closed-loop control (feedback). ◇. PLANT (effector) system to be controlled. ◇.
SET POINT desired value of the OUTPUT. ◇. SENSOR measures the output. ◇.
Closed Loop Systems to Facilitate Homestasis Robert F. Kirsch, Ph.D.
Homeostasis Maintenance of a balanced internal environment in the body and the tendency to automatically maintain this equilibrium when faced with external changes
Case Western Reserve University Cleveland FES Center (VA RR&D Service Center of Excellence)
Homeostasis is a state of equilibrium
Homeostasis involves almost every body system
Blood O2 and CO2 concentrations
Body temperature
Blood volume and blood pressure
Removal of waste products and toxins
Balance between cell proliferation and cell death
Nutrient balance (ions, glucose, …)
Posture and balance
Homeostasis is also an active process that maintains equilibrium
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Mechanism of homeostasis: closed-loop control (feedback)
Disturbance disrupts equilibrium (1) Sensor measures variables of interest (2-3)
Controller notes deviation from equilibrium and computes response (3-4)
Effector acts to restore equilibrium (5)
Process is automatic, reacts to ERROR, and is compensatory
Engineering terminology for closed-loop control (feedback)
PLANT (effector) system to be controlled
SET POINT desired value of the OUTPUT
SENSOR measures the output
CONTROLLER: computes a compensatory command to the plant based on the ERROR between set point and output
Prostheses Prosthesis: a device, either external or implanted, that substitutes for or supplements a missing or defective part of the body
Controller Set point
+ -
Σ
Error
Control law
Plant
Output
Sensor
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Homeostasis and prostheses
Some prostheses restore internal, life-essential homeostasis mechanisms
Purpose of tutorial
(e.g., artificial kidney, artificial pancreas, artificial heart)
Some prostheses restore ability to interact with external world (e.g., joint replacements, artificial legs and arms, neuroprostheses, etc.)
Overview basic control concepts that might be utilized by “smart prostheses” Î
Feedback
Î
Feedforward
Î
Adaptation
Existing prostheses are fairly crude approximations to natural systems
Provide numerous examples from both natural and artificial systems
Could benefit from both existing control systems knowledge and from mimicking natural systems
Explore lessons from natural systems about control
Feedback
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Feedback
Feedback 101: home temperature regulation
Error-driven (difference between desired and actual outputs)
Essential elements:
SENSOR (thermometer)
Automatically compensates for external disturbances
SET POINT (usercontrolled dial referenced to thermometer)
Automatically follows changes in desired state
CONTROLLER
Can improve undesirable properties of system being controlled
Can be very simple
Does have several limitations
Feedback: resists disturbances that cause errors
(temperature error turns gas valve ON or OFF)
PLANT (furnace and radiator)
Temperature maintained by automatic reaction to ERROR
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Body temperature control
Bone remodeling
Glucose control (artificial pancreas)
SENSOR (specialized neurons in the hypothalamus)
SET POINT (normally 37° C)
CONTROLLER (hypothalamic “thermostat”)
Joanna Gilbert at
[email protected]
PLANT (blood vessel dilation or constriction; shivering via muscles; sweat glands)
Roche Diagnostics
Osteocytes are strain sensors that trigger osteoclast and osteoclast activity ÎOsteoclasts ÎOsteoblasts
resorb old bone lay down new bone
Result is bone with appropriate mechanical properties
Artificial system to substitute for pancreatic beta cells ÎBlood
glucose measured with artificial sensor released at appropriate time and with appropriate levels
ÎInsulin
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Specific features of feedback F(s)
+ -
Σ
G(s)
Feedback can improve dynamics
Y(s)
H (s)
Y (s) G(s) = F ( s) 1 + G ( s) H ( s)
(System transfer function)
Y (s) 1 For G(s)H(S) >> 1, ≈ F ( s) H ( s) Î For sufficiently large “loop gain”, overall
With feedback
No feedback
Feedback can improve stability
Sluggish 1st order plant
Oscillatory 2nd order plant
Constant-gain feedback greatly increases speed of response
Derivative feedback eliminates damped oscillation
system properties become INDEPENDENT of the plant!
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Limitations of feedback
Effects of delay in feedback path
Relies on an error between desired and actual state to work: disturbances will always cause an error and the response to the error will always be delayed
Tradeoff between performance and stability: higher loop gain gives improved performance but at the cost of stability (oscillatory behavior) …
No delay Delay= 0.050 s Delay=0.200 s
Delays negatively impact stability Delays are a very common problem, especially in biological systems
Examples of poor stability
Artificial systems: Î
“feedback” when using a microphone near a speaker
Î
Heat capacitance of radiators causing overshoot in home heating
Natural systems: Î
Nystagmus (involuntary oscillatory eyes movements)
Î
Central sleep apnea
Î
Visual control of standing balance
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Summary: closed-loop feedback control
Reactive controller based on error between desired and actual states
Automatically compensates for external disturbances and follows changes in command
Significant impact on overall system response
Used extensively in both natural and artificial systems
Limitations: Î
Error must be present before actions taken
Î
Tradeoff between performance and stability
Feedforward definition:
Feedforward
Control element that responds to a change in command or to a measured disturbance in a pre-defined way (not error driven)
Based on PREDICTION of the response that will be needed to cancel a disturbance or follow an input command change
Can react BEFORE an error actually occurs to overcome sluggish dynamics and delays in the system without jeopardizing stability
Requires some model of the system in order to produce appropriate predictive responses
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Pre-requisites for feedforward:
Effects of disturbance or command input change must be predictable
Effects of feedforward controller must be faster than response of plant (otherwise feedback would be fine)
Feedforward I: model-based prediction of input needed to achieve desired output desired output
Disturbances must be measurable
Inverse model of system
Input needed for desired output
system
Feedforward II: model-based prediction of response needed to compensate for disturbances Inverse model of system
output
Ideally consists of an exact inverse model of the real system Î Inverse model is backwards from real system: determines inputs needed to achieve a desired output
Can compensate for known plant dynamics and delays BEFORE ERRORS ACTUALLY DEVELOP
No sensors needed
System response must be predictable
external disturbance sensor
input needed to cancel disturbance
desired output
+
Σ
system
Σ
output
Same model used to predict change in the input needed to cancel an external DISTURBANCE
Disturbances must be measurable, sensor needed
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Feedforward: compensate for expected
Anticipatory control of posture
errors through measurement and prediction
Vestibulo-ocular reflex: stabilizing gaze based on head acceleration
Model
Radiator capacitance and carryover
Neural controller anticipates disturbance to posture produced by arm actions Leg muscle EMG signals (muscle activations) precede arm muscle activations Compensation is based on planned movement rather than sensory inputs
Eyes
Semicircular canals in inner ear sense head acceleration
Neural controller predicts eye movements needed to compensate and stabilize gaze
Extraocular muscles Neural controller Vestibular apparatus (semicircular canals)
http://www.ncbi.nlm.nih.gov
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Other feedforward examples:
Circadian rhythms: periodic, light-triggered changes in temperature, increase in growth hormone levels, digestion, overall activity level – prediction of what processes should be emphasized during sleep vs. awake states
Implementing feedforward:
Computed torque robotic control: actuator commands pre-computed to take robot mass dynamics into account
The model must be accurate and include measurements of ALL important inputs and disturbances
The model must be invertible
Machine learning approaches: (black box
May not generalize to conditions outside of training experience
identification) Î Artificial neural networks Î Reinforcement learning
Will not be accurate if system changes: growth, fatigue, use of a tool, etc.
Mechanistic model of system (based on first principles of physics, chemistry, etc. and explicit knowledge of the system)
Autonomic “flight or fight” response to a threat: prepares body for a POTENTIAL threat
Limitations of feedforward :
Statistical models
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Combining feedback and feedforward:
Control of standing posture: combining feedback and feedforward elements
Feedforward and feedback often used together Î Î
Feedforward provides rapid response Feedback fills in rest of response accurately
Very typical in natural systems
Standing is inherently unstable Disturbances are common: nudges, arm movements, dropping held items
Adaptation
Proprioceptive feedback:
Feedback of body posture; rapid response Visual feedback: position relative to world; slow response
Vestibular feedforward:
prediction of future postural errors caused by disturbances Note fusion of information from multiple sensors – very common in natural systems
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Adaptation:
Adaptation:
Appropriate modifications to the controller in response to changes in the system being controlled
Can be done in a pre-defined way or result from continuously learning the properties of the controlled system
Can be used with both feedback control and feedforward control
Typically works on a much longer time scale than feedback or feedforward
Adapting feedback control:
Gain scheduling feedback properties modified in a fixed, predetermined manner based on conditions ÎKnown
disturbances (e.g., mass held by robot arm) or changes in plant properties
Adaptation learns plant properties using measures of its inputs and outputs Feedback or feedforward properties are modified to optimize performance as the plant changes
Continuous tuning of feedback properties based on continuously updated plant model ÎOptimize
feedback control of slowly changing system
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Adapting feedforward control:
Feedforward adaptation examples:
Learning to control external devices: Î Î
Feedforward block continuously changes to optimize performance (e.g. minimize error)
Engineering implementations: Î
Online training of neural network from measured input-output data
Î
Optimization of a mechanistic model
Î
Reinforcement learning
Using tools, play video games, drive a car Using a new artificial arm or leg
Learning to control a growing or damaged system: Î Î Î Î Î
Controlling a larger body during development Adjusting to new eyeglasses, regaining equilibrium after inner ear infection Physical therapy (e.g., constraint-induced therapy after stroke) Controlling surgical transferred muscles acting in new ways Controlling a paralyzed arm through coordinated stimulation
Adaptation summary:
Adaptation: changes in controller properties to optimize performance
Adaptation is useful for both feedback and feedforward approaches
Adaptation is widespread in natural systems (“learning”)
Mechanisms of adaptation in physiological systems Î
Nudo tutorial on brain plasticity
Î
Byl tutorial on sensoriomotor training
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Hierarchical control
Control at multiple levels: Î
Lessons from natural systems for smart prosthetics
Î
Multivariable control
More than one variable important for some systems and need to be regulated simultaneously
Variables often interact (e.g., temperature and pressure; force and distance)
Engineering techniques exist for optimizing artificial systems
Multivariable control is very common in natural systems
Task level: global goals Coordination level: multiple mechanisms
Î
Local level: individual mechanisms
Different time scales: Î
Rapid: local, maybe feedforward, approximate
Î
Slow: global, more accurate
Examples: Movement
control buffering Blood pressure control Acid
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Interactions of natural and artificial control systems:
Summary
Summary
Homestasis: life-sustaining equilibria and the active processes that sustain them
Prosthetics inherently involve interaction of an artificial system with natural systems
Prostheses: replace natural body components and should play appropriate homeostatic roles
Artificial control systems must take into account natural control systems for optimal performance
Feedback (closed-loop) control: reactive (error-
Both artificial and natural control systems can be adaptive – this adaptation should be cooperative rather than competitive Î
Bennett tutorial on smart orthotics
driven), automatic, determines system dynamics; performancestability tradeoff
Feedforward control: predictive, no threat to stability; need accurate model of inverse system
Adaptive mechanisms: adjusts feedforward and
Lessons from natural systems: hierarchical,
feedback controllers as plant changes to optimize performance
multivariable control; complementary artificial & natural control
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