Instability In Feedback Systems

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China

Lean Manufacturing Academy

Europe

Jung, Aust & Partner

Australia

Peter J. Ellis

North America

Sims Consulting Group

Strategic Impact

Instability In Feedback Systems

In some feedback systems amplification continues with each cycle resulting in larger and larger excursions. Figure 1 illustrates. In theory, the system oscillates to infinity. In reality, some physical constraint limits the excursions.

For example, inventory and shortages may alternate getting larger and larger until the warehouse is full and there is no room for additional inventory. The company may run out of cash to pay for the inventory and thus force limitation. There is lots of inventory but never the right inventory.

Instability results primarily from amplification and time delays. Time delays in the feedback loop have larger effects than in the forward loop but any unnecessary amplification can contribute to instability.

Stabilization Series

Stabilizing Production Scheduling

Feedback System Basics
Instability In Feedback Systems
Complexity
Chaos In Scheduling
Using The Knowledge

unstable feedback

Figure 1-- Instability In A Feedback System

feedback oscillations

These affects are common in everyday life. Most of us have heard the awful squeal that sometimes affects public address systems. In such a situation, the speakers voice enters a microphone. An amplifier increases the signal and sends it out via loudspeakers. When the signal from the loudspeakers reenters the microphone it is amplified a second time, a third time and so on. The signal increases until the limits of the amplifier or speaker have been exceeded.

Instability & Oscillation

Instability In Feedback Systems

Instability results primarily from amplification and time delays. Time delays in the feedback loop have larger effects than in the forward loop but any unnecessary amplification can contribute to instability.

Stabilization Series