Transmitancja operatorowa obiektu:

$$G\left( s \right) = \frac{1}{\left( sT_{1} + 1 \right)\left( sT_{2} + 1 \right)(sT_{3} + 1)}$$

$$T_{1} = \frac{\text{Li}}{\text{Ln}} = \ \frac{6}{5} = 1,2$$

$$T_{2} = \frac{\text{Li}}{10} = \ \frac{6}{10} = 0,6$$

$$T_{3} = \frac{\text{Li} + \text{Ln}}{\text{Li}*\text{Ln}} = \ \frac{6 + 5}{6*5} = \ \frac{11}{30} = 0,36$$

:

$$Y\left( s \right) = \ \frac{1}{s\left( 1,2s + 1 \right)\left( 0,6s + 1 \right)\left( 0,36s + 1 \right)}$$

N{Y(s)} = 1

D{Y(s)} = s(1,2s+1)(0,6s+1)(0,36s+1) = (1,2s²+s)(0,216s²+0,96s+1) = 0, 264s⁴ + 1, 16s³ + 1, 2s² + 0, 22s³ + 0, 966s² + s=0, 264 + 1, 38s³ + 2, 166s² + s

D{Y(s)} = 0, 264s⁴ + 1, 38s³ + 2, 166s² + s

$$Y\left( s \right) = \frac{A}{s} + \frac{B}{s + 0,833} + \frac{C}{s + 1,666} + \frac{D}{s + 2,7272}$$

D^′{Y(s)}=1, 056s³ + 4, 14s² + 4, 333s + 1

$$\mathbf{A} = \frac{N(s)}{D^{'}(s)}|_{0} = \frac{1}{1,056s^{3} + 4,14s^{2} + 4,333s + 1}|_{0} = \frac{1}{1} = 1$$

$$\mathbf{B} = \frac{N\left( s \right)}{D^{'}\left( s \right)}|_{- 0,833} = \frac{1}{1,056s^{3} + 4,14s^{2} + 4,333s + 1}|_{- 0,833} = \frac{1}{- 0,3445} = - 2,88$$

$\mathbf{C} = \frac{N\left( s \right)}{D^{'}\left( s \right)}|_{- 1,666} = \frac{1}{1,056s^{3} + 4,14s^{2} + 4,333s + 1}|_{- 1,666} = \frac{1}{0,3889} =$2,57069

$$\mathbf{D} = \frac{N(s)}{D^{'}(s)}|_{- 2,7272} = \frac{1}{1,056s^{3} + 4,14s^{2} + 4,333s + 1}|_{- 2,7272} = \frac{1}{- 1,4449} = - 0,69204$$

y(t) = 1 − 2, 88e^−0, 833t + 2, 57069e^−1, 666t − 0, 69204e^{−2, 7272t}