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Unformatted text preview: Tutorial: Limit cycle analysis Answer sheet Dani¨ el Karssen ([email protected]) & Martijn Wisse Exercise 1 Matlab code: par.L = 0.132; par.R = 0.06; par.m = 0.07; par.I = 0.00018; par.B = 0; par.C = 0.061; par.gamma = 0.005; par.g = 9.81; s0 = [0.2; -0.2; -2.5; -2.0]; t0 = 0; [s end, t end, data] = Step(s0, t0, par); plot(data.t,data.s) legend(’phi st’,’phi sw’,’phi st d’,’phi sw d’) xlabel(’time [s]’), ylabel(’angle [rad], angular rate [rad/s]’) Animation(data,par) 0.05 0.1 0.15 0.2 0.25 0.3 0.35-3-2-1 1 2 3 4 time [s] angle [rad], angular rate [rad/s] φ st φ sw φ st d φ sw d Figure 1: A plot of the four state variables during a step Exercise 2 Matlab code: nr steps = 10; [s end, t end, data] = Walk(s0, t0, par, nr steps); 1 Exercise 3 Matlab code: optimset(’TolFun’,1e-10,’TolX’,1e-10,’LargeScale’,’off’); s star = lsqnonlin(@(s) Step(s,0,par)-s,s0,,,options); The state of the limit cycle is: s * = . 1989- . 1989-...
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