Section 3

Question 1

What is the difference between the Regression Equation and the Simulation Response?

Answer 1

Both equations are methods of predicting a models output, which is useful in measuring the accuracy of our parameter estimations.
The Regression Equation uses a real value of Y(k-1) so the prediction is only ever a single step.
The Simulation Response recursively uses the predicted values of Y(k-1). Any errors will propagate making the Simulation Response better for testing a model.

Question 2

Define System Identification

Answer 2

Estimating the parameters; the order, the time delay, and model coefficients.

Question 3

Define Responce Error

Answer 3

Responce Error is the difference between the real system responce to an input and the estimated model responce to the same input.
e(k) = y(k) - (estimated)y(k)

Question 4

What is the Responce Error Cost Function?

Answer 4

The Responce Error Cost Function is a measure of the models accuracy compared to a real system.

J = The sum of Responce Error Squared for all values of k.

Question 5

Numerical Optimisation is used to adjust model parameters to yeild a minimum cost function for Responce Error. What are the pitfalls of this approach?

Answer 5

• Requires computation resources/time
• It may yeild local minimum and not a global minimum value
• Requires initial conditions which may influence the solution.

Question 6

How do you obtain the inverse of a matrix?

Answer 6

1. Obtain the determinent
2. Obtain the Cofactor Matrix
3. Transpose the cofactor matrix
4. Divide the transposed cofactor matrix by the determinent

Question 7

What is the difference between Responce Error and Equation Error

Answer 7

Both are measures of the difference between a ‘real’ system responce and an estimated systems responce.
However Responce Error estimates the responce with a single step estimate (Regression Equation) whilst Equation Error estimates with Simulation Responce.
Responce Error Cost Functions can be optimised numerically (with a computer).
Equation Error Cost Functions can be analytically solved but noise results in biased parameter estimates.