Block Diagrams BIOE 4200 Interpreting block diagrams l

Block Diagrams BIOE 4200

Interpreting block diagrams l Block diagrams are used as schematic representations of mathematical models l The various pieces correspond to mathematical entities l Can be rearranged to help simplify the equations used to model the system l We will focus on one type of schematic diagram – feedback control systems

Variables are represented by arrows in block diagrams l Variables correspond to a physical and measurable quantity l – Example: suppose you’re modeling a process for producing a dye for clothing – You must have a way of quantifying the dye color! l Variables must have physical units – Actual speed units are MPH or km/hr – Blood glucose units are mg/dl

Physical units l l l 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 l Processes are represented by the blocks in block diagrams: variable Processes must have at least one input variable and at least one output variable l Reclassify processes without input or output: l Input variable Output variable

Processes l Most processes transform units: Accelerator depth (deg) Engine glucagon (mg/dl) insulin (mg/dl) Tissues Engine speed (rpm) Glucose (mg/sec)

Processes can encompass sub-processes l A system is just a process w/ sub-processes! l Actual glucose a & b cells measure glucose Actual glucose Measured glucose a & b cell process a & b cells release hormones Glucagon Insulin

Measurement Processes that measure system outputs are called sensors l Input is physical property (MPH, mg/dl, etc. ) l Output is electrical or mechanical signal l Typically model output to have units of input l Actual speed Speedometer Measured speed

Feedback Control Systems Many systems measure their output and use this measurement to control system behavior l This is known as feedback control – the output is “fed back” into the system l The summing junction is a special process that compares the input and the feedback l Inputs to summing junction must have same units! l input process sensor output

Generic Feedback Control System l l l 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 controller actuator sensor plant output

Generic Feedback Control System This is a general model, and may not be the same for every feedback control system l Systems can have additional inputs known as disturbances into or between processes l Can combine processes; typically controller and actuator are combined l Describe and draw schematic, then recast your model into this form if possible l desired output controller actuator sensor plant output

Cruise Control System Revisited input: desired speed l output: actual speed l error: desired speed minus measured speed l disturbance: wind, hills, etc. l controller: cruise control unit l actuator: engine l plant: vehicle dynamics l sensor: speedometer l wind, hills desired speed cruise control engine speedometer vehicle actual speed

Glucose Regulation Revisited input: desired blood glucose l output: actual blood glucose l error: desired minus measured blood glucose l disturbance: eating, fasting, etc. l desired glucose a&b cells controller: a and b cells l actuator: glucose storing or releasing tissues l plant: glucose metabolism l sensor: a and b cells (again) l eating, fasting glucose tissues a&b cells glucose metabol. actual glucose

Thermostat Example Set thermostat to desired room temperature l Thermostat measures room temperature l Furnace or AC turn on if measured <> desired l Air from furnace or AC changes room air temperature l external air desired temp. thermostat furnace or AC thermostat room air actual temp.

Toilet Flush Example Float height determines desired water level l Flush empties tank, float is lowered and valve opens l Open valve allows water to enter tank l Float returns to desired level and valve closes l flush desired level float valve float water tank actual level