Question

A colleague gave you a Simulink model (figure 5) for a non-linear mass-spring-damper system but forgot to provide yo u with the corresponding equation. (i) Find the non-linear equation of the mass-spring-damper system (ii) Find the equilibrium position (iii Find the Jacobian (linearise the equation about ts equilibrium) (iv) Comment on the stability of the system. (v) Plot the response of the linearised and non-linear model. What is the difference in mag of the non-linear equation. nitude between the linear and non-linear response of at t 4 Initial condition: 0 nitial condition: 1 0.5 0.5 2 c1 C4 с5 2 c2 Figure 5: The Simulink model for question 6

Answer 1

tom tee simulim k mo dul we cau sec So s o fr

for tindg equlbriun pout podrt so S o -O utibriun poes Cii) o-f2 2 atco-o)

-20.5 As this an auto nenor 50 24 2- +2 λ+0.5 杠-A)-。 Both egn valun have wytie real pant tHonee the sylem ts stable (V). Non lineaun 七

The simulations are given as follows

Nonlinear

1 0.5 2 Non linear

Non linear plot

NON LINEAR PLOT 0.4 18 20 Ofiset

Linear

Linear -2

Linear plot

INEAR PLOT 18 20 Ofiset

Linear and non linear plot comparison

LINEAR PLOT BLUE NON LINEAR PLOT YELLOW 18 20

Difference at 4 sec is 0.8.