Automatic Control• Ballistic vs guided• Compare Actual Output to Desired Output• Automatic Gain Control (feedforward)• Negative feedback (desired – actual) = error • Op Amp as example of negative feedback• Use of SIMULINK [ F(s) represents f(t)… ] • Proportional control • Effects of transport delay • Integral control • Linear vs nonlinear control: Bang Bang• Adaptive gain control• Stability

Feedforward→• Is there subtraction of actual from desired?

No, it’s “then” subtracted from “now” …• Consider delay in one path: differentiation• AGC = Automatic Gain Control… • Or noise subtracted from signal+noise…• Examples:

Fetal heart monitorMuffler-less exhaust: noise cancellation

+

_Delay line

Negative feedback:

1. Automatic Control vs Homeostatics Automatic control is imagined to be carried out by sensors that transduce physical data into voltage; control itself is achieved by motors, heaters, pumps, and other electromechanical devices. To account for sensing and control by biological tissue and organs, physiologists use the term homeostatis. It implies that important physiological parameters need to be kept in limited, “static” ranges, by means of negative feedback.

•Blood presssure (vessel dilation)•Blood sugar (insulin)•Potassium ions (actions in kidney)•Pupil diameter of the eye (light level, emotion) •Sense of balance (vestibular apparatus)•Temperature (metabolism, cooling by evaporation)•Stretch reflex (golgi tendon organs)•Intracellular cyclic GMP (phosphodiesterase enzyme activity)

Negative feedback output as a function of IN and G(S)Below: G(ain) = Plant + Compensation (control)

Output is less than “open loop” but insensitive to changesin G, if G >> 1. G is an “internal” factor

Negative feedback with dynamics in F(s):(the problem of algebraic loops…)

Generating the inverse of a functionuse in “linearizing” a complex machine (motor)

Let G be a large “algebraic” gain;the only dynamics is in F(s)

• Increase speed of response of LP filter with negative feedback

www.biomathdynamics.com 

And see fold23/SpeedChangeLPHP13.m for speed of HP filter in feedback

Deriving exp(+at) Laplace transform

Second order plantSpeed increase:

with feedback as gainincreases it becomes underdamped.

• Reduced sensitivity to changes in Load:

suppose the load changes suddenly, at t=0, from 0 to 2: a step of magnitude 2:

instead of 2.0

• Stabilize a system:

Let the input be an impulse function with L(δ(t)) = 1

open loop response;then place in (unity) negative feedback system

Virtues of negative feedback:

• system less sensitive to internal parameter changes• can be used to generate inverse to a transfer function• system less sensitive to external parameter changes• increase system speed• help stabilize an unstable system

• What you’ve seen here is PROPORTIONAL control:Control effort proportional to error…

Vestibular Nystagmus as a marker of velocity storage

• http://www.youtube.com/watch?v=jAE1hr_cLFw

Notice quick phase of VN…

Paroxysmal alternating skew deviation and nystagmus after partial destruction of the uvulaA Radtkea, A M Bronsteina, M A Grestya, M Faldona, W Taylorb, J M Stevensb, P Rudgea

A use for positive feedback: loop gain less than one…

Example of a positive feedback loop inside a negative loop:Velocity storage in the VOR and optokinesis…

Lcturs/vstopt05

First Top is increased by X4 with 0.75 gain + feedback then when “the lights are turned on” it reverts back to faster than normal

Example of feedback quiz

http://www.brown.edu/Departments/Engineering/Courses/En123/Exams/FDBKquizes/FDBK06y.htm

Push-Pull Amplifier modelling vestibular recurrent inhibition

Example of op amp NGSA feedback

• http://www.brown.edu/Departments/Engineering/Courses/En123/Lectures/FDBKopamp.htm

Transport delay

• Flip side of conduction velocity

• A “nonlinear” Laplace transform

approximating transport delay

Transport delay of a leaky integrator

And see fold23/TransDly13.mdl

Integral compensation drives the error to zero

PID control: for inverted pendulum balance

• Derivative compensation: predictive, but a way to amplify noise in system…

• Motion-sensitive g-cells at retinal output…

• see PoleSim_PID.mdl in work/PoleBal_10

• try modifying the D on PID→more D, better score.

• fold23/PID_first_ord12.mdl• Approx deriv in Simulink: (s)/(s+a) at low freq

a>>s=jᵚhttp://www.mathworks.com/help/simulink/slref/derivative.html

Bang bang—where is the feedback? • Bang-bang controller for…The Fan Lab: in LabVIEW• Always allowing the “actual” to drift between HI-LO limits

Simulink and SR latch for bang-bang oscillator

Adaptive Gain Control of VOR

• neural network adapting to visual disturbance of VOR: Robinson JNP 1976:

• http://jn.physiology.org/content/39/5/954.abstract?ijkey=127029d171b72a8dc8037f9bbcc8abb6ed3863c8&keytype2=tf_ipsecsha

• 122JDD/Asgn06/II_VORgainMOD.htm

• C:/MatlabR12/work/fold22/asg5B04.mdl

• B. Widrow & Peter N. Stearns, Adaptive Signal Processing (1985)

Adaptive Gain Control:Learning to be a D→A converter

• We, the designers of a D→A converter, figured out that resistors of size 1K, 2K, 4K and 8K would be required for a 4-bit conversion.

• Think of the resistances as representing “gain” blocks of 1, 2, 4, 8 for LSB to MSB inputs.

• Can the weight be learned, by training? • See code in script: • C:/MatlabR12/work/fold23/D2A_learn_2010.m • The weights start at random then are updated on each

presentation of a learning stimulus/response pair. • ΔW(i) = input(i) * error ε * learning rate μ Hebb’s Law

Fuzzy Controllers• See description of Matlab Fuzzy Logic

Toolbox• http://www.mty.itesm.mx/dtie/centros/csi/materias/

ia4002-1/docs/Fuzzy_Toolbox.pdf

• Application Examples: Inverted pendulum balancingnoise cancellationbacking up tractor-trailer truck to loading dockball juggling