Block Diagrams
BIOE 4200
Interpreting block diagrams
Block diagrams are used as schematic
representations of mathematical models
 The various pieces correspond to
mathematical entities
 Can be rearranged to help simplify the
equations used to model the system
 We will focus on one type of schematic
diagram – feedback control systems
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Variables

Variables are represented by arrows in block
diagrams
 Variables correspond to a physical and
measurable quantity
– Example: suppose you’re modeling a process for
producing a dye for clothing
– You must have a way of quantifying the dye color!

Variables must have physical units
– Actual speed units are MPH or km/hr
– Blood glucose units are mg/dl
Physical units
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Determining the physical units of some quantities is
not a trivial task!
Example - setting the desired speed in the cruise
control system
This is actually an electrical signal in volts, but can
we still call it MPH?
It depends on what you’re looking at – how the
vehicle speed will vary on a steep slope vs. the
function of the cruise control electronics
What is the physical signal that encodes desired
blood glucose levels in a and b cells?
Processes

Processes are represented by the blocks in block
diagrams:
variable
variable
Process

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Processes must have at least one input variable and
at least one output variable
Reclassify processes without input or output:
Input
variable
Output
variable
Processes

Most processes transform units:
Accelerator
depth (deg)
Engine
speed (rpm)
Engine
glucagon
(mg/dl)
insulin
(mg/dl)
Glucose
(mg/sec)
Tissues
Processes

Processes can encompass sub-processes
 A system is just a process w/ sub-processes!
Actual
glucose
a & b cells
measure
glucose
Actual
glucose
Measured
glucose
a & b cell
process
a & b cells
release
hormones
Glucagon
Insulin
Glucagon
Insulin
Measurement Processes

Processes that measure system outputs are
called sensors
 Input is physical property (MPH, mg/dl, etc.)
 Output is electrical or mechanical signal
 Typically model output to have units of input
Actual
speed
Speedometer
Measured
speed
Feedback Control Systems
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Many systems measure their output and use this
measurement to control system behavior
This is known as feedback control – the output is “fed
back” into the system
The summing junction is a special process that
compares the input and the feedback
Inputs to summing junction must have same units!
input
process
sensor
output
Generic Feedback Control System

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desired
output
Input is the output we want the system to have
Summing junction subtracts the measured output
from the desired output, difference is error signal
Controller acts based on magnitude of error signal
Actuator provides external power to system and
effects changes based on controller output
Plant is the process we are trying to control
controller
actuator
sensor
plant
output
Generic Feedback Control System
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desired
output
This is a general model, and may not be the same for
every feedback control system
Systems can have additional inputs known as
disturbances into or between processes
Can combine processes; typically controller and
actuator are combined
Describe and draw schematic, then recast your
model into this form if possible
controller
actuator
sensor
plant
output
Cruise Control System Revisited
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input: desired speed
output: actual speed
error: desired speed minus
measured speed
disturbance: wind, hills, etc.
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controller: cruise control unit
actuator: engine
plant: vehicle dynamics
sensor: speedometer
wind,
hills
desired
speed
cruise
control
engine
speedometer
vehicle
actual
speed
Glucose Regulation Revisited
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input: desired blood glucose
output: actual blood glucose
error: desired minus
measured blood glucose
disturbance: eating, fasting,
etc.
desired
glucose
a&b
cells
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controller: a and b cells
actuator: glucose storing or
releasing tissues
plant: glucose metabolism
sensor: a and b cells (again)
eating,
fasting
glucose
tissues
a&b
cells
glucose
metabol.
actual
glucose
Thermostat Example
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Set thermostat to desired room temperature
Thermostat measures room temperature
Furnace or AC turn on if measured <> desired
Air from furnace or AC changes room air temperature
external
air
desired
temp.
thermostat
furnace
or AC
thermostat
room air
actual
temp.
Toilet Flush Example
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Float height determines desired water level
Flush empties tank, float is lowered and valve opens
Open valve allows water to enter tank
Float returns to desired level and valve closes
flush
desired
level
float
valve
float
water
tank
actual
level