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

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

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 and cells?

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:

Input variable

Output variable

Processvariablevariable

Processes

Most processes transform units:

Engine

Engine speed (rpm)

Accelerator depth (deg)

Tissues

Glucose (mg/sec)

glucagon (mg/dl)

insulin (mg/dl)

Processes

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

& cells release

hormones

& cells measure glucose

GlucagonMeasured glucose

Actual glucose

Insulin

& cell process

GlucagonActual

glucoseInsulin

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

Speedo-meter

Measured speed

Actual speed

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

sensor

input output

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

actuator

sensor

desired output

outputcontroller plant

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

actuator

sensor

desired output

outputcontroller plant

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

engine

speedo-meter

desired speed

actual speed

cruise control

vehicle

wind, hills

Glucose Regulation Revisited

input: desired blood glucose output: actual blood glucose error: desired minus

measured blood glucose disturbance: eating, fasting,

etc.

controller: and cells actuator: glucose storing or

releasing tissues plant: glucose metabolism sensor: and cells

(again)

glucose tissues

& cells

desired glucose

actual glucose

& cells

glucose metabol.

eating, fasting

Thermostat Example

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

furnace or AC

thermo-stat

desired temp.

actual temp.

thermo-stat

room air

external air

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

valve

float

desired level

actual level

floatwater tank

flush