Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Trusses<br />
Trusses consist of straight members (‘bars’) connected at jo<strong>in</strong>ts.<br />
One dist<strong>in</strong>guishes free and fixed jo<strong>in</strong>ts.<br />
Connections at the jo<strong>in</strong>ts can rotate.<br />
The loads (or the weights) are assumed to be applied at the free<br />
jo<strong>in</strong>ts.<br />
This implies that all <strong>in</strong>ternal forces are directed along the members,<br />
(so no bend<strong>in</strong>g forces occur).<br />
Construction reacts based on pr<strong>in</strong>ciple of statics: the sum of the<br />
forces <strong>in</strong> any direction, or the moments of the forces about any jo<strong>in</strong>t,<br />
are zero.<br />
This results <strong>in</strong> a displacement of the jo<strong>in</strong>ts and a new tension<br />
distribution <strong>in</strong> the truss.<br />
Many applications (roofs, cranes, bridges, space structures, . . . ) !!<br />
Design your own bridge<br />
Siep Weiland and Carsten Scherer (DISC) <strong>L<strong>in</strong>ear</strong> <strong>Matrix</strong> <strong>Inequalities</strong> <strong>in</strong> <strong>Control</strong> Class 1 52 / 59
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