Robust Analysis of a Hybrid System Controlled by a  -Synthesis Method Kyu-Sik Park, Post Doctoral Researcher, UIUC, USA Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea Woo-Hyun Yoon, Professor, Kyungwon Univ., Korea In-Won Lee, Professor, KAIST, Korea The Third International Workshop on Advanced Smart Materials and Smart Structures Technology

Smart Structures Technology Lab., UIUC 2 Introduction Robust hybrid control system Numerical examples Conclusions Contents

Smart Structures Technology Lab., UIUC 3 Introduction Hybrid control system (HCS)  A combination of passive and active control devices Passive devices: insure the control system robustness Active devices: improve the control performances  The overall system robustness may be negatively impacted by active device or active controller may cause instability due to small margins.

Smart Structures Technology Lab., UIUC 4 Objective  Apply a hybrid control system for vibration control of a seismically excited cable-stayed bridge  Apply a  -synthesis method to improve the controller robustness

Smart Structures Technology Lab., UIUC 5 Robust Hybrid Control System (RHCS) Control devices  Passive control devices Lead rubber bearings (LRBs) Design procedure: Ali and Abdel-Ghaffar (1995) Bouc-Wen model

Smart Structures Technology Lab., UIUC 6  Active control devices Hydraulic actuators (HAs) An actuator capacity has a capacity of 1000 kN. The actuator dynamics are neglected.

Smart Structures Technology Lab., UIUC 7 Control algorithm:  -synthesis method where : structured singular value : transfer function of closed-loop system : perturbation  Cost function (1)  Advantages Combine uncertainty in the design procedure Guarantee the stability and performance (robust performance)

Smart Structures Technology Lab., UIUC 8  Frequency dependent filters Kanai-Tajimi filter (2)

Smart Structures Technology Lab., UIUC 9 High-pass and low-pass filters (3), (4)

Smart Structures Technology Lab., UIUC 10 Additive uncertainty filter (5) Multiplicative uncertainty filter (6)

Smart Structures Technology Lab., UIUC 11 Block diagram of robust hybrid control system Bridge Model Sensor  -synthesis method HA LRB MUX

Smart Structures Technology Lab., UIUC 12 Analysis model  Bridge model Bill Emerson Memorial Bridge · Benchmark control problem · Located in Cape Girardeau, MO, USA · 16 shock transmission devices (STDs) are employed between the tower-deck connections. Numerical Examples

Smart Structures Technology Lab., UIUC 13 Configuration of control devices (LRBs+HAs) m350.6 m m

Smart Structures Technology Lab., UIUC 14 PGA: 0.348g PGA: 0.143g PGA: 0.265g  Historical earthquake excitations

Smart Structures Technology Lab., UIUC 15 Analysis results  Control performances Displacement under El Centro earthquake (a) STDs(b) RHCS

Smart Structures Technology Lab., UIUC 16 Deviation of cable tension under El Centro earthquake (a) STDs(b) RHCS

Smart Structures Technology Lab., UIUC 17 Shear force of tower under El Centro earthquake (a) STDs(b) RHCS

Important responses of bridge El Centro Deck Dis.Deck Shear Base Mom. Deviation of Cable Tension

Smart Structures Technology Lab., UIUC 19  Controller robustness The dynamic characteristic of as-built bridge is not identical to the numerical model. There are large differences at high frequencies between evaluation and design models. There is a time delay of actuator introduced by the controller dynamics and A/D input and D/A output conversions.  Robust analysis should be performed to verify the applicability of the control system.

Smart Structures Technology Lab., UIUC 20 where: nominal stiffness matrix : perturbed stiffness matrix : perturbation amount (  5,  10,  15,  20%) Stiffness matrix perturbation Mass matrix perturbation · Additional snow loads (97.7 kg/m 2, UBC) are added to the deck. where: time delay : time delay amount : sampling time (0.02 sec) Time delay of actuator (7) (8)

Smart Structures Technology Lab., UIUC 21 J 1 /J 7 : Peak/Normed base shear; J 2 /J 8 : Peak/Normed shear at deck level J 3 /J 9 : Peak/Normed overturning moment; J 4 /J 10 : Peak/Normed moment at deck level J 5 /J 11 : Peak/Normed cable tension deviation; J 6 : Peak Deck dis. at abutment` Stiffness perturbation w/o snow loadw/ snow load · Cable tension deviation (J 5, J 11 ) is more sensitive. · Deck dis. (J 6 ) is relatively insensitive. · Normed cable tension deviation (J 11 ) is varied more than 100% when there are -20% stiffness perturbation with snow load under Gebze earthquake.

Smart Structures Technology Lab., UIUC 22 Deviation of cable tensions Deviation of tension of cable no. 10 · However, the cable tension is well within the bounds and dies out after seismic event.

Smart Structures Technology Lab., UIUC 23 Time delay w/o snow loadw/ snow load J 1 /J 7 : Peak/Normed base shear; J 2 /J 8 : Peak/Normed shear at deck level J 3 /J 9 : Peak/Normed overturning moment; J 4 /J 10 : Peak/Normed moment at deck level J 5 /J 11 : Peak/Normed cable tension deviation; J 6 : Peak Deck dis. at abutment` · Deck shear and dis. (J 2,J 6,J 8 ) is more sensitive. · Variation is much less than compare to stiffness perturbation.

Smart Structures Technology Lab., UIUC 24 Stiffness perturbation and time delay w/o snow loadw/ snow load · The effect of stiffness perturbation is larger than time delay. · As the stiffness perturbation increases, the effect of time delay decreases.

Smart Structures Technology Lab., UIUC 25 Additional earthquakes · Chi-Chi (1999) – PGA = 0.42g > design PGA · Hachnohe (1968) – PGA = 0.23g < design PGA Chi-Chi Hachinohe

Smart Structures Technology Lab., UIUC 26 Hybrid system controlled by a  -synthesis method  shows similar performance with conventional one  has excellent robustness without loss of control performances  could be proposed as an improved control strategy for a seismically excited cable-stayed bridges containing many uncertainties Conclusions

Smart Structures Technology Lab., UIUC 27 Thank you for your attention! Acknowledgements This research was supported by the Korea Research Foundation (Grant no. KRF D00169) and author also acknowledges NSF for partial travel support.