I do not have any questions about the document. It appears to be a technical research paper on modeling and control of semi-active suspension systems using magnetorheological dampers.

1. LINEAR QUADRATIC REGULATOR AND SKYHOOK
APPLICATION IN SEMIACTIVE MR DAMPER FULL
CAR MODEL
FARGHAM SANDHU
DR HAZLINA SELAMAT

2. INTRODUCTION
(Literature Review)
• USED QUARTER CAR MODEL [2,5] AND LATER USED SIMPLIFIED FULL CAR MODEL
[9].
• ROLL AND PITCH EFFECTS ON THE SUSPENSION[13].
• SIMPLE MODELS WITHOUT TIRES
• PASSIVE AND FULLY ACTIVE SUSPENSION WAS REPLACED BY SEMIACTIVE
SUSPENSION
• IMPROVE RIDE COMFORT [2,3,4,5].
• FULLY ACTIVE SUSPENSION REQUIRED MORE POWER
• NOT FAILSAFE [1]
• BETTER CONTROL SCHEMES WERE REQUIRED
• MR DAMPER LIMITED DAMPING RESOLUTION[6,7,8].
• GOOD CONTROL PERFORMANCE [2].

3. INTRODUCTION (PROBLEM STATEMENT)
• BETTER CONTROL IS REQUIRED BECAUSE
• UNIPOLAR FUNCTION OF THE DAMPER [4].
• SKYHOOK CAN SWITCH ONLY[2].
• LQR FOR OPTIMAL CONTROL ONLY WHEN ESSENTIAL [10].

4. PLANT MODEL(FULL CAR SUSPENSION
SYSTEM)
MR Damper
Controller
Design
Suspension
Dynamics
F
c
0
k
0
c
1
k
1
Bouc-Wein
x
y
MR
Damper
Controller
Design
Suspension
Dynamics
•

5. DAMPER CHARACTERISTICS
• MR fluid to response after a
delay 𝜂 .
𝑣 + 𝑣𝜂 = 𝜂𝑢
• The applied potential causes the
damping coefficient to change.
𝐶0 = 𝑐0𝑐1
𝑐0+𝑐1
• The input to the system consists of the
fictitious displacements and the control
signal inputs from the controller
𝑢 =
𝑢1
𝑢2
𝑢3
𝑢4
𝑐1𝐹𝐿𝛼1𝑧1 (𝑐0𝐹𝐿 + 𝑐1𝐹𝐿)
𝑐1𝐹𝑅𝛼2𝑧2 (𝑐0𝐹𝑅 + 𝑐1𝐹𝑅)
𝑐1𝑅𝐿𝛼3𝑧3 (𝑐0𝑅𝐿 + 𝑐1𝑅𝐿)
𝑐1𝐹𝐿𝛼4𝑧4 (𝑐0𝑅𝑅 + 𝑐1𝑅𝑅)

6. STATE DEFINITION
• 𝑥1~𝑥5 𝑎𝑟𝑒 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠 𝑡ℎ𝑒 𝑠𝑢𝑠𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑎𝑡𝑒𝑠 𝑖𝑛 𝑚𝑒𝑡𝑒𝑟𝑠 𝑤ℎ𝑖𝑙𝑒
• 𝑥6 = 𝜃 𝑖𝑠 𝑟𝑜𝑙𝑙 𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛𝑠.
• 𝑥7 = ∅ 𝑖𝑠 𝑝𝑖𝑡𝑐ℎ 𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛𝑠.
• 𝑥8 ~ 𝑥12 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑖𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑠𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑥1~𝑥7 = 𝑥8 ~𝑥14
• 𝐶𝑖 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡ℎ𝑒 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑠
• 𝑘𝑖 𝑟𝑒𝑝𝑟𝑠𝑒𝑛𝑡 𝑡ℎ𝑒 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑠
• 𝛼 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑀𝑅 𝑑𝑎𝑚𝑝𝑒𝑟 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟.
• 𝑧 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑠𝑜𝑚𝑒 𝑓𝑖𝑐𝑡𝑖𝑜𝑢𝑠 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑑𝑢𝑒 𝑡𝑜 𝑐𝑜𝑚𝑝𝑎𝑐𝑡𝑖𝑜𝑛.
MR Damper
Controller
Design
Suspension
Dynamics

7. MODEL EQUATIONS
•

8. •
STATE DEPENDENT COEFFICIENT
FORM
𝑥 = 𝐴 𝑥 𝑥 + 𝐵𝑥
•
•

9. STATE DEPENDENT COEFFICIENT FORM
(STATE CO MATRICES)
•

10. STATE DEPENDENT COEFFICIENT FORM(SDC)
(STATE CO MATRICES)
•

11. CONTROLLER DESIGN
• CONTROL LAW
𝑢 = 𝑢𝑑 + 𝐺𝑠𝑥
• CLOSED LOOP CONTROL
𝑥 = 𝐴 − 𝐺𝑠𝐵 𝑥 + 𝐵𝑢𝑑
• OUTPUT LOOP
𝑦 = 𝐶𝑥
• COST FUNCTION
𝐽 =
0
∞
(𝑥𝑇
𝑄𝑥 + 𝑢𝑑
𝑇
𝑅𝑢𝑑)𝑑𝑡, 𝑄 = 𝐼14𝑥14, 𝑅 = 𝐼4𝑥4

12. CONTROLLER DESIGN(LQR)
• LQR CONTROLLER
• Recatti Equation
𝐴𝑇
𝑃 + 𝑃𝐴 − 𝑃𝐵𝑅𝐵𝑇
𝑃 + 𝑄 = 0
• LQR Gain
𝐺𝑠 = 𝑅𝐵𝑇
𝑃
• SKYHOOK CONTROL
𝐹𝑠𝑎 =
𝐺𝑠 𝑥5𝑉
𝑟 𝑥5𝑉
𝑟 ≥ 0
0 𝑥5𝑉
𝑟 ≤ 0
, 𝑉
𝑟=
𝑥1 − 𝑥5 − 𝑟11∅ − 𝑟12𝜃 𝑓𝑜𝑟 𝐹𝐿 𝑤ℎ𝑒𝑒𝑙
𝑥2 − 𝑥5 − 𝑟21∅ + 𝑟22𝜃 𝑓𝑜𝑟 𝐹𝑅 𝑤ℎ𝑒𝑒𝑙
𝑥3 − 𝑥5 + 𝑟31∅ − 𝑟32𝜃 𝑓𝑜𝑟 𝑅𝐿 𝑤ℎ𝑒𝑒𝑙
𝑥4 − 𝑥5 + 𝑟41∅ + 𝑟42𝜃 𝑓𝑜𝑟 𝑅𝑅 𝑤ℎ𝑒𝑒𝑙

13. RESULTS AND DISCUSSION (DISTURBANCE
INPUT)

14. OUTPUT RESPONSE

15. Test
Transient State Response of Semiactive suspension System
Suspension
Type
Disturbance Maximum
Displacement(m)
Steady State
Time(s)
1
Passive
Suspension
0.050628 1.8863
0.03874 1.3894
2
Fixed-Bias-
SA
Suspension
0.051246 1.532
0.039687 1.0353
3
LQR-
Skyhook
Suspension
0.046744 1.8323
0.036358 1.3478
4
LQR 0.050927 1.8744
RMS Error (Comparison)
(Displacement and velocity)

16. CONCLUSION
• SKYHOOK SCHEME HAS THE SMALLEST STEADY STATE
TIME BUT HIGHER MAXIMUM DISPLACEMENT.
• LQR (ONLY) HAS LOWER MAXIMUM DISPLACEMENT BUT
WORSE STEADY STATE TIME.
• LQR + SKYHOOK HAS BETTER STEADY STATE TIME AND
LOWEST MAXIMUM DISPLACEMENT(OVERALL BEST RESULT
IN BOTH CRITERIA)

17. LITERATURE REVIEW
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Istanbul, Turkey, 2011.
[4] W.H.Kuo, Y.P.Wang, Y.Shiao, J.Guo, M.H.Chiang and Y.K.Din, "Semiactive Control of Vehicle Suspension System Using Electrorheological Dampers," Ting Nan Institute of
Technology, Taipai, Taiwan.
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[6] X. Q. Ma, E. R. Wang, S.Rakheja and C.-Y.Su, "Modelling Hysteretic Characteristics of MR Damper and Model Validation," Las Vegas, Nevada USA, 2002.
[7] C. Sandu, S. Southward and R. Richards, "Comparison of Linear, Nonlinear, Hysteretic and Probabilistic Models for Magnetorheological Fluid Dampers," Journal of Dynamic Systems
Measurement and Control, ASME, vol. 132, pp. 1-9, 2010.
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[14] C. P. M. a. J. R. Cloutier, "Control Design for Nonlinear Benchmark Problem via the State Dependent Recatti Equation," Int J.Robust Nonlinear Control, vol. 8, pp. 401-433, 1998.
[15] J.S.Lin and I.Kanellakopoulos, "Non-Linear Design of Active Suspension System," vol. 17, 1997, pp. 45-49.
[16] F.J.D'Amato and D.E.Viasallo, "Fuzzy Control for Active Suspensions," Mechatronics, vol. 10, pp. 897-920, 2000.
[17] C. C. W.-H. L. Yan Chan, "Regenerative Damper with MR Fluids working between gear transmissions," 2013.
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13-18, 2009.

18. Q & A