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

2. 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

3. 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

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

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

6. Centered Parameter Study

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

8. Centered Parameter Study

9. Latin Hypercube Sampling (LHS) - UQ

10. Correlation

11. Correlation

12. Correlation

13. Correlation

14. Correlation

15. LHS Sampling

16. Correlation with data samples

17. 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, Print.

18. Thank you !