View source for Question: How are stability, performance and robustness different?

{{Question
|Chapter=Introduction
|Author(s)=Ling Shi
|Date=2006/09/25
}}
The concepts of stability, performance and robustness can seem very similar because they all related to the properties of a feedback system. The detailed definitions of these concepts are given later in the text, but a simple example can be used to illustrate the basic concepts.

Consider the problem of an inverted pendulum on a cart (a special case of a balance system), as shown in the diagram below:

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[[Image:anim_pend.gif]]
</center>

Suppose we wish to design a controller such that the pendulum stays balanced in the inverted position (roughly as shown in the animation). The controller should be designed such that it has the following properties:
* Stability: the controller should ensure that the pendulum never falls down.
* Performance: the controller should be able to move the cart from one position to another position, keeping the pendulum stabilized in the inverted position, in minimum time.
* Robustness: suppose that we change the length of the pendulum slightly. The controller should continue to stabilize the system and provide good (perhaps not optimal) performance in the presence of this perturbation.