Quarter Car Suspension Gautam Lageju ME 498/599: Sensitivity Propagation and Uncertainty Quantification

𝒎 𝒃 →𝒎𝒂𝒔𝒔(𝒄𝒂𝒓 𝒃𝒐𝒅𝒚+𝒂𝒅𝒅_𝒘𝒕) 𝒌 𝒔 →𝒔𝒑𝒓𝒊𝒏𝒈 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕(𝒔𝒖𝒔𝒑𝒆𝒏𝒔𝒊𝒐𝒏) 𝒃 𝒔 →𝒅𝒂𝒎𝒑𝒆𝒓 𝒇 𝒔 →𝒂𝒄𝒕𝒖𝒂𝒕𝒐𝒓 𝒇𝒐𝒓𝒄𝒆 𝒎 𝒘 →𝒎𝒂𝒔𝒔 (𝒘𝒉𝒆𝒆𝒍 𝒔𝒚𝒔𝒕𝒆𝒎) 𝒌 𝒕 →𝒔𝒑𝒓𝒊𝒏𝒈 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕(𝒘𝒉𝒆𝒆𝒍) 𝑿 𝒃 → 𝒎 𝒃 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝑿 𝒘 → 𝒎 𝒘 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝒓→𝒓𝒐𝒂𝒅 𝒅𝒊𝒔𝒕𝒖𝒓𝒃𝒂𝒏𝒄𝒆

Linearized State Space Model 𝑿 𝟏 = 𝑿 𝒃 𝑿 𝟐 = 𝑿 𝒃 → 𝑿 𝟐 = 𝑿 𝒃 𝑿 𝟑 = 𝑿 𝒘 𝑿 𝟒 = 𝑿 𝒘 → 𝑿 𝟒 = 𝑿 𝒘 𝒎 𝒃 𝑿 𝟐 =− [𝒌 𝒔 𝑿 𝟏 − 𝑿 𝟑 + 𝒃 𝒔 𝑿 𝟐 − 𝑿 𝟒 − 𝒇 𝒔 ] 𝒎 𝒘 𝑿 𝟒 =− 𝒌 𝒔 𝑿 𝟏 − 𝑿 𝟑 + 𝒃 𝒔 𝑿 𝟐 − 𝑿 𝟒 − 𝒌 𝒕 𝑿 𝟑 −𝒓 −𝒇 𝒔

Actuator Force – Active Suspension Actuator force = -350 N Amplitude = 0.13 cm

No Actuator Force Actuator force = 0 N Amplitude = 3.22 cm

Centered Parameter Study

Centered Parameter Study Road input has clearly a dominant effect on response Shock absorber and weight on car has nominal effects

Centered Parameter Study

Latin Hypercube Sampling (LHS) - UQ

Correlation

Correlation

Correlation

Correlation

Correlation

LHS Sampling

Correlation with data samples

References "Robust Control of an Active Suspension." Robust Control of an Active Suspension - MATLAB & Simulink. MATLAB, n.d. Web. 07 June 2017. Hines, William W. Probability and Statistics in Engineering. Hoboken, NJ: Wiley, 2003. Print.

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