57d68fb3-7302-4e26-8c2e-706f29ada748 25 3 3 decimal

&[DATE] &[TIME] - &[FILENAME]

Linear Quadratic State Feedback Regulator for Discrete State Space Systems

A B Q.x Q.u NumIt dlqr T NumIt el Q.x : j NumIt 1 - 1 range T j el Q.x A transpose T j 1 + el T j 1 + el B * Q.u B transpose T j 1 + el * B * + (1 -^* B transpose * T j 1 + el * - (* A * + : for Q.u B transpose T 1 el * B * + (1 -^B transpose * T 1 el * A * 31 line :

EXAMPLES

2 states, 1 input:

A 1.1 00 2.1 - 22 mat :

B 11 - 21 mat :

Qx 2 identity :

Qu 1 :

K.Matlab K ≡

K A B Qx Qu 30 dlqr :

K 0.32 1.345 12 mat

3 states, 2 inputs:

A 111 - 1 - 1101 - 133 mat :

B 111 - 10132 mat :

Qx 3 identity :

Qu 2 identity :

K A B Qx Qu 30 dlqr :

K 0.914 0.657 - 0.625 - 0.08 - 0.699 0.129 23 mat

K.Matlab K ≡

Scalar System:

A 111 mat :

B 111 mat :

Qx 1 :

Qu 1 :

even for a first order system A and B must be given as matrices

K A B Qx Qu 10 dlqr :

K 0.618

K.Matlab K ≡

3 states, 3 inputs:

A 011 - 1.5 101 1. - 133 mat :

B 0.1 0.2 0.5 0.5 0.1 0.5 00033 mat :

Qx 3 identity :

Qu 3 identity :

K A B Qx Qu 20 dlqr :

K 0.787 1.116 0.224 - 0.099 0.219 0.25 - 0.657 1.106 0.68 - 33 mat

K.Matlab K ≡

6 states, 3 inputs:

A 0.6 01 - 0000 0.3 000001 0.4 - 00000 0.3 1 - 0001111 0.5 01 - 11 - 0166 mat :

B 0.1 - 0110001000000000063 mat :

Qx 6 identity :

Qu 3 identity :

K A B Qx Qu 20 dlqr :

K 6.063 103 -^* - 0.63 0.298 0.078 - 0.266 0.014 8.369 103 -^* - 0.682 0.265 0.264 0.273 0.602 0.325 0.011 - 0.407 - 0.01 0.063 0.105 36 mat

K.Matlab K ≡