Lecture 7 - Feedback Flashcards
What does feedback mean?
output of a system returns as input to the same system (loop)
Positive feedback
feedback signal adds to the system’s input
Formula for pos feedback
S = Gx + Au
what is Δt?
feedback delay around the loop
in pos feedback (biological), what is G?
the strength of the synapse between a collateral and cell body
in pos feedback (biological), what is the summation junction?
neuron cell body
in pos feedback (biological), what is the feedback path?
recurrent collateral
in pos feedback (biological), what is A?
synapse between input u and the cell body (summation junction)
how to make pos feedback an integrator? what does the equation look like?
G = 1, A = Δt
Assume Δt is small:
u = x’
How to do integrator calculations on positive feedback loop?
old x = G(new x) + u
what happens when G > 1 on pos feedback integrator? What kind of biological systems use this?
exponential increase to infinity (runaway outputs)
- systems where powerful amplification is desired
- action potential
what happens when G < 1 on pos feedback integrator? What biological systems use this?
circuit is leaky integrator (exponential decrease)
- many integrators in the brain
- velocity-stroage integraror
- oculomotor integrator
why are all known neural integrators leaky?
hard to make G = 1 exactly, and it’s safer to make it <1 than >1
time constant for oculomotor integrator. What does it do?
20s;
in the dark if you try to hold a weird eye position, as activity leaks away, eyes drift back to straight ahead
____ damange can increase the leak of the oculomotor integrator. What does this look like?
cerebelluar;
Can’t hold eccentric eye position - slow drift away from target and quickly snap back (saccade)
nystagmus
slow-fast movement as you nod off to sleep
eye movement where you slow drift - fast saccade back is called…
it is caused by…
gaze-paretic nystagmus;
caused by leaky oculomotor integrator (paralysis of gaze control)
neg feedback can guide…
a system to a target
parts of a neg feedback loop?
target → comparator → amplifier → velocity → integrator → output → feedback error (→comparator)
what is a comparator?
computes the error
define: error
difference between system’s output and its traget value
define: amplifier
takes in the error and computes a desired rate of change (velocity command)
e.g. if target is 30 and output is 10, then error is 20 and amplifier orders a velocity in the positive direction
define: integrator
computes output based on velocity command
feedback guides the system ____ to its target
gradually;
go around the loop multiple times, feedback delay is small
what happens to the velocity as output gets closer to the target value?
velocity decreases, causing output to get closer to target more slowly :(
What if we boost the amplifier signal? The demostrates what advantage about feedback?
increases speed which output = target, but there is still drift going on;
accuracy not affected;
advantage: malfunctions inside the loop doesn’t impair performance