DPS Blockset Demo String of "smart" structure

The string of "smart" structure deviation by means of piezoceramic actuators is modeled by lumped-input / distrinuted-output system. System dynamics is given by distributed transfer function of oscillating string $S(x, \xi, s)$, corresponding to hyperbolic type partial differential equation and transfer functions of piezoceramic actuators: $SA_{i}(s)$, $SG_{i}(s)$ and $T_{i}(x)$, where $T_{i}(x)$ is shaping unit of i-th distributed input quantity (i=1-4).

Contents

Scheme

Description

S - oscillating string

K - frictionless bedding

$T_{1}$ - exciting smart structure with transfer function $SA_{1}(s)SG_{1}(s)T_{1}(x)$

$T_{2}$ - exciting smart structure with transfer function $SA_{2}(s)SG_{2}(s)T_{2}(x)$

$T_{3}$ - exciting smart structure with transfer function $SA_{3}(s)SG_{3}(s)T_{3}(x)$

$T_{4}$ - exciting smart structure with transfer function $SA_{4}(s)SG_{4}(s)T_{4}(x)$

$U_{1} - U_{4}$ - exciting input voltages

$g_{1},g_{2}$ - boundary conditions

Model

$$\left \{ SA_{i}\left ( s \right ) = \frac{1}{TA_{i}s+1} \right \};
TA_{1} = 2, TA_{2} = 3, TA_{3} = 2, TA_{4} = 3$$

$$\left \{ SG_{i}\left ( s \right ) = \frac{1}{TG_{i}s+1} \right \};
TG_{1} = 4, TG_{2} = 4, TG_{3} = 5, TG_{4} = 3$$

$$S\left ( x,\xi ,s \right
)=\frac{2}{L}\sum_{n=1}^{\infty}\frac{sin\frac{n\pi x}{L}sin\frac{n\pi
\xi }{L}}{s^{2}+2\alpha s+\frac{n^{2}\pi ^{2}a^{2}}{L^{2}}}$$

$$\frac{\partial Y\left ( 0,t \right )}{\partial t} = 0; Y\left ( x,0
\right ) = 0, Y\left ( 0,t \right ) = 0, Y\left ( L,t \right ) = 0, L =
1, a = 0.2, \alpha = 0.05$$

$T_{1}(x)$ - constant shape on the interval [0,0.2]

$T_{2}(x)$ - triangle shape on the interval [0.3,0.5]

$T_{3}(x)$ - sinusoidal shape on the interval [0.6,0.8]

$T_{4}(x)$ - general shape on the interval [0.7,1]

LDS block characteristics

Analysed system response at first actuator voltage $U_{1}$ step change.

Analysed system response at second actuator voltage $U_{2}$ step change.

Analysed system response at third actuator voltage $U_{3}$ step change.

Analysed system response at fourth actuator voltage $U_{4}$ step change.