Der Entwurf Linearer Regelungssysteme Im Zustandsraum

Authors

Jurgen Ackermann

Year

1972

Journal Paper

Algorithm

Ackermann Pole Placement Formula

Source

Regelungstechnik

Abstract¶

A simple method for obtaining a desired characteristic equation for a system x[k + 1] = A x[k] + b u[k] by state variable feedback u = -k'x is derived. It does not require a transformation of the state equations to a canonical form. The result is: Obtain k' by substituting the given dynamic matrix A into the desired characteristic polynomial and premultiplying by the last row of the inverse of the controllability matrix. The dual result for the observers of order n and n-1 is shown.

Summary¶

Derives Ackermann's explicit formula for assigning the closed-loop characteristic polynomial of a controllable single-input linear system without transforming it into canonical form. Applies the dual construction to full-order and reduced-order observers.