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2. Introduction to the Principles of Feedback

2.8 Trade-offs Involved in Choosing the Feedback Gain

The preliminary insights of the previous two sections could seem to imply that all that is needed to generate a controller is to place high-gain feedback around the plant. This is true in so far that it goes. However, nothing in life is cost free, and this also applies to the use of high-gain feedback.

For example, if a plant disturbance leads to a nonzero error, e(t), in Figure 2.10, then high-gain feedback will result in a very large control action, u(t). This might lie outside the available input range and thus invalidate the solution.

Another potential problem with high-gain feedback is that it is often accompanied by the very substantial risk of instability. Instability is characterized by self-sustaining (or growing) oscillations. As an illustration, the reader will probably have witnessed the high-pitch whistling sound that is heard when a loudspeaker is placed too close to a microphone. This is a manifestation of instability resulting from excessive feedback gain. Tragic manifestations of instability include aircraft crashes and the Chernobyl, disaster in which a runaway condition occurred.

Yet another potential disadvantage of high loop gain was hinted at in subsection §2.3.4. There, we saw that increasing the controller gain leads to increased sensitivity to measurement noise.

In summary, high loop gain is desirable from many perspectives, but it is undesirable when viewed from other perspectives. Thus, when choosing the feedback gain, one needs to make a conscious trade-off between competing issues.

The previous discussion can be summarized in the following statement.

High loop gain gives approximate inversion, which is the essence of control. However, in practice, the choice of feedback gain is part of a complex web of design trade-offs. Understanding and balancing these trade-offs is the essence of control-system design.