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 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

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 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?

5. Process Output variable Input variable 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. Engine Processes • Most processes transform units: Accelerator depth (deg) Engine speed (rpm) 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! Actual glucose Measured glucose Glucagon a & b cells measure glucose a & b cells release hormones Insulin Actual glucose Glucagon 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 Actual speed Measured 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 controller actuator 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 controller actuator plant sensor

12. 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 Cruise Control System Revisited wind, hills desired speed actual speed cruise control engine vehicle speedo-meter

13. 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) Glucose Regulation Revisited eating, fasting desired glucose actual glucose a & b cells glucose tissues 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 <> desired • Air from furnace or AC changes room air temperature external air desired temp. actual temp. thermo-stat furnace or AC 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 float valve water tank float