Tartalomjegyzék

Computer controlled systems (2019)

Lecture notes of the seminar

Homeworks
hw_1_2019.pdf	2120 days	40.3 KB
hw_2_2019.pdf	2111 days	36.77 KB
hw_3_2019.pdf	2096 days	189.57 KB
Lecture slides
lec_01_2019.pdf	2136 days	4.92 MB
lec_02_2019.pdf	2130 days	461.3 KB
lec_03_2019.pdf	2117 days	905.26 KB
lec_04_2019.pdf	2115 days	401.72 KB
lec_05_2019.pdf	2109 days	1009.69 KB
lec_06_2019.pdf	2101 days	1.3 MB
lec_07_2019.pdf	2095 days	1.63 MB
lec_08_2019.pdf	2080 days	1.09 MB
lec_09_2019.pdf	2074 days	1.03 MB
Seminars (1st midterm)
sem_01_2019.pdf	2123 days	114.78 KB
sem_02_2019.pdf	2135 days	107.51 KB
sem_03_2019.pdf	2122 days	141.71 KB
sem_04_2019.pdf	2122 days	340.58 KB
sem_05_2019.pdf	2111 days	252.81 KB
Seminars (2nd midterm)
sem_06_2019.pdf	2079 days	347.98 KB
sem_06_2019_TP_matlab.zip	1713 days	28.71 KB
sem_08_2019_matlab1.pdf	2073 days	311.2 KB
sem_08_2019_matlab1.zip	1713 days	4.26 KB
sem_08_2019_matlab1_sol.zip	1713 days	4.44 KB
sem_09_2019.pdf	2096 days	209.94 KB
sem_10_2019_matlab2.pdf	2073 days	493.63 KB
sem_10_2019_matlab2.zip	1713 days	3.14 KB
Extra homeworks (not compulsary)
xtra_hw_dynamical_system_simulations.pdf	2072 days	173.68 KB
xtra_hw_linear_algebra.pdf	2072 days	337.11 KB
Extra material and tutorial
xtra_material_Convex_optimization.pdf	2421 days	370.89 KB
xtra_material_DC_motor_model.pdf	2421 days	302.86 KB
xtra_material_Dissipativity_L2gain_LTI_LPV.pdf	2421 days	316.85 KB
xtra_material_Dissipativity_L2gain_LTI_LPV_dark.pdf	2421 days	3.02 MB
xtra_material_Laplace_table.pdf	2421 days	98.74 KB
xtra_material_lqservo.pdf	2421 days	30.01 KB
Model descriptions
xtra_model_crane.pdf	2072 days	217.07 KB
xtra_model_double_crane.pdf	2421 days	318.02 KB
xtra_model_gantry_crane_Ospina_Henao.pdf	2421 days	686.56 KB
midterm seating
zh1_seating.pdf	2101 days	28.51 KB
zh2_seating.pdf	2101 days	26.85 KB

Important built-in linear algebra functions:
Q = orth(A) - Gives an orthonormal basis of the image space of a matrix
Z = null(A) - Returns an orthonormal basis for the null space of matrix A. W = null(V') returns an orthonormal basis of the orthogonal complement of subspace V spanned by the column vectors collected in matrix V
[U,S,V] = svd(A) - Singluar value decomposition of matrix A (see also Fundamental theorem of linear algebra)
k = rank(A,) - Rank of matrix A
[R,p] = rref(A) - Reduced row echelon form (Gauss-Jordan elimination). p gives the indices of the first k nr of linearly independent rows of matrix A, where k = rank(A)
[r,p,k] = residue(b,a); [b,a] = residue(r,p,k) - Partial fractional decomposition (numerical)
w = conv(u,v) - Convolution and polynomial multiplication
[q,r] = deconv(u,v) - Deconvolution and polynomial division
Important functions of Matlab's Symbolic Math Toolbox (SMT):
syms a x y z real; syms f(x) g(x,y,z) - Declare (create) multiple scalar symbolic variables or functions
A = sym('a_%d%d',[3 4]) - Create a single symbolic matrix, vector or scalar variable
simplify - Simplify symbolic expression
simplifyFraction - Simplify fraction of polynomials expression to its irreducible form
f_sym = x^2+y*z; symvars(f_sym) - List symbolic variables appearing in the object passed as an argument
subs(f_sym, [x z], [x+y x^2]) - Substitute variables or expression by other variables or expression in a symbolic expression
f_fh = matlabFunction(f_sym, 'vars', {x [y z]}) - Generate a function handle from a symbolic expression
charpoly - Compute the characteristic polynomial of a matrix
partfrac - Partial fractional decomposition of a rational function (useful when producing inverse Laplace transformation of a transfer function). FactorMode: real/complex/full/rational. See also its numerical pair: residue.
laplace
ilaplace
Important function of the Control System Toolbox:
[b,a] = ss2tf(A,B,C,D) - State-space model to transfer function model
[A,B,C,D] = tf2ss(b,a) - Transfer function model to state-space model
ss - State space model
tf - Transfer function model
impulse(sys) - Impulse response function
step(sys) - Step response function
lsim(sys,u,t,x0) - Simulate an LTI system (sys) with arbitrary input u(t) from initial condition x0
On = obsv(A,B) - Compute the observability matrix of LTI system (A,B,C,D)
Cn = ctrb(A,B) - Compute the controllability matrix of LTI system (A,B,C,D)
Important built-in linear algebra functions:
r = rank(A) - Compute the rank of matrix A
Ker = null(A) - Compute an orthonormal basis for the kernel space of matrix A
Im = orth(A) - Compute an orthonormal basis for the image space of matrix A using Gram-Schmidt orthogonalization
A_GJ = orth(A) - Compute the reduced row echelon form of matrix A (Gauss-Jordan elimination)

Seminar 1. - Laplace transformation, non-dimensional ODEs

Matlab examples

Compute a polynomial division (see lecture notes nr. 3).
Compute the partial fractional decomposition of $H(s) = \frac{5s^2+3s+1}{s^3+6s^2+11s+6}$.
```
syms s
H = (5*s^2 + 3*s + 1)/(s^3 + 6*s^2 + 11*s + 6);
partfrac(H)
```
Output:
```
ans = 3/(2*(s + 1)) - 15/(s + 2) + 37/(2*(s + 3))
```
$H(s) = \frac{3}{2(s+1)}-\frac{15}{s+2}+\frac{37}{2(s+3)}$
Compute the Laplace transformation of $h(t) = \cos(at)+\sin(at)+e^{-ct}\cos(bt)+e^{-ft}\sin(et)$.
```
syms t a b c e f
h = cos(a*t) + sin(a*t) + exp(-c*t)*cos(b*t) + exp(-f*t)*sin(e*t)
laplace(h,t)
```
Output:
```
ans = a/(a^2 + t^2) + (c + t)/((c + t)^2 + b^2) + e/((f + t)^2 + e^2)
```
$H(s) = \frac{a}{a^2+t^2}+\frac{t}{a^2+t^2}+\frac{c+t}{{(c+t)}^2+b^2}+\frac{e}{{(f+t)}^2+e^2}$
Compute the inverse Laplave transformation of $H(s) = \frac{1}{s^2 + s + 1}$.
```
syms s
ilaplace(1/(s^2+s+1))
```
Output:
$h(t) = \frac{2\sqrt{3}{e}^{-\frac{t}{2}}\sin(\frac{\sqrt{3}t}{2})}{3}$

Seminar 3. - System representations

Matlab examples

Give a possible stat-space realization for LTI system $H(s) = \frac{b(s)}{a(s)}$.

b = [1 0 1]; a = [1 0 2 3 2];
H = tf(b,a)

Output:

H =

         s^2 + 1
  ---------------------
  s^4 + 2 s^2 + 3 s + 2

Continuous-time transfer function.

sys = ss(H)

Output:

sys =

  A =
         x1    x2    x3    x4
   x1     0    -1  -1.5    -1
   x2     2     0     0     0
   x3     0     1     0     0
   x4     0     0     1     0

  B =
       u1
   x1   1
   x2   0
   x3   0
   x4   0

  C =
        x1   x2   x3   x4
   y1    0  0.5    0  0.5

  D =
       u1
   y1   0

Continuous-time state-space model.

[A,B,C,D] = ssdata(sys)

Output:

A =

         0   -1.0000   -1.5000   -1.0000
    2.0000         0         0         0
         0    1.0000         0         0
         0         0    1.0000         0


B =

     1
     0
     0
     0


C =

         0    0.5000         0    0.5000


D =

     0

Compute the transfer function representation of an LTI system given by a state-space realization $(A,B,C,D)$.

A = randn(6); B = randn(6,2); C = randn(3,6); D = zeros(3,2);
sys = ss(A,B,C,D)

Output:

sys =

  A =
             x1        x2        x3        x4        x5        x6
   x1   -0.1241    0.7172    0.2939    -2.944   -0.1022   -0.1649
   x2      1.49      1.63   -0.7873     1.438   -0.2414    0.6277
   x3     1.409    0.4889    0.8884    0.3252    0.3192     1.093
   x4     1.417     1.035    -1.147   -0.7549    0.3129     1.109
   x5    0.6715    0.7269    -1.069      1.37   -0.8649   -0.8637
   x6    -1.207   -0.3034   -0.8095    -1.712  -0.03005   0.07736

  B =
              u1         u2
   x1     -1.214    -0.2256
   x2     -1.114      1.117
   x3  -0.006849     -1.089
   x4      1.533    0.03256
   x5    -0.7697     0.5525
   x6     0.3714      1.101

  C =
            x1       x2       x3       x4       x5       x6
   y1    1.544  -0.7423  -0.6156   0.8886   -1.422  -0.1961
   y2  0.08593   -1.062   0.7481  -0.7648   0.4882    1.419
   y3   -1.492     2.35  -0.1924   -1.402  -0.1774   0.2916

  D =
       u1  u2
   y1   0   0
   y2   0   0
   y3   0   0

Continuous-time state-space model.

H = tf(sys)

Output:

H =

  From input 1 to output...
          1.34 s^5 - 11.81 s^4 + 51.54 s^3 - 67.91 s^2 + 15.52 s + 8.946
   1:  ---------------------------------------------------------------------
       s^6 - 0.852 s^5 + 2.835 s^4 - 11.81 s^3 + 8.768 s^2 + 5.545 s - 5.529

         0.05174 s^5 + 1.64 s^4 + 26.25 s^3 - 30.64 s^2 - 15.04 s + 10.24
   2:  ---------------------------------------------------------------------
       s^6 - 0.852 s^5 + 2.835 s^4 - 11.81 s^3 + 8.768 s^2 + 5.545 s - 5.529

         -2.709 s^5 + 12.98 s^4 - 52.9 s^3 + 73.51 s^2 - 0.02814 s - 32.15
   3:  ---------------------------------------------------------------------
       s^6 - 0.852 s^5 + 2.835 s^4 - 11.81 s^3 + 8.768 s^2 + 5.545 s - 5.529

  From input 2 to output...
          -1.48 s^5 + 1.224 s^4 - 31.77 s^3 + 47.39 s^2 - 4.437 s - 12.79
   1:  ---------------------------------------------------------------------
       s^6 - 0.852 s^5 + 2.835 s^4 - 11.81 s^3 + 8.768 s^2 + 5.545 s - 5.529

         -0.2133 s^5 - 3.697 s^4 - 14.09 s^3 + 15.6 s^2 + 4.706 s - 7.059
   2:  ---------------------------------------------------------------------
       s^6 - 0.852 s^5 + 2.835 s^4 - 11.81 s^3 + 8.768 s^2 + 5.545 s - 5.529

          3.35 s^5 - 0.9953 s^4 + 37.94 s^3 - 58.62 s^2 - 7.658 s + 25.87
   3:  ---------------------------------------------------------------------
       s^6 - 0.852 s^5 + 2.835 s^4 - 11.81 s^3 + 8.768 s^2 + 5.545 s - 5.529

Continuous-time transfer function.

[b,a] = tfdata(H)

Output:

b =

  3×2 cell array

    {1×7 double}    {1×7 double}
    {1×7 double}    {1×7 double}
    {1×7 double}    {1×7 double}


a =

  3×2 cell array

    {1×7 double}    {1×7 double}
    {1×7 double}    {1×7 double}
    {1×7 double}    {1×7 double}

Seminar 4. - Controllability, observability

Matlab examples

Compute the controllable and unobservable subspace of LTI state-space model $(A,B,C,D)$.

A = [1 2 -2 ; 0 1 0 ; 1 0 1]; B = [0 0 2]'; C = [1 0 0]; D = 0;
Cn = ctrb(A,B), rank(Cn)

Output:

Cn =
     0    -4    -8
     0     0     0
     2     2    -2

ans = 2

Ctrb_Subsp = orth(Cn)

Output:

Ctrb_Subsp =
    0.9933   -0.1153
         0         0
    0.1153    0.9933

Ctrb_Subsp = orth(sym(Cn))

Output:

Ctrb_Subsp =
[ 0, -1]
[ 0,  0]
[ 1,  0]

On = obsv(A,C), rank(On)

Output:

On =
     1     0     0
     1     2    -2
    -1     4    -4

ans = 2

Unobsv_Subsp = null(On)

Output:

Unobsv_Subsp =
         0
    0.7071
    0.7071

Unobsv_Subsp = null(sym(On))

Output:

Unobsv_Subsp =
 0
 1
 1

Published Matlab scripts

Manipulations with Matlab's Symbolic Math Toolbox: d2017_09_14_gyak1. Basic symbolic routines, Laplace transformation, inverse Laplace transformation, partial fractional decomposition.
State-space transformations: d2017_09_19_gyak2.
Dynamic systems simulations:
- d2017_09_20_Rossler_attractor
- d2017_09_20_Lorentz_system
- d2017_09_20_brussellator
- d2017_09_21_ccs_gyak2_eloben
- Approximate solution of the heat equation with ode45 by considering the discretization along the spacial coordinate. (See also: solution using pdepe.)
- Example for a discrete-time dynamical system: d2018_01_20_ex1_sim
Analysis in frequency/operator domain
- d2017_09_27_gyak3_freqdom
- d2017_09_28_gyak3_eloben
- d2017_10_25_gyak6_PID_live
- Advanced frequency domain analysis: minimum_phase_systems.
- System inversion of minimum phase SISO systems.
Controllability, observability, subspaces: d2017_10_02_gyak4_subspaces.
Geometrical meaning, staircase forms: d2017_10_04_gyak4_ctrb_obsb_geometrical_meaning.
Fundamental theorem of the linear argebra, demonstration: d2017_10_05_gyak4_basicthm_LA.
Lyapunov function demonstration for a non-proper Lyapunov function (Hamiltonian system): d2017_10_11_gyak5_Lyapunov_improper.
Lyapunov function demonstration for the pendulum system: d2017_10_11_gyak5_Lyapunov_pendulum_plain_vid
Matlab solutions of former homeworks (2017 fall)
- Homework #1
- Homework #2

Control systems demonstrations

Inverted pendulum model (inverz inga modell)

Model description and task sheet for the first Matlab practice: sem_08_2019_matlab1.pdf

Framework for the first Matlab practice

Model description and task sheet for the first Matlab practice: sem_10_2019_matlab2.pdf

Framework for the second Matlab practice

Model linearization around stable and unstable equilibrium point, simulation and analysis.

Inverted pendulum control and integral reference tracking.

Inverted pendulum control and integral reference tracking (augmented, corrected).

Inverted pendulum nonlinear control - 2018.07.30. (július 30, hétfő), 11:02

Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (Symbolic Math Toolbox) and pole placement

Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (with uncertain frictional coefficient) - feedback design for LPV with LMIs

Crane model (rakodó daru modellje)

Model description and derivation using calculus of variations (ccs_model_crane.pdf)

State space model derivation using symbolic computations

Simulink model and simulation (without control): sim_nonlinear_model_demo

Recommended literature

G. Szederkényi, K. M. Hangos, J. Bokor: Computer Controlled Systems (CCS)
Karl J. Åström and Richard M. Murray: Feedback Systems: An Introduction for Scientists and Engineers (FSB)

Additionally:

Andrew_Lewis_A_Mathematical_Approach_to_Classical_Control.pdf	2421 days	9.32 MB
Scherer.Weiland_2000_Linear_Matrix_Inequalities_in_Control.pdf	2421 days	1.25 MB
The_Fundamental_Theorem_of_Linear_Algebra.pdf	2421 days	330.57 KB

Extra material for the midterm tests

Former midterm examples
2014_ccs_1zh_A_feladatsor.pdf	2421 days	213.5 KB
2014_ccs_1zh_B_feladatsor.pdf	2421 days	201.93 KB
2015_ccs_1zh_elm.pdf	2421 days	111.9 KB
2015_ccs_1zh_gyak_MO.pdf	2421 days	124.17 KB
2015_ccs_2zh_elm.pdf	2421 days	104.75 KB
2015_ccs_2zh_gyak_MO.pdf	2421 days	114.2 KB
2015_ccs_gyakorlo_zh.pdf	2421 days	104.09 KB
2016_ccs_1zh_elm.pdf	2421 days	97.13 KB
2016_ccs_1zh_gyak.pdf	2421 days	84.4 KB
2016_ccs_2zh_elm.pdf	2421 days	83.64 KB
2016_ccs_2zh_gyak.pdf	2421 days	103.98 KB
2017a_ccs_1zh_computational.pdf	2421 days	87.01 KB
2017a_ccs_1zh_theoretical.pdf	2421 days	111.83 KB
2017a_ccs_2zh_elm.pdf	2421 days	104.28 KB
2017a_ccs_2zh_gyak.pdf	2421 days	131.4 KB
2017b_ccs_1zh_elm.pdf	2421 days	76.62 KB
2017b_ccs_1zh_elm_SOL.pdf	2421 days	136.01 KB
2017b_ccs_1zh_gyak.pdf	2421 days	90.72 KB
2017b_ccs_2zh.pdf	2421 days	162.78 KB
2017b_ccs_2zh_elm.pdf	2421 days	62.41 KB
2017b_ccs_2zh_gyak.pdf	2421 days	87.26 KB
2018_ccs_zh1_elm.pdf	2459 days	104.3 KB
2018_ccs_zh1_gyak.pdf	2459 days	107.2 KB
2018_ccs_zh2_elm.pdf	2417 days	90.57 KB
2018_ccs_zh2_gyak.pdf	2417 days	163.59 KB
2019_ccs_zh1_elm.pdf	2094 days	108.05 KB
2019_ccs_zh1_gyak.pdf	2097 days	112.16 KB
2019_ccs_zh1_gyak_MO.pdf	2095 days	175.28 KB
2019_ccs_zh1_gyak_TG.pdf	2093 days	122.07 KB
2019_ccs_zh1_gyak_TG_MO.pdf	2097 days	124.27 KB
Additional material
kawski_Lyapunov1.pdf	2421 days	481.87 KB
kawski_Lyapunov2.pdf	2421 days	262.33 KB

Extra material for the supplementary midterm

2015_ccs_potzh_elm.pdf	2421 days	101.32 KB
2015_ccs_potzh_gyak_MO.pdf	2421 days	117.14 KB
2016_ccs_potzh_elm.pdf	2421 days	96.75 KB
2016_ccs_potzh_elm_en.pdf	2048 days	100.7 KB
2016_ccs_potzh_gyak.pdf	2421 days	82.16 KB
2016_ccs_potzh_gyak_en.pdf	2048 days	84.95 KB
2017a_ccs_potzh.pdf	2421 days	139.12 KB
2017b_ccs_potpotzh .pdf	2421 days	117.83 KB
2017b_ccs_potzh.pdf	2421 days	85.86 KB
2018_ccs_potzh_elm.pdf	2403 days	91.27 KB
2018_ccs_potzh_gyak.pdf	2403 days	109.1 KB

Computer controlled systems (2018)

Lecture notes of the seminar

ccs_gyak02.pdf	2369 days	396.26 KB
ccs_hf3.pdf	2073 days	271.82 KB
Homeworks
hw_1_2018.pdf	2421 days	184.01 KB
hw_1_2018_sol_VM.pdf	2421 days	151 KB
hw_2_2018.pdf	2421 days	203.32 KB
hw_2_2018_sol_VM.pdf	2421 days	143.9 KB
hw_3_2018.pdf	2421 days	200.6 KB
hw_4_2018.pdf	2420 days	192.44 KB
hw_x_2018.pdf	2421 days	232.88 KB
hw_x_2018_extended_deadline.pdf	2421 days	232.88 KB
Matlab packages for TP students
lab_02_2018_TP_2018_09_18.zip	1713 days	323.69 KB
lab_02_2018_TP_exercises_for_Matlab_practice.pdf	2421 days	347.61 KB
lab_08_2018_TP_2018_11_06.zip	1713 days	1.75 MB
Lecture slides
lec_01_2018.pdf	2421 days	4.53 MB
lec_02_2018.pdf	2421 days	463.09 KB
lec_03_2018.pdf	2421 days	906.03 KB
lec_04_2018.pdf	2421 days	405.57 KB
lec_05_2018.pdf	2421 days	1017.58 KB
lec_06_2018.pdf	2421 days	991.21 KB
lec_07_2018.pdf	2421 days	1.63 MB
lec_08_2018.pdf	2421 days	1.09 MB
lec_09_2018.pdf	2421 days	1.03 MB
Seminars
sem_01_2018.pdf	2421 days	444.77 KB
sem_02_2018.pdf	2421 days	386.85 KB
sem_03_2018.pdf	2421 days	441.7 KB
sem_04_2018.pdf	2421 days	540.02 KB
sem_05_2018.pdf	2421 days	459.25 KB
sem_06_2018.pdf	2421 days	399.38 KB
sem_08_2018_matlab1.pdf	2421 days	311.63 KB
sem_09_2018.pdf	2420 days	210.95 KB
sem_10_2018_matlab2.pdf	2421 days	493.54 KB
sem_11_2018.pdf	2415 days	234.97 KB
Extra material and tutorial
xtra_material_Convex_optimization.pdf	2421 days	370.89 KB
xtra_material_DC_motor_model.pdf	2421 days	302.86 KB
xtra_material_Dissipativity_L2gain_LTI_LPV.pdf	2421 days	316.85 KB
xtra_material_Dissipativity_L2gain_LTI_LPV_dark.pdf	2421 days	3.02 MB
xtra_material_Laplace_table.pdf	2421 days	98.74 KB
xtra_material_lqservo.pdf	2421 days	30.01 KB
Model descriptions
xtra_model_crane.pdf	2421 days	217.4 KB
xtra_model_double_crane.pdf	2421 days	318.02 KB
xtra_model_gantry_crane_Ospina_Henao.pdf	2421 days	686.56 KB

Extra material

Former midterm examples
2014_ccs_1zh_A_feladatsor.pdf	2421 days	213.5 KB
2014_ccs_1zh_B_feladatsor.pdf	2421 days	201.93 KB
2015_ccs_1zh_elm.pdf	2421 days	111.9 KB
2015_ccs_1zh_gyak_MO.pdf	2421 days	124.17 KB
2015_ccs_2zh_elm.pdf	2421 days	104.75 KB
2015_ccs_2zh_gyak_MO.pdf	2421 days	114.2 KB
2015_ccs_gyakorlo_zh.pdf	2421 days	104.09 KB
2016_ccs_1zh_elm.pdf	2421 days	97.13 KB
2016_ccs_1zh_gyak.pdf	2421 days	84.4 KB
2016_ccs_2zh_elm.pdf	2421 days	83.64 KB
2016_ccs_2zh_gyak.pdf	2421 days	103.98 KB
2017a_ccs_1zh_computational.pdf	2421 days	87.01 KB
2017a_ccs_1zh_theoretical.pdf	2421 days	111.83 KB
2017a_ccs_2zh_elm.pdf	2421 days	104.28 KB
2017a_ccs_2zh_gyak.pdf	2421 days	131.4 KB
2017b_ccs_1zh_elm.pdf	2421 days	76.62 KB
2017b_ccs_1zh_elm_SOL.pdf	2421 days	136.01 KB
2017b_ccs_1zh_gyak.pdf	2421 days	90.72 KB
2017b_ccs_2zh.pdf	2421 days	162.78 KB
2017b_ccs_2zh_elm.pdf	2421 days	62.41 KB
2017b_ccs_2zh_gyak.pdf	2421 days	87.26 KB
2018_ccs_zh1_elm.pdf	2459 days	104.3 KB
2018_ccs_zh1_gyak.pdf	2459 days	107.2 KB
2018_ccs_zh2_elm.pdf	2417 days	90.57 KB
2018_ccs_zh2_gyak.pdf	2417 days	163.59 KB
2019_ccs_zh1_elm.pdf	2094 days	108.05 KB
2019_ccs_zh1_gyak.pdf	2097 days	112.16 KB
2019_ccs_zh1_gyak_MO.pdf	2095 days	175.28 KB
2019_ccs_zh1_gyak_TG.pdf	2093 days	122.07 KB
2019_ccs_zh1_gyak_TG_MO.pdf	2097 days	124.27 KB
Additional material
kawski_Lyapunov1.pdf	2421 days	481.87 KB
kawski_Lyapunov2.pdf	2421 days	262.33 KB

TP Seminar 1. (2018-09-11)

Basic linear algebra, Labplace transformation, solution of ODEs with Laplace transformation.

TP Seminar 2. (2018-09-18), Matlab practice

Sources:

List of exercises for Matlab practice: ccs_lec02_TP_exercises_for_Matlab_practice.pdf
Package for Matlab practice: ccs_lec2_TP_2018_09_18.zip
Package after the Matlab practice (what we have done): ccs_lec2_TP_2018_09_18_after.zip

Solved Matlab exercises:

Important built-in linear algebra functions:

Q = orth(A) - Gives an orthonormal basis of the image space of a matrix
Z = null(A) - Returns an orthonormal basis for the null space of matrix A. W = null(V') returns an orthonormal basis of the orthogonal complement of subspace V spanned by the column vectors collected in matrix V
[U,S,V] = svd(A) - Singluar value decomposition of matrix A (see also Fundamental theorem of linear algebra)
k = rank(A,) - Rank of matrix A
[R,p] = rref(A) - Reduced row echelon form (Gauss-Jordan elimination). p gives the indices of the first k nr of linearly independent rows of matrix A, where k = rank(A)
[r,p,k] = residue(b,a); [b,a] = residue(r,p,k) - Partial fractional decomposition (numerical)
poly - Polynomial with specified roots or characteristic polynomial
polyval - Polynomial evaluation
roots - Polynomial roots
w = conv(u,v) - Convolution and polynomial multiplication
[q,r] = deconv(u,v) - Deconvolution and polynomial division

TP Seminar 3. (2018-09-25), Convex optimization

Convex optimization, primal-dual problem, introductio to LMIs.

Handwritten lecture notes: dark, original

TP Seminar 4. (2018-10-02)

System inversion of minimum phase SISO systems

TP Seminar 5. (2018-10-09)

Observability, controllability, model transformation into/from different model representations. Controllability staircase form.

TP Seminar 6. (2018-10-16), Dissipativity, stability

Dissipativity, stability, estimating induced $\mathcal L_2$ operator gain for LTI and affine LPV systems.

Handwritten lecture notes: dark, original

TP Seminar 8. (2018-11-06), Controllability and observability with LMIs

Tasks:

Compute controllability and observability staircase form for LTI systems and check their stabilisability and detectability.
Check stabilisability and detectability of LTI and affine LPV systems with LMIs (and design state feedback gain K and observer gain L).
Estimate the induced L2 operator norm of LTI and affine LPV systems using LMIs.
Design an optimal state feedback gain for LIT and affine LPV systems that minimizes the induced L2 operator norm.

Package for Matlab practice: lab_08_2018_TP_2018_11_06.zip

Things to do:

Extract the zip file.
Run Matlab in the root folder (ccs_lec8_2018_11_06) of the zip file, or navigate to the given directory in Matlab and run the startup script.
To test your environment run yalmiptest.

Published Matlab scripts:

Published Matlab scripts

Manipulations with Matlab's Symbolic Math Toolbox: d2017_09_14_gyak1. Basic symbolic routines, Laplace transformation, inverse Laplace transformation, partial fractional decomposition.
State-space transformations: d2017_09_19_gyak2.
Dynamic systems simulations:
- d2017_09_20_Rossler_attractor
- d2017_09_20_Lorentz_system
- d2017_09_20_brussellator
- d2017_09_21_ccs_gyak2_eloben
- Approximate solution of the heat equation with ode45 by considering the discretization along the spacial coordinate. (See also: solution using pdepe.)
- Example for a discrete-time dynamical system: d2018_01_20_ex1_sim
Analysis in frequency/operator domain
- d2017_09_27_gyak3_freqdom
- d2017_09_28_gyak3_eloben
- d2017_10_25_gyak6_PID_live
- Advanced frequency domain analysis: minimum_phase_systems.
- System inversion of minimum phase SISO systems.
Controllability, observability, subspaces: d2017_10_02_gyak4_subspaces.
Geometrical meaning, staircase forms: d2017_10_04_gyak4_ctrb_obsb_geometrical_meaning.
Fundamental theorem of the linear argebra, demonstration: d2017_10_05_gyak4_basicthm_LA.
Lyapunov function demonstration for a non-proper Lyapunov function (Hamiltonian system): d2017_10_11_gyak5_Lyapunov_improper.
Lyapunov function demonstration for the pendulum system: d2017_10_11_gyak5_Lyapunov_pendulum_plain_vid
Matlab solutions of homeworks (2017 fall)
- Homework #1
- Homework #2

Control systems demonstrations

Inverted pendulum model (inverz inga modell)

Model description and derivation using calculus of variations: coming spoon.

Model linearization around stable and unstable equilibrium point, simulation and analysis.

Framework for the first Matlab practice

Model description and task sheet for the first Matlab practice: ccs_gyak08_matlabgyak1.pdf

Framework for the second Matlab practice

Model description and task sheet for the first Matlab practice: ccs_gyak08_matlabgyak2.pdf

Inverted pendulum control and integral reference tracking.

Inverted pendulum control and integral reference tracking (augmented, corrected).

Inverted pendulum nonlinear control - 2018.07.30. (július 30, hétfő), 11:02

Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (Symbolic Math Toolbox) and pole placement

Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (with uncertain frictional coefficient) - feedback design for LPV with LMIs

Crane model (rakodó daru modellje)

Model description and derivation using calculus of variations (ccs_model_crane.pdf)

State space model derivation using symbolic computations

Simulink model and simulation (without control): sim_nonlinear_model_demo

Computer controlled systems (2017 fall)

Eredmények

Events (midterms)

October 19th - 1st midterm
December 7th - 2nd midterm

Lecture notes of the seminar

Midterm sample test sheets for the 2nd midterm
2015_ccs_2zh_elm.pdf	2421 days	104.75 KB
2015_ccs_2zh_gyak_MO.pdf	2421 days	114.2 KB
2015_ccs_gyakorlo_zh.pdf	2421 days	104.09 KB
2015_ccs_potzh_gyak_MO.pdf	2421 days	117.14 KB
2016_ccs_2zh_elm.pdf	2421 days	83.64 KB
2016_ccs_2zh_gyak.pdf	2421 days	103.98 KB
2017_ccs_2zh_elm.pdf	2421 days	104.28 KB
2017_ccs_2zh_gyak.pdf	2421 days	131.4 KB
Lecture notes
ccs_gyak01.pdf	2421 days	311.19 KB
ccs_gyak02.pdf	2421 days	407.6 KB
ccs_gyak02_eng.pdf	2421 days	261.36 KB
ccs_gyak03.pdf	2421 days	441.73 KB
ccs_gyak04.pdf	2421 days	539.06 KB
ccs_gyak05.pdf	2421 days	459.68 KB
ccs_gyak06.pdf	2421 days	399.69 KB
ccs_gyak07.pdf	2421 days	260.77 KB
ccs_gyak08_matlabgyak1.pdf	2421 days	184.64 KB
ccs_gyak09.pdf	2421 days	150.44 KB
ccs_gyak10_matlabgyak2.pdf	2421 days	390.06 KB
ccs_gyak11.pdf	2421 days	181.51 KB
ccs_gyakorlo.pdf	2421 days	114.22 KB
Homework exercises
ccs_hf1.pdf	2421 days	351.62 KB
ccs_hf1_mo.pdf	2421 days	371 KB
ccs_hf2.pdf	2421 days	239.88 KB
ccs_hf2_mo.pdf	2421 days	289.16 KB
ccs_hf3 másolata.pdf	2421 days	224.15 KB
ccs_hf3.pdf	2421 days	224.15 KB
ccs_hf3_mo.pdf	2421 days	231.13 KB
ccs_hf4.pdf	2421 days	94.95 KB
ccs_lec01.pdf	2421 days	445.89 KB
ccs_lec02.pdf	2421 days	263.84 KB
ccs_lec02_v2.pdf	2421 days	261.76 KB
Model descriptions
ccs_model_crane.pdf	2421 days	217.4 KB
ccs_model_double_crane.pdf	2421 days	318.02 KB
ccs_model_gantry_crane_Ospina_Henao.pdf	2421 days	686.56 KB
ccs_segedlet_Matrixok.pdf	2421 days	141.88 KB
Extra material and tutorial
segedlet_Laplace_table.pdf	2421 days	98.74 KB
segedlet_szorgalmi_lqservo.pdf	2421 days	30.01 KB
midterm seating
zh1_beosztas.pdf	2421 days	44.72 KB
zh2_beosztas.pdf	2421 days	44.71 KB

Computer controlled systems (2017 spring)

week. Preliminaries

week. Laplace transformation

gyak2_Laplace

week. System representations

Matlab script (system representation, transfer between representations, Bode diagram, controllability, observability): gyak3_sysrep_ctrb_obsb

week. Controllability, observability

gyak4_ctrb_obsb_geometrical_meaning

week. BIBO and Lyapunov stability

gyak5_BIBO

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Tartalomjegyzék

Computer controlled systems (2019)

Lecture notes of the seminar

Seminar 1. - Laplace transformation, non-dimensional ODEs

Output:

Output:

Output:

Seminar 3. - System representations

Output:

Output:

Output:

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Output:

Output:

Seminar 4. - Controllability, observability

Output:

Output:

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Published Matlab scripts

Control systems demonstrations

Recommended literature

Additionally:

Extra material for the midterm tests

Extra material for the supplementary midterm

Computer controlled systems (2018)

Lecture notes of the seminar

Extra material

TP Seminar 1. (2018-09-11)

TP Seminar 2. (2018-09-18), Matlab practice

TP Seminar 3. (2018-09-25), Convex optimization

TP Seminar 4. (2018-10-02)

TP Seminar 5. (2018-10-09)

TP Seminar 6. (2018-10-16), Dissipativity, stability

TP Seminar 8. (2018-11-06), Controllability and observability with LMIs

Published Matlab scripts

Control systems demonstrations

Computer controlled systems (2017 fall)

Events (midterms)

Lecture notes of the seminar

Computer controlled systems (2017 spring)

week. Preliminaries

week. Laplace transformation

week. System representations

week. Controllability, observability

week. BIBO and Lyapunov stability