Question

A system that is BIBO stable,
is necesarily asymptotically stable as well
is outrightly unstable
O is marginally stale
is not necassarily asymptotically stable​

Answer 1

Answer:

Course roadmap Course roadmap

Laplace transform

Transfer function

Models for systems Models for systems

• electrical electrical

• mechanical mechanical

• electromechanical electromechanical

Block diagrams Block diagrams

Linearization

Modeling Modeling Analysis Analysis Design

Time response

• Transient Transient

• Steady state

Frequency response

• Bode plot Bode plot

Stability Stability

• Routh-Hurwitz Hurwitz

• (Nyquist Nyquist)

Design specs Design specs

Root locus Root locus

Frequency domain

PID & Lead-lag

Design examples Design examples

(Matlab simulations &) laboratories simulations &) laboratories

Fall 2008 3

Simple mechanical examples Simple mechanical examples

We want mass to stay at x=0, but wind gave some We want mass to stay at x=0, but wind gave some

initial speed ( initial speed (F(t)=0). What will happen? )=0). What will happen?

How to characterize different behaviors with TF? How to characterize different behaviors with TF?

M

x(t)

f(t)

M

x(t)

K f(t)

M

x(t)

f(t)

B

M

x(t)

f(t)

B

K

Fall 2008 4

Stability Stability

Utmost important specification in control design! Utmost important specification in control design!

Unstable systems have to be stabilized by Unstable systems have to be stabilized by

feedback. feedback.

Unstable closed Unstable closed-loop systems are useless. loop systems are useless.

What happens if a system is unstable? What happens if a system is unstable?

• may hit mechanical/electrical may hit mechanical/electrical “stops” (saturation) (saturation)

• may break down or burn out may break down or burn out

Explanation: