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 and 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: Input variable Output variable Process variable

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

7. Processes Processes can encompass sub-processes A system is just a process w/ sub-processes! & cells release hormones & cells measure glucose Glucagon Measured glucose Actual glucose Insulin & cell process Glucagon Actual glucose 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 Speedo- meter Measured speed Actual speed

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 sensor inputoutput

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 actuator sensor desired output output controllerplant

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 actuator sensor desired output output controllerplant

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 engine speedo- meter desired speed actual speed cruise control vehicle wind, hills

13. 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

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 furnace or AC thermo- stat desired temp. actual temp. thermo- stat room air external air

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 valve float desired level actual level float water tank flush