MATH319 Slides 5 Feedback 7 Positive feedback

6 Negative Feedback

Here we take the output $y$ , integrate $y$ and amplify $\int y$ , and add to the integrated input $\int\int u$ . Then we add these to obtain $y$ as the final output. Later, we’ll use feedback to stabilise linear systems.

Example. A cyclist pedals harder, hence goes faster, but the faster the cyclist goes, the greater the air resistance. Let $m$ be the mass of the cyclist, $v$ the velocity, $k$ a constant of proportionality, and $u$ the force imparted on the pedals. Then by Newton’s second law of motion,

m{{dv}\over{dt}}=-kv+u

which we can express as a feedback system

v={{-k}\over{m}}\int v+{{1}\over{m}}\int u,

and the sign of $-k/m$ indicates negative feedback.