Karteikarten
Regtek
Karten in diesem Stapel (26)
- 1Formel för komplementär känslighetsfunktionen T(s)1-S(s), där S(s) är överföringsfunktionen som multipliceras med störningar. V(s)*S(s)
- 2Hur vet man om ett system är observerbart?O = C
CA
.
.
CA^n-1
Determinanten av O är skild från 0. N är antalet tillstånd - 3Hur vet man om ett system är styrbart?S = (B AB A^n-1B)
determinanten av S är nollskild. - 4What is an observer?an estimator with a correction term =
K *(y − Cxˆ), where xˆ is an estimation of x - 5What is the time constant?1-e^-1, den tid det tar att nå 63% av slutvärdet
- 6When checking for damping, what is the standard form?s^2+2*w*g*s+w^2,
g is the damping ratio. If g=0 -> lot of oscillations, if g=1, no oscillations.
w is the distance of the poles to the origin - 7How does a system with a PID controller change when you vary Kp, Ki and Kd?larger Kp-> faster system, but less stab
Ki -> can eliminate error, but less stab
Kd -> improves stab, less oscillations - 8How to sketch BODE plot1. sort abs(p) and abs(z) by distance from origin
2. evaluate abs(G(iw)) for key points (w=0->infinity)
3. Each zero - slope +1
Each pole - slope -1 - 9Perfomance metrics for controller1. Quickness - the rise time = bandwidth
2. Damping: overshoot M = max(abs(Gc(iw))
3. Accuracy: static controll error Gc(0) - 10Rules for Nyquist curve:If Go has no poles in right half plane => Gc(s) is stable => Nyquist curve Go(iw) does not encircle -1.
If it goes through -1 it is marginally stable - 11What is the crossover frequency wc?Where the nyquist curve cuts the unity circle: abs(Go(iwc)) = 1
wc = wb, which is the bandwidth of Gc - 12Minimum phase systemThe system with the least phase shift => it has no poles nor zeros in the right half plane, and contains NO time delays
- 13what is the downside with no minimum phase system?hard to control
- 14Are state variables unique?NO. Y(s) -> { state space form }, not the other way
- 15Stability of state space formA:s eigenvalues are strictly in the left half plane
- 16What is the minimal realisation of a state space system?vector x has the smallest dimension => the system is controllable and observable <=> A:s eigenvalues = G(s):s poles!!
- 17How do you feedback in statespace formu = -Lx + lo*r
- 18What is the transfer function for the closed loop system when using feedback in state space form?Gc(s)=C(sI-(A+BL)^-1 * B * lo
Y(s)=Gc(s)*R(s) - 19When using state feedback u = -Lx + lo*r, what do you design with lo?We want to have at least G(0)=1 => Gc(0)=C(-A+BL)^-1 * B * lo
(OBS vi sätter s=0) - 20What happens with the transfer function when we use estimated states (i.e observer)it does not change!!
- 21If we have an observer, how can we see how quickly the error decays?The error is given by the eigenvalues of
(A − KC)
where the pole with the largest real value is the decay of the system
i.e pole -1 => decay e^-1 - 22Robustness theoremif T(iw) < 1/|relative model error|
the real system is stable!
relative model error:
delta(G(s)) = Go- G(s) / G(s)
where Go is the real system - 23Def of phase-marginφm = arg{Go(iωc)} + 180°
- 24Pole in discrete time to continous time etcpole s in cont time =>
pole p = e^s*T
in discrete time
T = sampling period - 25if the phase margin is positive we have astable system
- 26sin(wt) in|G(iw)| * sin(wt - arg(G(iw)) out
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- Beschreibung
- Engineering Karteikarten am Regtek, erstellt von Emma Tysk am 28/02/2018.
- Erstellt von
- Emma Tysk
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