Deprecated : Constant E_STRICT is deprecated in /home/polpe/public_html/system/core/Exceptions.php on line 75
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_URI::$config is deprecated
Filename: core/URI.php
Line Number: 101
Backtrace:
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Router::$uri is deprecated
Filename: core/Router.php
Line Number: 127
Backtrace:
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$benchmark is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$hooks is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$config is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$log is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$utf8 is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$uri is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$exceptions is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$router is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$output is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$security is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$input is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$lang is deprecated
Filename: core/Controller.php
Line Number: 75
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$load is deprecated
Filename: core/Controller.php
Line Number: 78
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$parser is deprecated
Filename: core/Loader.php
Line Number: 1290
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$form_validation is deprecated
Filename: core/Loader.php
Line Number: 1290
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$MyModel is deprecated
Filename: core/Loader.php
Line Number: 353
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 282
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 289
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 304
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 314
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 315
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 316
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 317
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: ini_set(): Session ini settings cannot be changed after headers have already been sent
Filename: drivers/Session_files_driver.php
Line Number: 94
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent
Filename: Session/Session.php
Line Number: 108
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: Warning
Message: session_start(): Session cannot be started after headers have already been sent
Filename: Session/Session.php
Line Number: 141
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Main::$session is deprecated
Filename: core/Loader.php
Line Number: 1290
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$benchmark is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$hooks is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$config is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$log is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$utf8 is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$uri is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$exceptions is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$router is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$output is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$security is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$input is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$lang is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$load is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$parser is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$form_validation is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$MyModel is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property CI_Loader::$session is deprecated
Filename: core/Loader.php
Line Number: 925
Backtrace:
File: /home/polpe/public_html/application/controllers/Main.php
File: /home/polpe/public_html/index.php
Polcz Péter honlapja
Tartalomjegyzék
\[
\newenvironment{dcases}{\left\{\begin{array}{ll}}{\end{array}\right.}
\]
Inverted pendulum, local linearization
Teljes Matlab script
kiegészítő függvényekkel .
File: ccs_nonlin_ipend_localin.m
Directory: 4_gyujtemegy/11_CCS/Modellek/inverse_pendulum/2018b_nonlin_pannon
Author: Peter Polcz (ppolcz@gmail.com)
First created on 2017.05.02. Tuesday, 22:39:05
Modified on 2018. August 26.
Nonlinear model
% Time
syms t real
% State variables
syms position v phi omega real
% Input
syms u real
% State vector
x = [
position
v
phi
omega
];
% Known model parameters
M = 0.5;
m = 0.2;
l = 1;
g = 9.8;
b = 0;
q = 4*(M+m) - 3*m*cos(phi)^2;
f_sym = [
v
(4*m*l*sin(phi)*omega^2 - 1.5*m*g*sin(2*phi) -4*b*v) / q
omega
3*(-m*l*sin(2*phi)*omega^2 / 2 + (M+m)*g*sin(phi) + b*cos(phi)*v) / (l*q)
];
g_sym = [
0
4*l
0
-3*cos(phi)
] / (l*q);
Linearized model around the unstable equilibrium point
A = double(subs(jacobian(f_sym,x), x, [0;0;0;0]));
B = double(subs(g_sym, x, [0;0;0;0]));
C = [
1 0 0 0
0 0 1 0
];
D = [ 0 ; 0 ];
Static feedback design using LQR or pole placement
K = lqr(A,B,eye(4),1);
K = place(A,B,[-1+1i -1-1i -2+1i -2-1i]);
% Equation of the closed loop system
f_cls_sym = f_sym - g_sym*K*x;
% Simulation of the closed loop system
f_cls_ode = matlabFunction(f_cls_sym, 'vars', {t x});
[tt,xx] = ode45(f_cls_ode, [0 10], [0 0 0.7 0]');
uu = -K*xx';
% Visualization
ipend_simulate_0(tt,xx,uu)
