intro

system dynamics and modeling

time response

frequency response

stability analysis

control system design

applications

stability analysis

There are multiple definitions of stability.

  1. Stability is the measure of the tendency of a system's response to return to zero after being disturbed.

  2. There is also what is known as BIBO stability: for a stable a system, the output is bounded for a bounded input.

Need to add margin to designs to make stability more robust. Very stable systems are slower to command however.

open loop stability

Find the roots of the denominator polyinomial in the systems transfer function.

If all of the roots are in the left-hand half of the complex plane, then the system is stable.

  • A root in the left half of the complex plane means the root has negative real components

Taking the inverse Laplace transform of the transfer function gices system equations with exponential terms.

G(s)=1(s+1)(s+2)⇒L−1(G(s))⇒Ae−t+Be−λtG(s) = \frac{1}{(s+1)(s+2)} \Rightarrow \mathscr{L}^{-1}(G(s)) \Rightarrow Ae^{-t} + Be^{-\lambda t}