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Polcz Péter honlapja

Tartalomjegyzék

Computer controlled systems (2019)

Official website of the course

Lecture notes of the seminar

Homeworks
hw_1_2019.pdf2037 days40.3 KB
hw_2_2019.pdf2027 days36.77 KB
hw_3_2019.pdf2012 days189.57 KB
Lecture slides
lec_01_2019.pdf2053 days4.92 MB
lec_02_2019.pdf2047 days461.3 KB
lec_03_2019.pdf2034 days905.26 KB
lec_04_2019.pdf2032 days401.72 KB
lec_05_2019.pdf2026 days1009.69 KB
lec_06_2019.pdf2018 days1.3 MB
lec_07_2019.pdf2011 days1.63 MB
lec_08_2019.pdf1997 days1.09 MB
lec_09_2019.pdf1990 days1.03 MB
Seminars (1st midterm)
sem_01_2019.pdf2040 days114.78 KB
sem_02_2019.pdf2052 days107.51 KB
sem_03_2019.pdf2038 days141.71 KB
sem_04_2019.pdf2038 days340.58 KB
sem_05_2019.pdf2027 days252.81 KB
Seminars (2nd midterm)
sem_06_2019.pdf1996 days347.98 KB
sem_06_2019_TP_matlab.zip1630 days28.71 KB
sem_08_2019_matlab1.pdf1989 days311.2 KB
sem_08_2019_matlab1.zip1630 days4.26 KB
sem_08_2019_matlab1_sol.zip1630 days4.44 KB
sem_09_2019.pdf2012 days209.94 KB
sem_10_2019_matlab2.pdf1989 days493.63 KB
sem_10_2019_matlab2.zip1630 days3.14 KB
Extra homeworks (not compulsary)
xtra_hw_dynamical_system_simulations.pdf1989 days173.68 KB
xtra_hw_linear_algebra.pdf1989 days337.11 KB
Extra material and tutorial
xtra_material_Convex_optimization.pdf2337 days370.89 KB
xtra_material_DC_motor_model.pdf2337 days302.86 KB
xtra_material_Dissipativity_L2gain_LTI_LPV.pdf2337 days316.85 KB
xtra_material_Dissipativity_L2gain_LTI_LPV_dark.pdf2337 days3.02 MB
xtra_material_Laplace_table.pdf2337 days98.74 KB
xtra_material_lqservo.pdf2337 days30.01 KB
Model descriptions
xtra_model_crane.pdf1989 days217.07 KB
xtra_model_double_crane.pdf2337 days318.02 KB
xtra_model_gantry_crane_Ospina_Henao.pdf2337 days686.56 KB
midterm seating
zh1_seating.pdf2017 days28.51 KB
zh2_seating.pdf2017 days26.85 KB

Important built-in linear algebra functions:

Important functions of Matlab's Symbolic Math Toolbox (SMT):

Important function of the Control System Toolbox:

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

  1. Compute a polynomial division (see lecture notes nr. 3).
  2. 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))
    $H(s) = \frac{3}{2(s+1)}-\frac{15}{s+2}+\frac{37}{2(s+3)}$

  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)
    $H(s) = \frac{a}{a^2+t^2}+\frac{t}{a^2+t^2}+\frac{c+t}{{(c+t)}^2+b^2}+\frac{e}{{(f+t)}^2+e^2}$

  4. 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

  1. 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

  2. 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

  1. 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

  1. Manipulations with Matlab's Symbolic Math Toolbox: d2017_09_14_gyak1. Basic symbolic routines, Laplace transformation, inverse Laplace transformation, partial fractional decomposition.
  2. State-space transformations: d2017_09_19_gyak2.
    Dynamic systems simulations:
  3. Analysis in frequency/operator domain
  4. 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.
  5. 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
  6. Matlab solutions of former homeworks (2017 fall)

Control systems demonstrations

Inverted pendulum model (inverz inga modell)
  1. Model description and task sheet for the first Matlab practice: sem_08_2019_matlab1.pdf
  2. Framework for the first Matlab practice
  3. Model description and task sheet for the first Matlab practice: sem_10_2019_matlab2.pdf
  4. Framework for the second Matlab practice
  5. Model linearization around stable and unstable equilibrium point, simulation and analysis.
  6. Inverted pendulum control and integral reference tracking.
  7. Inverted pendulum control and integral reference tracking (augmented, corrected).
  8. Inverted pendulum nonlinear control - 2018.07.30. (július 30, hétfő), 11:02
  9. Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (Symbolic Math Toolbox) and pole placement
  10. Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (with uncertain frictional coefficient) - feedback design for LPV with LMIs
Crane model (rakodó daru modellje)
  1. Model description and derivation using calculus of variations (ccs_model_crane.pdf)
  2. State space model derivation using symbolic computations
  3. Simulink model and simulation (without control): sim_nonlinear_model_demo

Recommended literature

Additionally:
Andrew_Lewis_A_Mathematical_Approach_to_Classical_Control.pdf2337 days9.32 MB
Scherer.Weiland_2000_Linear_Matrix_Inequalities_in_Control.pdf2337 days1.25 MB
The_Fundamental_Theorem_of_Linear_Algebra.pdf2337 days330.57 KB

Extra material for the midterm tests

Former midterm examples
2014_ccs_1zh_A_feladatsor.pdf2337 days213.5 KB
2014_ccs_1zh_B_feladatsor.pdf2337 days201.93 KB
2015_ccs_1zh_elm.pdf2337 days111.9 KB
2015_ccs_1zh_gyak_MO.pdf2337 days124.17 KB
2015_ccs_2zh_elm.pdf2337 days104.75 KB
2015_ccs_2zh_gyak_MO.pdf2337 days114.2 KB
2015_ccs_gyakorlo_zh.pdf2337 days104.09 KB
2016_ccs_1zh_elm.pdf2337 days97.13 KB
2016_ccs_1zh_gyak.pdf2337 days84.4 KB
2016_ccs_2zh_elm.pdf2337 days83.64 KB
2016_ccs_2zh_gyak.pdf2337 days103.98 KB
2017a_ccs_1zh_computational.pdf2337 days87.01 KB
2017a_ccs_1zh_theoretical.pdf2337 days111.83 KB
2017a_ccs_2zh_elm.pdf2337 days104.28 KB
2017a_ccs_2zh_gyak.pdf2337 days131.4 KB
2017b_ccs_1zh_elm.pdf2337 days76.62 KB
2017b_ccs_1zh_elm_SOL.pdf2337 days136.01 KB
2017b_ccs_1zh_gyak.pdf2337 days90.72 KB
2017b_ccs_2zh.pdf2337 days162.78 KB
2017b_ccs_2zh_elm.pdf2337 days62.41 KB
2017b_ccs_2zh_gyak.pdf2337 days87.26 KB
2018_ccs_zh1_elm.pdf2376 days104.3 KB
2018_ccs_zh1_gyak.pdf2376 days107.2 KB
2018_ccs_zh2_elm.pdf2333 days90.57 KB
2018_ccs_zh2_gyak.pdf2333 days163.59 KB
2019_ccs_zh1_elm.pdf2011 days108.05 KB
2019_ccs_zh1_gyak.pdf2014 days112.16 KB
2019_ccs_zh1_gyak_MO.pdf2012 days175.28 KB
2019_ccs_zh1_gyak_TG.pdf2010 days122.07 KB
2019_ccs_zh1_gyak_TG_MO.pdf2014 days124.27 KB
Additional material
kawski_Lyapunov1.pdf2337 days481.87 KB
kawski_Lyapunov2.pdf2337 days262.33 KB

Extra material for the supplementary midterm

2015_ccs_potzh_elm.pdf2337 days101.32 KB
2015_ccs_potzh_gyak_MO.pdf2337 days117.14 KB
2016_ccs_potzh_elm.pdf2337 days96.75 KB
2016_ccs_potzh_elm_en.pdf1964 days100.7 KB
2016_ccs_potzh_gyak.pdf2337 days82.16 KB
2016_ccs_potzh_gyak_en.pdf1964 days84.95 KB
2017a_ccs_potzh.pdf2337 days139.12 KB
2017b_ccs_potpotzh .pdf2337 days117.83 KB
2017b_ccs_potzh.pdf2337 days85.86 KB
2018_ccs_potzh_elm.pdf2319 days91.27 KB
2018_ccs_potzh_gyak.pdf2320 days109.1 KB

Computer controlled systems (2018)

Lecture notes of the seminar

ccs_gyak02.pdf2285 days396.26 KB
ccs_hf3.pdf1989 days271.82 KB
Homeworks
hw_1_2018.pdf2337 days184.01 KB
hw_1_2018_sol_VM.pdf2337 days151 KB
hw_2_2018.pdf2337 days203.32 KB
hw_2_2018_sol_VM.pdf2337 days143.9 KB
hw_3_2018.pdf2337 days200.6 KB
hw_4_2018.pdf2336 days192.44 KB
hw_x_2018.pdf2337 days232.88 KB
hw_x_2018_extended_deadline.pdf2337 days232.88 KB
Matlab packages for TP students
lab_02_2018_TP_2018_09_18.zip1630 days323.69 KB
lab_02_2018_TP_exercises_for_Matlab_practice.pdf2337 days347.61 KB
lab_08_2018_TP_2018_11_06.zip1630 days1.75 MB
Lecture slides
lec_01_2018.pdf2337 days4.53 MB
lec_02_2018.pdf2337 days463.09 KB
lec_03_2018.pdf2337 days906.03 KB
lec_04_2018.pdf2337 days405.57 KB
lec_05_2018.pdf2337 days1017.58 KB
lec_06_2018.pdf2337 days991.21 KB
lec_07_2018.pdf2337 days1.63 MB
lec_08_2018.pdf2337 days1.09 MB
lec_09_2018.pdf2337 days1.03 MB
Seminars
sem_01_2018.pdf2337 days444.77 KB
sem_02_2018.pdf2337 days386.85 KB
sem_03_2018.pdf2337 days441.7 KB
sem_04_2018.pdf2337 days540.02 KB
sem_05_2018.pdf2337 days459.25 KB
sem_06_2018.pdf2337 days399.38 KB
sem_08_2018_matlab1.pdf2337 days311.63 KB
sem_09_2018.pdf2337 days210.95 KB
sem_10_2018_matlab2.pdf2337 days493.54 KB
sem_11_2018.pdf2331 days234.97 KB
Extra material and tutorial
xtra_material_Convex_optimization.pdf2337 days370.89 KB
xtra_material_DC_motor_model.pdf2337 days302.86 KB
xtra_material_Dissipativity_L2gain_LTI_LPV.pdf2337 days316.85 KB
xtra_material_Dissipativity_L2gain_LTI_LPV_dark.pdf2337 days3.02 MB
xtra_material_Laplace_table.pdf2337 days98.74 KB
xtra_material_lqservo.pdf2337 days30.01 KB
Model descriptions
xtra_model_crane.pdf2337 days217.4 KB
xtra_model_double_crane.pdf2337 days318.02 KB
xtra_model_gantry_crane_Ospina_Henao.pdf2337 days686.56 KB

Extra material

Former midterm examples
2014_ccs_1zh_A_feladatsor.pdf2337 days213.5 KB
2014_ccs_1zh_B_feladatsor.pdf2337 days201.93 KB
2015_ccs_1zh_elm.pdf2337 days111.9 KB
2015_ccs_1zh_gyak_MO.pdf2337 days124.17 KB
2015_ccs_2zh_elm.pdf2337 days104.75 KB
2015_ccs_2zh_gyak_MO.pdf2337 days114.2 KB
2015_ccs_gyakorlo_zh.pdf2337 days104.09 KB
2016_ccs_1zh_elm.pdf2337 days97.13 KB
2016_ccs_1zh_gyak.pdf2337 days84.4 KB
2016_ccs_2zh_elm.pdf2337 days83.64 KB
2016_ccs_2zh_gyak.pdf2337 days103.98 KB
2017a_ccs_1zh_computational.pdf2337 days87.01 KB
2017a_ccs_1zh_theoretical.pdf2337 days111.83 KB
2017a_ccs_2zh_elm.pdf2337 days104.28 KB
2017a_ccs_2zh_gyak.pdf2337 days131.4 KB
2017b_ccs_1zh_elm.pdf2337 days76.62 KB
2017b_ccs_1zh_elm_SOL.pdf2337 days136.01 KB
2017b_ccs_1zh_gyak.pdf2337 days90.72 KB
2017b_ccs_2zh.pdf2337 days162.78 KB
2017b_ccs_2zh_elm.pdf2337 days62.41 KB
2017b_ccs_2zh_gyak.pdf2337 days87.26 KB
2018_ccs_zh1_elm.pdf2376 days104.3 KB
2018_ccs_zh1_gyak.pdf2376 days107.2 KB
2018_ccs_zh2_elm.pdf2333 days90.57 KB
2018_ccs_zh2_gyak.pdf2333 days163.59 KB
2019_ccs_zh1_elm.pdf2011 days108.05 KB
2019_ccs_zh1_gyak.pdf2014 days112.16 KB
2019_ccs_zh1_gyak_MO.pdf2012 days175.28 KB
2019_ccs_zh1_gyak_TG.pdf2010 days122.07 KB
2019_ccs_zh1_gyak_TG_MO.pdf2014 days124.27 KB
Additional material
kawski_Lyapunov1.pdf2337 days481.87 KB
kawski_Lyapunov2.pdf2337 days262.33 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:

Solved Matlab exercises:

  1. Basic linear algebra operations
  2. Dynamic systems' simulation in Matlab
  3. Also consider: approximate solution of the heat equation with ode45 by considering the discretization along the spacial coordinate. (See also: solution using pdepe.)

Important built-in linear algebra functions:

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

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

Recommended literature: Scherer.Weiland_2000_Linear_Matrix_Inequalities_in_Control.pdf

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.

Recommended literature: Scherer.Weiland_2000_Linear_Matrix_Inequalities_in_Control.pdf

Handwritten lecture notes: dark, original

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

Tasks:

  1. Compute controllability and observability staircase form for LTI systems and check their stabilisability and detectability.
  2. Check stabilisability and detectability of LTI and affine LPV systems with LMIs (and design state feedback gain K and observer gain L).
  3. Estimate the induced L2 operator norm of LTI and affine LPV systems using LMIs.
  4. 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:

  1. Extract the zip file.
  2. 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.
  3. To test your environment run yalmiptest.

Published Matlab scripts:

  1. Check if stabilisable (Success)
  2. Check if stabilisable (Infeasible)
  3. Affine LPV system computations with LMIs

Published Matlab scripts

  1. Manipulations with Matlab's Symbolic Math Toolbox: d2017_09_14_gyak1. Basic symbolic routines, Laplace transformation, inverse Laplace transformation, partial fractional decomposition.
  2. State-space transformations: d2017_09_19_gyak2.
    Dynamic systems simulations:
  3. Analysis in frequency/operator domain
  4. 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.
  5. 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
  6. Matlab solutions of homeworks (2017 fall)

Control systems demonstrations

Inverted pendulum model (inverz inga modell)
  1. Model description and derivation using calculus of variations: coming spoon.
  2. Model linearization around stable and unstable equilibrium point, simulation and analysis.
  3. Framework for the first Matlab practice
  4. Model description and task sheet for the first Matlab practice: ccs_gyak08_matlabgyak1.pdf
  5. Framework for the second Matlab practice
  6. Model description and task sheet for the first Matlab practice: ccs_gyak08_matlabgyak2.pdf
  7. Inverted pendulum control and integral reference tracking.
  8. Inverted pendulum control and integral reference tracking (augmented, corrected).
  9. Inverted pendulum nonlinear control - 2018.07.30. (július 30, hétfő), 11:02
  10. Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (Symbolic Math Toolbox) and pole placement
  11. Advanced Nonlinear Control Methods (PhD course): Inverted pendulum linearization (with uncertain frictional coefficient) - feedback design for LPV with LMIs
Crane model (rakodó daru modellje)
  1. Model description and derivation using calculus of variations (ccs_model_crane.pdf)
  2. State space model derivation using symbolic computations
  3. Simulink model and simulation (without control): sim_nonlinear_model_demo

Computer controlled systems (2017 fall)

Eredmények

Events (midterms)

Lecture notes of the seminar

Midterm sample test sheets for the 2nd midterm
2015_ccs_2zh_elm.pdf2337 days104.75 KB
2015_ccs_2zh_gyak_MO.pdf2337 days114.2 KB
2015_ccs_gyakorlo_zh.pdf2337 days104.09 KB
2015_ccs_potzh_gyak_MO.pdf2337 days117.14 KB
2016_ccs_2zh_elm.pdf2337 days83.64 KB
2016_ccs_2zh_gyak.pdf2337 days103.98 KB
2017_ccs_2zh_elm.pdf2337 days104.28 KB
2017_ccs_2zh_gyak.pdf2337 days131.4 KB
Lecture notes
ccs_gyak01.pdf2337 days311.19 KB
ccs_gyak02.pdf2337 days407.6 KB
ccs_gyak02_eng.pdf2337 days261.36 KB
ccs_gyak03.pdf2337 days441.73 KB
ccs_gyak04.pdf2337 days539.06 KB
ccs_gyak05.pdf2337 days459.68 KB
ccs_gyak06.pdf2337 days399.69 KB
ccs_gyak07.pdf2337 days260.77 KB
ccs_gyak08_matlabgyak1.pdf2337 days184.64 KB
ccs_gyak09.pdf2337 days150.44 KB
ccs_gyak10_matlabgyak2.pdf2337 days390.06 KB
ccs_gyak11.pdf2337 days181.51 KB
ccs_gyakorlo.pdf2337 days114.22 KB
Homework exercises
ccs_hf1.pdf2337 days351.62 KB
ccs_hf1_mo.pdf2337 days371 KB
ccs_hf2.pdf2337 days239.88 KB
ccs_hf2_mo.pdf2337 days289.16 KB
ccs_hf3 másolata.pdf2337 days224.15 KB
ccs_hf3.pdf2337 days224.15 KB
ccs_hf3_mo.pdf2337 days231.13 KB
ccs_hf4.pdf2337 days94.95 KB
ccs_lec01.pdf2337 days445.89 KB
ccs_lec02.pdf2337 days263.84 KB
ccs_lec02_v2.pdf2337 days261.76 KB
Model descriptions
ccs_model_crane.pdf2337 days217.4 KB
ccs_model_double_crane.pdf2337 days318.02 KB
ccs_model_gantry_crane_Ospina_Henao.pdf2337 days686.56 KB
ccs_segedlet_Matrixok.pdf2337 days141.88 KB
Extra material and tutorial
segedlet_Laplace_table.pdf2337 days98.74 KB
segedlet_szorgalmi_lqservo.pdf2337 days30.01 KB
midterm seating
zh1_beosztas.pdf2337 days44.72 KB
zh2_beosztas.pdf2337 days44.71 KB

Computer controlled systems (2017 spring)

week. Preliminaries

week. Laplace transformation

week. System representations

week. Controllability, observability

week. BIBO and Lyapunov stability