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
Is there subtraction of actual from desired? No, its then subtracted from now Consider delay in one path: differentiation AGC = Automatic Gain Control Or noise subtracted from signal+noise Examples: Fetal heart monitor
Muffler-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 changes in G, if G >> 1. G is an internal factor
Negative feedback with dynamics in F(s): (the problem of algebraic loops) Let G be a large algebraic gain; the only dynamics is in F(s) Generating the inverse of a function
use in linearizing a complex machine (motor) Increase speed of response of LP filter with negative feedback And see fold23/SpeedChangeLPHP13.m for speed of HP filter in feedback
Deriving exp(+at) Laplace transform www.biomathdynamics.com Second order plant Speed increase: with feedback as gain
increases 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: open loop response; then place in (unity)
negative feedback system Let the input be an impulse function with L((t)) = 1 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 youve 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 uvula
A 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=j http://www.mathworks.com/help/simulink/slref/derivative.html Bang bangwhere is the feedback?
Bang-bang controller forThe 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_ipsecsh a
B. Widrow & Peter N. Stearns, Adaptive Signal Processing (1985) Adaptive Gain Control: Learning to be a DA converter We, the designers of a DA 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. W(i) = input(i) * error * learning rate Hebbs 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 balancing noise cancellation backing up tractor-trailer truck to loading dock
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