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Balancing Loop with Delay Systems Archetype
From SystemsWiki
This structure is a variation of the standard Balancing Loop. The variation being that there are one or more delays in the structure which are responsible for producing a very different behavior pattern than with the standard balancing loop.
Contents |
[edit] Causal Loop Diagram
Fig. 1 is the standard Balancing Loop Systems Archetype with a delay between the gap and the action.
Standard Balancing Loop
The desired state interacts with the current state to produce a gap. The desired state is considered to be fixed during this consideration. The gap created by the difference between the desired state and the current state is really the motivation for action, and the larger the gap the grater the tendency to produce action. The action taken then adds to the current state. The current state subtracts from the gap, thus reducing it. When the action succeeds in moving the current state to a point where it is equal to the desired state the gap is reduced to zero and there is no more motivation for action.
<Implications of Delay</b>
Delays within this structure could exists between the time the action is taken and the time current state changes, or between the time current state actually changes and the time it is realized in order to affect the extent of the action being taken. A delay at either location will have essentially the same affect. The affect being that the action will continue to add to the current state at a level above what it should. This is essentially an overreaction which will tend to drive the current state beyond the desired state and the gap will go negative. The structure's reaction to this is to run in reverse, if this is possible for the particular instance described by the structure. The delay may be such as to cause overreaction in the opposite direction to move the current state below the current state. With a sufficient delay the structure will result in larger and larger oscillations over time.
[edit] Stock & Flow Diagram
Fig. 2 represents the Fig. 1 Causal Loop Diagram as a Stock & Flow Diagram with an explicit element for the time delay.
In insertion of the explicit time delay makes is much more evident.
[edit] Simulation
Fig. 3 represent the Balancing Loop with Delay as a Simgua simulation model.
With various settings for time delay and pct change factor the pattern of behavior for this model can be very different.
With pct chg factor = 0.5 and time delay = 0 the model displays the typical Balancing Loop behavior as depicted in Fig. 4.
As the time delay increases the model will begin to exhibit damped oscillations. Fig. 5 is with time delay = 1. Notice the desired state overshoot and undershoot by the Current State.
With time delay = 0 and pct chg factor = 0.75 Fig. 5 demonstrates uncontrolled oscillations.
Click Balancing Loop with Delay to run this model in your web browser.
[edit] Effective Strategies
- Advice for dealing with this structure is quite simple. Patience is a virtue. If you know you're dealing with a balancing structure and things are not going as expected then study the structure to see if there could be one or more delays that your impatience is simply having difficulty dealing with. This structure proves that there are times when taking additional action is worse than not taking additional action. More is not always better. If things are waffling back and forth endlessly or out of control a little less effort might be appropriate. An alternative is to monitor the Current State on a more frequent basis and ensure the result of the monitoring impacts the action appropriately in a more timely manner. In short, take the delay out of the structure.
[edit] Areas of Concern
- There are currently no known Systems Archetypes which are direct derivatives of the Balancing Loop with Delay Systems Archetype.
[edit] Examples
[edit] References
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