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Unformatted text preview: Recipes for Pole Placement Task: Consider an n th order linear controllable single-input (i.e., u being scalar) system x = Ax + Bu . With the linear state feedback u = Kx , the closed-loop system is x = ( A + BK ) x . Given a set of n desired eigenvalues p 1 ,... ,p n for the closed-loop system matrix ( A + BK ), find a K which places the eigenvalues of ( A + BK ) at those desired values. You can use either of the two recipes given below for this task. Recipe 1: 1. Find the controllability matrix n = [ B,AB,A 2 B,... ,A n- 1 B ]. 2. Find the characteristic polynomial p ( ) = n + a n- 1 n- 1 + ... + a 1 + a of the matrix A . 3. Find the column vector q 1 = ( T n )- 1 e n where e n = [0 ,... , , 1] T is the 1 n column vector with 1 as the n th element and zero everywhere else. Define Q = q T 1 q T 1 A q T 1 A 2 . . . q T 1 A n- 1 ....
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This note was uploaded on 12/06/2010 for the course EL 625 taught by Professor Khorami during the Spring '10 term at NYU Poly.
- Spring '10