Block Diagrams

1
Block Diagrams

• BIOE 4200

2
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

3
Variables

• Variables are represented by arrows in block
  diagrams
• Variables correspond to a physical and measurable
  quantity
• Example suppose youre 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

4
Physical units

• 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 youre 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?

5
Processes

• Processes are represented by the blocks in block
  diagrams
• Processes must have at least one input variable
  and at least one output variable
• Reclassify processes without input or output

variable
variable
6
Processes

• Most processes transform units

Engine speed (rpm)
Accelerator depth (deg)
glucagon (mg/dl)
Glucose (mg/sec)
Tissues
insulin (mg/dl)
7
Processes

• Processes can encompass sub-processes
• A system is just a process w/ sub-processes!

Glucagon
Measured glucose
Actual glucose
a b cells release hormones
a b cells measure glucose
Insulin
Glucagon
Actual glucose
a b cell process
Insulin
8
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

Measured speed
Actual speed
Speedo-meter
9
Feedback Control Systems

• 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!

process
input
output
sensor
10
Generic Feedback Control System

• 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

desired output
output
actuator
controller
plant
sensor
11
Generic Feedback Control System

• 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

desired output
output
actuator
controller
plant
sensor
12
Cruise Control System Revisited

• input desired speed
• output actual speed
• error desired speed minus measured speed
• disturbance wind, hills, etc.

• controller cruise control unit
• actuator engine
• plant vehicle dynamics
• sensor speedometer

wind, hills
desired speed
actual speed
engine
cruise control
vehicle
speedo-meter
13
Glucose Regulation Revisited

• input desired blood glucose
• output actual blood glucose
• error desired minus measured blood glucose
• disturbance eating, fasting, etc.

• controller a and b cells
• actuator glucose storing or releasing tissues
• plant glucose metabolism
• sensor a and b cells (again)

eating, fasting
desired glucose
actual glucose
glucose tissues
a b cells
glucose metabol.
a b cells
14
Thermostat Example

• Set thermostat to desired room temperature
• Thermostat measures room temperature
• Furnace or AC turn on if measured ltgt desired
• Air from furnace or AC changes room air
  temperature

external air
desired temp.
actual temp.
furnace or AC
thermo-stat
room air
thermo-stat
15
Toilet Flush Example

• 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
actual level
valve
float
water tank
float