sim and newlin State transition is faster than ODE solvers for LTI systems Large time step stability is guaranteed Discretization is slow for large order systems(e.g. SIM v2. 2 has 2184 state variables) Block diagonal a matrix allows fast discretization Memory is not enough for the big state matrix required by Ititr (14Gb for SIM simulation) Subsystem simulations are less memory consuming State transition cost goes with O(n 2), even worse for large-order ystems Lsim. m does not recognize special structure(e.g. sparse matrix) Simulink discrete state space(DSS)solver exploits matrices sparsity (i.e. O(n)cost) Multiple sampling rates trade efficiency with accuracy However newlsim must first diagonalize the a matrix Newlsim flowchart x Original System(ABCD) Diagonalization md n modal system↓ Subsystem seg_plan_xm subsystems PI anner subsystem bandwidth build- multirate sys.m Discretization Downsampling:Original Input DT LTI downsampled input DT subsystems ] System Solver st_sim.m process subsystem responses Interpolation interp. m Superposition mfiles Final responseLsim and Newlsim • State transition is faster than ODE solvers for LTI systems. • Large time step stability is guaranteed. • Discretization is slow for large order systems (e.g. SIM v2.2 has 2184 state variables). • Memory is not enough for the big state matrix required by ltitr (14Gb for SIM simulation). • State transition cost goes with O(ns 2), even worse for large-order systems. • Lsim.m does not recognize special structure (e.g. sparse matrix). • Block diagonal A matrix allows fast discretization. • Subsystem simulations are less memory consuming. • Simulink discrete state space (DSS) solver exploits matrices sparsity (i.e.O(ns) cost). • Multiple sampling rates trade efficiency with accuracy. • However, newlsim must first diagonalize the A matrix. Newlsim Flowchart Diagonalization Subsystem Planner Discretization Downsampling DT LTI System Solver Interpolation Superposition Original System (ABCD) Final Response md.m seg_plan_x.m build_multirate_sys.m st_sim.m interp.m Original Input 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 nz = 292 modal system subsystems subsystem bandwidth DT subsystems downsampled input 0 50 100 150 200 250 -25 -20 -15 -10 -5 0 5 10 15 20 25 subsystem responses 0 50 100 150 200 250 -0.5 0 0.5 1 1.5 2 2.5 3 x 10 data -7 process mfiles original