L23- Fast Time Domain simulation via decomposition Prof olivier de Weck imulation of lti systems LTI systems are very common in engineering applications and simulating them is of great importance small dynamic urge dynamic Mathematical l0000 range model 5000 ext generatio x(1)=Ax(t)+B() 2000 order Telescope Interest 1000 stems y(1)=Cx(1)+D()500 medium order A∈mB∈囗"m司 切100 stems Middeck Starlight Active origi C∈D∈日p Testbed rder MIT stems 3-mass Problems of interest are I single mdl usually complex oscillator 10 normalized dynamic bandwidth min(o,)L23 – Fast Time Domain Simulation via Decomposition Prof. Olivier de Weck Simulation of LTI Systems large order systems medium order systems small order number of state variables n systems s 10000 5000 2000 1000 500 200 100 50 20 10 5 2 1 normalized dynamic bandwidth max( ) min( ) n n ω ω small dynamic range large dynamic range 0 10 2 10 4 10 6 10 8 10 Next Generation Space Telescope region of interest SIM v2.2 NEXUS Starlight Middeck Active Control Experimen t Origins Testbed (MIT) 3-mass model single DOF oscillator x t Ax t Bu t y t Cx t Du t • = + = + () () () () () () nn nm p n pm A B C D × × × × ∈ ∈ ∈ ∈ ￾ ￾ ￾ ￾ • LTI systems are very common in engineering applications and simulating them is of great importance. Mathematical model: Problems of interest are usually complex!