How to apply input constraint using LQR control in MATLAB

Hello,

I have a state space model of a system.I have Got LQR control Gain Matrix "K". And have also been successful

in simulating the system response using MATLAB code but at the end there is something missing.I want to apply input

contraint on the Plant's input.Now, i am stuck like "How do give it?" And "Where to give it" I am attaching my Matlab

Code.The start position of the system is y1 = 450 & y2 = 650 and final reference position is set to (0,0).

I would appreciate your help.

Thank you.

K = [0.0071 -3.4736 * 10 ^ -6 2.2392 -0.0011

3.4736 * 10 ^ -6 0.0071 -0.0011 2.2392];

n = 1.1 * 10 ^ -3;

A = [0 0 1 0;

0 0 0 1;

3. * n ^ 2 0 0 2. * n;

0 0 -2. * N 0];

B = [0 0;

0 0;

Ten;

0 1];

C = [1 0 0 0;

0 1 0 0;

0 0 1 0;

0 0 0 1];

D = [0 0;

0 0;

0 0;

0 0];

Ac = [(AB * K)];

Bc = [B];

Cc = [C];

Dc = [D];

states = {'x1' 'x2' 'x3' 'x4'};

inputs = {'u1' 'u2'};

outputs = {'y1'; 'y2'; 'y3'; 'y4'};

sys = ss (Ac, Bc, Cc, Dc, 'statename', states, 'inputname', inputs, 'outputname', outputs);

t = 0: 0.01: 2000;

u = [0 * t; 0 * t];

[y, t, x] = lsim (sys, u, t, [450,650,0,0]);

[A, h1, h2] = plotyy (t, y (:, 1), t, y (:, 2), 'plot')

set (get (A (1), 'Ylabel'), 'String', 'y1 (Position)')

set (get (A (2), 'Ylabel'), 'String', 'y2 (Position)')

title ('Reference position (0,0) with LQR Control')