Ackermann's formula

In control theory, Ackermann's formula provides a method for designing controllers to achieve desired system behavior by directly calculating the feedback gains needed to place the closed-loop system's poles (eigenvalues) at specific locations (pole allocation problem).

These poles directly influence how the system responds to inputs and disturbances. Ackermann's formula provides a direct way to calculate the necessary adjustments—specifically, the feedback gains—needed to move the system's poles to the target locations. This method, developed by Jürgen Ackermann, is particularly useful for systems that don't change over time (time-invariant systems), allowing engineers to precisely control the system's dynamics, such as its stability and responsiveness.

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