Zero Order Systems Flashcards
What is the function of system architecture?
Systems Architecture – order of a system determines its dynamic response.
What are the features of zero order systems? (2)
§ Rate is constant
§ Rate is not affected by a level – independent
- System responds instantly to changes in inputs – ____ and _____.
inflow
outflow
- Output is _____ to input no matter how input varies
- E.g. IV drip and taking blood at a constant rate
proportional
What is the inflow rate diagram for a ZOS?
What is the outflow rate diagram for a ZOS?
What is the combined rate diagram for a ZOS?
What is the solution?
What is the graph for an inflow rate?
What is the graph for an outflow rate?
Net flow rate =
inflow rate - outflow rate
But a level is the incremental accumulation of net rates;
level =
Where t0 is the initial time, and tf is the final time.
All levels have to have initial conditions;
level =
Where the initial condition represent the level at time t0.
Integration: (3)
§ Levels are found by determining the area under a rate curve
§ Level are found by integrating net rates in Vensim
§ Integration could be defined as the sum of areas under a curve (rate curve)
Differentiation: (4)
- The gradient is constant for all time
- Zero-Order system is shown in the graph above
- Rate is NOT always constant as seen in First-Order systems
- From the level, we can get the rate using differentiation
Summary of Integration and Differentiation: (3)
- Integration can be defined as the sum of areas under a curve (rate curve)
- The Reimann Sum can be used to determine integrals
- Differentiation can be defined as the rate of change i.e. the gradient of a level curve
