Practical class #6 group of Wednesday

4 abril 2018, 09:00 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 45 (questions 1,  2 and beginning of 3).

Solution in time domain -- state space models

3 abril 2018, 11:00 • Luis Marcelino Ferreira

Solution in time domain -- state space models

Ordinary diff eqs are easy to solve (just integrate) by a computer

Euler’s formula

Importance of h -- the step length

Importance of the step direction

Modified Euler’s

Runge-Kutta formulas (4^th order)

What about solution w/out a computer?

What if linear?

Formal solution formula: the integral convolution

Proof: that formula is indeed the solution

The exponential of A is the state transition matrix: e^A(t-t’)

A definition for an exponential: McLaurin series (Taylor’s)

Is it good for computers -- convergence

How do you compute it?

Better if A is diagonal -- diag of simple exponentials

Similarity transformation

Change of bases: x=Mq

M is modal -- going to get modal decomposition

Meaning of x=Mq -- a linear combination of v’s

J=inv(M)*A*M is diagonal

It’s a Jordan matrix of the eigenvalues of A

Show that, prove by deductive reasoning

Questions about eigenvalues, eigenvectors, singularity of A-sI, etc

Practical class #5 group of Thursday

22 março 2018, 09:30 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 3. Quiz #2 (group of Thursday)

Review of frequency control -- ACE

22 março 2018, 08:00 • Luis Marcelino Ferreira

Review of previous class

Questions: role of H and references (frequency and power)

Stability and make deviations vanish

A quick review -- in pictures

Figs 11.1-11.18: see each of them attentively and look at parameter values

Fig11.21 Identify curves and remember turbine input is not a step; demand is

Fig11.22 Several units, same area: some units on primary control, a few selected ones for secondary control

Fig11.25 and ACE

ACE: it’s important, it’s an error -- aside: errare humanum est

ACEi = Bi*Dfi + sum(sum(DPij))

ACE feeds the integral control block (secondary control)

Fig11.27

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A new perspective -- computers, linear algebra, linear differential equations

dx/dt=f(x,u,p, ..., t) computers love it -- Euler’s will do

dx/dt=Ax+Bu, y=Cx+Du

Practical class #5 group of Wednesday

21 março 2018, 09:00 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 3. Quiz #2 (group of Wednesday)