What is the difference between a model and a simulation?
- 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
Why do we simulate?
- 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
What is control development and what are some examples?
It determines what inputs are needed to obtain a desired output
- Gain Tuning
- Preliminary Testing
- Model-based control
What are some simulation verification Techniques?
- Model in the Loop
- Simulation in the Loop
- Process in the Loop
- Hardware in the Loop
- Physical System Tests
What is model in the loop testing?
It tests if the controller logic works
- Testing on simulated system model
- Record and save IO behavior of model
What is Process in the Loop testing?
- 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
What is Hardware in the Loop testing?
- 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
What is a time invariant system?
Response signal does not change with time
Does not matter when in time an input is applied
What is an ordinary differential Equation?
- Depends on just one independent variable
What is a Partial Differential Equation?
Depends on more than one variables
What is the formula for the Laplace Transform?
F(s) = \int_{0}^{\infty} f(t)e^{-st} dt
What is the transfer function?
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
What are the limitations of the transfer function?
- Only works for linear time-invariant system
- Only single input output systems
What is mathematical representation of transfer function?
Y(s)/ U(s) = (2s+3)/(s+1)(s+4)
What are the poles of a transfer function?
Values of s for which G(s) approaches infinity
What are zeros of a transfer function?
Values of s for which G(s) approaches 0
What is the gain of a transfer function?
Steady state value of G(s), s=0
n
What is a state space system?
- 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
What is the notation used for the state space system ?
/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
What is the notation for Linear state space model?
\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
What is Linearity?
f(x+y) = f(x) + f(y)
What is homogeneity?
f(ax) = af(x)
When is a system linear?
If homogeneity and superposition hold
