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Polcz Péter honlapja

‹ › ×

Tartalomjegyzék

Computer controlled systems (2020)

Control Tutorials for Matlab & Simulink (University of Michigan)

Lecture notes of the seminar

CCS_requirements_2020_eng.pdf	1894 days	52.04 KB
CCS_schedule_2020 _eng.pdf	1892 days	36.97 KB
Seminars
sem_01_2020-09-11_online.pdf	1890 days	106.44 KB
sem_01_2020.pdf	1523 days	499.69 KB
sem_02_2020.pdf	1890 days	457.08 KB
sem_03_2020.pdf	1885 days	493.23 KB
sem_04_2020.pdf	1827 days	599.05 KB
sem_05_2020.pdf	1862 days	474.71 KB
sem_05_2020_handwritten.pdf	1862 days	224.53 KB
sem_06_2020.pdf	1827 days	401.46 KB
sem_08_2020_matlab1.pdf	2191 days	311.2 KB
sem_09_2020.pdf	1826 days	320.24 KB
Illustrative Matlab simulations
sim_04_waterfall.zip	1831 days	3.08 KB
Extra material and tutorial
xtra_material_convopt_MIT.pdf	1869 days	464.7 KB
xtra_material_convopt_Stanford.pdf	1869 days	5 MB
xtra_material_convopt_damtp.pdf	1869 days	180.81 KB
xtra_material_convopt_handwritten_notes_2018.pdf	2539 days	370.89 KB
xtra_material_lqservo.pdf	2539 days	30.01 KB

Seminar 1. - Laplace transformation, non-dimensional ODEs

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

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:
$h(t) = \frac{2\sqrt{3}{e}^{-\frac{t}{2}}\sin(\frac{\sqrt{3}t}{2})}{3}$

vanderpol_simulation vanderpol_DOA

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Tartalomjegyzék

Computer controlled systems (2020)

Lecture notes of the seminar

Seminar 1. - Laplace transformation, non-dimensional ODEs

Output:

Output:

Output: