

y: output vector

21
Q

What is the notation for Linear state space model?

A

\dot{x} = Ax + Bu, x(0) = x_0
y = Cx + Du

A: system matrix, represents system dynamics

B: input matrix, describes how inputs influence system

C: output matrix, defines how states are combined to yield desired output

D: feed-through matrix, ratio of output to input under steady state conditions

22
Q

What is Linearity?

A

f(x+y) = f(x) + f(y)

23
Q

What is homogeneity?

A

f(ax) = af(x)

24
Q

When is a system linear?

A

If homogeneity and superposition hold

25
Q

What do the eigenvalues of a system tell us?

A

How the system responds to disturbances over time

26
Q

What do the eigenvectors of a system tell us?

A

To what extent each state is involved in each mode

27
Q

How can we assess LTI system stability using eigenvalues

A

Left is stable right is unstable

28
Q

What are static and dynamic stability?

A

Static stability is the tendency of a body to return to its original position when disturbed

Dynamic stability is the response of a body to a disturbance over time

29
Q

What are global models?

A

Models that are valid across a whole envelope

30
Q

What is the difference between a continuous and discrete signals?

A

Continuous signals have uncountable number of states and discrete signals have finite number of states.

31
Q

What is an analog to digital converter?

A

Converts continuous signal to discrete signal using sampling

32
Q

What does bandwidth describe?

A

Difference between highest and lowest frequency

33
Q

What is the Nyquist theorem?

A

To reproduce a signal without any distortion or loss of data, the sampling frequency must be greater than twice the maximum signal frequency or twice the bandwidth.

34
Q

What do finite difference methods do?

A

Approximate the derivative of a signal at a specific point via a linear combination of values of that signal at a neighboring point

35
Q

What are three examples of FD methods and what do they do?

A

Forward euler: uses linear combination of values after f

Central Scheme: Uses linear combination of values before and after f

Backward euler: uses linear combination of values before point

36
Q

What is the order of accuracy of a FD scheme?

A

The power of delta x to which the truncation error is proportional.

37
Q

What are the truncation errors of forward euler, central and backward euler?

A

O(\delta x), O(\delta x^2) ,O(\delta x)

38
Q

What are the numerical methods for solving ODEs?

A

Single Step:
- x_{n+1} computed from x_n
- Eg. Forward euler, Rung Kutta
- Variable step size possible

Multi Step:
- E_{n+1} computed from multiple previous points
- Eg, Explicit midpoint method
- Variable step size difficult

39
Q

What is the formula for forward / explicit euler?

A

x_{n+1} = x_n + hf(t_n,x_n)

40
Q

What is the formula for backward/implicit euler?

A

x_{n+1} = x_n + hf(t_{n+1}, x_{n+1})

41
Q

What is a stiff ODE?

A

An ODE is stiff if two or more significantly different time scales occur in the system

42
Q

When is a numerical problem well-posed?

A
  • If a solution u exists
  • the solution is unique
  • solution u is stable
43
Q
A

TAS (12 decks)

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