Presentation on theme: "Higher order feedback loops"— Presentation transcript:
1 Higher order feedback loops One stock – first order systemMore stocks – higher orderBehaviorSecond order negative feedback – oscillating systemSecond order positive feedback – exponential growth and oscillations (unstable)
2 Higher order feedback loops Second order negative feedbackpendulum
8 Delays Delays occur frequently in many systems. When a pollutant is dumped into a river, it takes time to dissipate.Delays are divided into two types:(a) Material delays - resulting from the time involved in processing materials.(b) Information delays - resulting from time in perceiving and acting upon information.
9 Material delay example Construction of apartments in a large city.Builders construct apartments in response to the gap between the total number of apartments desired and available.Start with 10,000 apartments.Increase to 15,000.Delay - completion time 2 years.
11 Material delay example Initiation time = 1Apartments in construction = 0Completion rate=Apartments in construction/Completion timeTotal number of apartments =10,000Desired apartments = 10,000 + STEP(5000,1)Difference= Desired apartments – Total number of apartmentsCompletion time = 2
13 Information delay example Joe’s Cement Factory makes and sells cement blocks Monday through Friday.Each morning Joe has to decide how many blocks to make, and he relies on the average sales over the past five days in making his decision.
17 Solution interval DT System Principle 11 Solution interval is in all level equations and no others
18 Solution interval DT DT Period of measurementDelta timeTime stepDT is the time period in which the level is changed by the rate
19 DT in VensimThe best size of TIME STEP is determined by the following considerations:TIME STEP should allow test inputs to be accessed regularly.TIME STEP should allow data to be accessed with appropriate regularity.TIME STEP should be smaller than 1/3 of the shortest time constant in the model (not applicable with automatic step size adjustment in Runge-Kutta integration).TIME STEP should be smaller than the shortest period for which a significant change in model behavior is at all likely.
20 DT in VensimAn inappropriately long TIME STEP leads to incorrect behavior.In general if you see oscillation with a frequency that is near to twice TIME STEP you should test TIME STEP to see if it has an appropriate value.If you are using Runge-Kutta integration with automatic step size adjustment, the third and forth considerations do not apply.Vensim will automatically determine how small it needs to make TIME STEP in order to achieve the desired accuracy or issue an error if it is unable to do so.