防鎖死剎車系統是一個非線性系統，如果只用簡單的轉移函數、或是線性化過的方程式組來描述系統，難免會犧牲某些系統的動態特性，所以本文建立一組非線性數學方程式，來模擬剎車系統的動態行為，並據以設計控制器。除了數學模擬之外，本研究也架設動態實驗台，藉由實際的剎車結果與數學模擬相互印證。
在非線性控制器設計方面，本文採用具有強健特性的滑動模式控制器。對可能引起的抖顫現象，一則利用在滑動平面兩旁加入邊界層的作法，以平滑的控制訊號來減少抖顫現象的產生。這樣的控制方式，可以利用脈寬調變法則配合快速驅動電磁閥來達成；二則嘗試將傳統開關控制的取樣頻率提高，以及時控制來降低抖顫的幅度。文中將針對這兩種控制方式探討它們在強健性與控制平順度方面的表現。此外在應用脈寬調變法則時，為了避免電磁閥做過多不必要的開關動作而影響壽命，本文也特地設計了雙模滑動模式驅動方式以減少開關動作、延長電磁閥壽命。
在剎車測試時，本文先假設真實車速可以得知，來設計滑差回授控制器。這個控制器除了以數學模擬驗證外，在實驗台上，則是利用噴嘴噴水與否來模擬潮濕或是乾燥路面剎車。此外，經由特殊的設計，本實驗台可讓防鎖死剎車系統本身的控制單元(ECU: Electronic Control Unit)控制整個剎車，其間由電腦擷取各項資訊。也可實際測試左、右輪分別屬於乾燥與潮濕接觸面時的防鎖死剎車。
接著本文著眼於未來更精確控制剎車力的必要性，搭配壓力回授訊號，嚐試同樣利用滑動模式脈寬調變控制器來精準的控制剎車壓力，以間接控制各輪的剎車扭矩。在數學模擬、與實驗驗證後，利用此控制器搭配車輪減速度訊號設計防鎖死剎車控制器。除了驗證其剎車壓力追蹤能力外，也驗證其防鎖死效能。而因電磁閥不連續開關動作引發的水槌震盪現象在文中也有所討論。

The anti-lock braking system is a nonlinear system whose dynamic characteristics are very difficult to describe just using transfer functions or linearized equation sets. In order to take care of the dynamic motion as much as possible, this study tries to use original nonlinear equations without linearization to simulate the anti-lock braking system. Beside software simulation, a dynamic test stand is used to verify the software simulation results in parallel.
For the controller design, this study adopts sliding-mode control theorem because of its well-known robustness. Two approaches are investigated to reduce the chattering problem caused by the sliding-mode controller. First, the controller is modified to have a boundary layer, whose control signal varies smoothly inside the boundary layer. The pulse width modulation method (PWM) is used to realize this quasi-continuous control using fast solenoid valves. With respect to the lifetime issue, we apply a hybrid sliding-mode control algorithm to minimize the on-off frequency and prolong the lifetime. The other way to bring the chattering down is trying to promote the sampling rate of the traditional on-off controller and achieve real time control. The performances of these two controllers are compared and evaluated in this article.
To start the simulation and hardware testing, a closed-loop slip controller is designed to perform the anti-lock brake basing on the assumption that we know the real vehicle speed during the brake. Water sprays are used to simulate the brake on wet road surface or the brake on surface. Through special design, the four-wheel anti-lock brake controlled by the electric control unit (ECU) is also available on this test stand. The brake performance of the ECU is verified by the data gathered by the computer.
Looking into the future, precise brake pressure control would be necessary in order to provide precise brake torque. Therefore hybrid sliding-mode PWM controller is used to get precise brake pressure. Both the software simulation and the hardware testing are used to verify the controller’s performance. Besides, an anti-lock brake controller with the brake pressure-tracking controller is designed basing on the tire acceleration signal feedback instead of slip feedback. Simulation and harware testing verify the brakes on dry and wet roads afterwards. The water-hammer phenomenon is also noticed and discussed together with the brake pressure control.

參 考 文 獻
1.N. N., “自動車ABS研究,”日本 株式會社編,山海堂,平成5年。
2.P. Oppenheimer, “The implications of technical developments on future European braking regulations,” Proc. Instn. Mech. Engrs. Vol. 204, ImechE, pp. 147-160,1990.
3.N. N., “汽車用防鎖死剎車系統,” 經濟部標準檢驗局,D2201，民國88年。
4.L. Evans, “ABS and relative crash risk under different roadway, weather, and other conditions,” Society of Automotive Engineers Warrcrf1dale. PA. (SAE 950353). 1995.
5.L. Evans, and P. Gerrish, “Antilock brakes and risk of front and rear impact in two-vehicle crashes,” Accident Analysis and Prevention Vol. 28, pp. 315-323. 1996.
6.Charles M. Farmer, Adrian K. Lund, Rebecca E. Trempel and Elisa R. Braver,” Fatal crashes of passenger vehicles before and after adding antilock braking systems,” Author Affiliation: Insurance Inst for Highway Safety Source: Accident Analysis and Prevention Vol. 29 No. 6, pp. 745-757, Nov 1997.
7.A. Williams and J. Wells, “Driver experience with antilock brake systems,” Accident Analysis and Prevention 26, pp. 807-811. 1994.
8.Charles M. Farmer, ”New evidence concerning fatal crashes of passenger vehicles before and after adding antilock braking systems,” Author Affiliation: Insurance Inst for Highway Safety Source: Accident Analysis and Prevention Vol. 33 No.3, pp. 361-369, May 2001.
9.Robert K. Holzwarth and Kenneth A. May, “Analysis of traction control systems augmented by limited slip differentials’, SAE paper 940831, 1994.
10.Wolfgang Maisch, Wold-Dieter Jonner, Robert Mergenthaler, and Alfred Sigl, “ ABS5 and ASR5： The new ABS/ASR family to optimize directional stability and traction,” SAE paper 930505, 1993.
11.Akihiko Sekiguchi, Toshifumi Maehara, Takashi Sakai, Hideki Kakizaki, and Satomi Ohkubo, “ASR Built in an Add-On ABS,” SAE paper 930506, 1993.
12.Hirosi Kawakami, Hiroki Sato, Masaaki Tabata, Hideo Inoue and Hidenori Itimaru, “Development of integrated system between active control suspension, active 4WS, TRC and ABS,” SAE paper 920271, 1992.
13.N. Matsumoto and M. Tomizuka, “Vehicle lateral velocity and yaw rate control with two independent control inputs,” Trans. ASME, Journal of Dynamic System, Measurement and Control, Vol. 114, pp. 606-613, Dec. 1992.
14.S. V. Drakunov, B. Ashrafi and A. Rosiglioni, “ Yaw control algorithm via sliding mode control,” Proceedings of the American Control Conference Chicago US, Vol. 1, pp. 580-583, June 2000.
15.Honda Press Release, “Vehicle stability assist,” July 2, 1997.
16.M. Fodor, John Yester and D. Hrovat, “Active control of vehicle dynamics,” Digital Avoinics Systems Conference, 1998. Proceedings The AIAA/ IEEE/ SAE, Vol. 2, I 14, pp. 1-8, Nov. 1998.
17.Dieter Konik, ‘Development of the dynamic drive for the new 7 series of the BMW group’, Int. J. of Vehicle Design, Vol. 28, Nos. 1/2/3, pp. 131-149, 2002
18.J. Schuler, P. Brangs, R. Rothfuss, A. Lutz and R. Breit, “Development methodology for dynamic stability control systems,” International Journal of Vehicle Design, Vol. 28, No. 1/2/3, pp. 37-56, 2002.
19.R. Schwarz, M. Willimowski, R. Isermann and P. WiUimowski, “Improved wheel speed and slip determination considering influences of wheel-suspension dynamics and tire dynamics,” SAE Special Publications, Vol. 1229, pp. 123-133, February, 1997.
20.Ulrich Adler, “Bremsanlagen fur Kraftfahrzeuge,” Bosch, 1994.
21.Manfred Burckhardt, “Radschlupf-Regelsysteme,” Vogel Verlag und Druck KG, 1993.
22.Manfred Burckhardt, “Fahrwerktechnik: Bremsdynamik und Pkw- Bremsanlagen,” Vogel Verlag und Druck KG, 1991.
23.R. T. Fling and R. E. Fenton, “A describing-function approach to anti-skid design,”IEEE Trans. on Vehicular Technology, Vol.VT-30, No.3, pp. 134-143, August 1981.
24.陳立文, “滑差回授式防滑煞車系統之分析與控制,”國立清華大學動力機械研究所碩士論文,1987。
25.H. Tan and M. Tomizuka, “Discrete-time controller design for robust vehicle traction,” IEEE Control System Magazine, pp. 107-113, April 1990.
26.Y. K. Chin, W. C. Lin., D. M. Sidlosky, and D. S. Rule, “Sliding mode ABS wheel-slip control,”1992 American Control Conference , Chicago,IL ,June, pp. 1-5, 1992.
27.H. S. Tan. and Y. K. Chin, “Vehicle traction control: Variable structure control approach,” Trans. Of the ASME Journal of Dynamic System, Measurement and Control, Vol. 113, NO. 2, pp. 223-230, 1991.
28.J. R. Layne, K. M. Passino, and S. Yurkovich, ”Fuzzy learning control for antiskid braking systems,” IEEE Trans. on Control Systems Technology, Vol. 1., pp. 122-129, June 1993.
29.葉莒，王俊堯, “鎖相迴路式伺服型防鎖剎車系統,”中華民國專利，公告編號205084,1993。。
30.G. F. Mauer, “A fuzzy Logic Controller for an ABS Braking System,” IEEE Trans. on Fuzzy Systems, No.4, pp. 381-388, November 1995.
31.E. T. Bakker, H. B. Pacejka, and L. Lidner, “A new tire model with an application in vehicle dynamics studies,” SAE Paper No.890087, 1989.
32.F. Yuan, G. V. Puskorius, L. A. Feldkamp, and L. I. Davis, “Neural network control of a four-wheel ABS model,” Proc. of the 1995 IEEE Inter. Symp. on Intelligent Control, pp. 1503-1506 ,1995.
33.Y. S. Kueon and J. S. Bedi, “Fuzzy-neural-sliding mode controller and its applications to the vehicle anti-lock braking systems, ,” 1995 Inter. IEEE/IAS Conf. on Industrial Automation, pp. 391-397, May 1995.
34.M. C. Wu, L. C. Lee and M. C. Shih “Neuro-fuzzy controller design of the anti-lock braking system,” International Journal of JSME. Series C, Vol. 41 No. 4, pp. 836-843, Dec. 1998.
35.M. L. Kuang, M. Fodor, D. Hrovat and M. Tran, “Hydraulic brake system modeling and control for active control of vehicle dynamics,” Proceedings of the American Control Conference, San Diego, California, Vol. 6, pp. 4538-4542, June 1999.
36.Seongho Choi and Dong-Woo Cho, “ Control of wheel slip ratio using sliding ode controller with pulse width modulation,” Author Affiliation: Pohang Univ of Science and Technology Source: Vehicle System Dynamics Vol. 32, No. 4, pp. 267-284, 1999.
37.K. E. Holms and R. D. Stone, “Tyre forces as functions of cornering and braking slip on wet road surfaces,” Road Research Laboratory, Ministry of Transport, RRL Report LR 254, Crowthorne, 1969.
38.A. van Zanten, R. Erhardt, and Q. Lutz, “Measurement ans simulation of transients in longitudinal and lateral tire forces,” SAE Paper 900210, 1990.
39.J. L. Harned, L. E. Johnston and G. Scharpf, “Measurement of tire brake force characteristics as related to wheel slip control system design,” SAE Paper 690214, 1969.
40.H. Dugoff, P. S. Fancher and L. Segel, “An analysis of tire traction properties and their influence on vehicle dynamic performance,” SAE Paper No.700377, 1970.
41.Jack Erjavec, “Anti-Lock Brake Systems,” Delmar Publishers, 1996
42.TOYOTA Corolla汽車ABS資料手冊。1996.
43.福特汽車金全壘打ABS資料手冊。1992.
44.黃靖雄, “現代汽車底盤,’’全華科技圖書股份有限公司, 1995.
45.施明璋、吳銘欽, “液壓控制防鎖死煞車系統簡介,” 機械月刊，第285期, pp. 272~279, 1999.
46.施明璋, “液壓剎車系統分析與控制之研究(III),”國科會專題計劃成果報告,計劃編號: NSC 86-2212-E006-083, 1997。
47.Herbert E. Merritt, “Hydraulic control systems,” John Wiley & Sons, Inc. New York, 1967
48.Dennis Karl Fisher, “The dynamic characteristics of vehicle braking systems,” Thesis for P. D. degree, Mechanical Engineering, University of Michigan, USA, 1970.
49.朱賢明, “汽車油壓煞車系統之性能分析與實驗之研究,” 國立成功大學機械工程研究所碩士論文,1995。
50.M.C. Wu and M.C. Shih, “ Simulated and Experimental Study of Hydraulic Anti-Lock Braking System Control Using Sliding Mode Control Method,” (accepted) Mechatronics. May, 2001.
51.施明璋, “液壓剎車系統分析與控制之研究(II),”國科會專題計劃成果報告,計劃編號: NSC 85-2212-E006-041, 1996。
52.M. C. Wu and M. C. Shih, “ Hydraulic Anti-lock Braking Control Using Hybrid Sliding mode PWM Pressure Control Method,” Journal of System and Control Engineering, Proceeding of the Institution of Mechanical Engineering Part I, Vol. 215, pp.177-185, No.12, 2001.
53.T. S. Scafer, D.W. Howard, and R. W. Carp, “Design and Performance Considerations for Passenger Car Anti-Skid Systems,” SAE Paper No.680458, May 1968.
54.Yoshikazu Suematsu, Hironao Yamada, Tetsuya Tsukamoto, and Takayoshi Muto, “Digital control of electro-hydraulic servo system operated by differential pulse width modulation,” JSME International Journal, Series C, Vol. 36, No. 1, pp. 61-68, 1993.
55.M. C. Shih and C. G. Hwang, “Fuzzy PWM Control Position of a Pneumatic Robot Cylinder Using High Speed Solenoid Valves,” International Journal of JSME, Series C, Vol.40, No.3, pp. 469-476, Dec. 1997.
56.M. C. Shih and M. A. Ma, “ Position Control of a Pneumatic Rodless Cylinder Using Sliding Mode M-D-PWM Control the High Speed Solenoid Valves,” International Journal of JSME, Series C, Vol.41, No.2, pp. 236-241, 1998.
57.馬明安, “智慧型滑動模式脈寬調變控制於無桿式氣壓缸定位之研究,” 國立成功大學機械工程研究所碩士論文,1996。
58.J. J. Slotine, “Sliding controller design for nonlinear systems,” International Journal of Control, Vol. 40, No. 2, pp. 421-434, Feb. 1984.
59.Jean-Jacques E. Slotine and Weiping Li, “Applied Nonlinear Control,” Prentice-Hall International Inc., 1991.
60.E. B. Wylie and V. L. Streeter, ”Fluid Transients in System,” Prentice Hall, N. J. 1993.
61.D. Liu, “On the improvement of pressure behavior of hydraulic brake control system,” Acta Polytech. Scand., Mech. Engng Ser., Vol. 124, pp. 100-108,1997.
62.林明德，“水錘波傳遞特性及液柱分離現象分析”，國立成功大學水利及海洋工程研究所碩士論文，1999.
63.邱翎倫，“水柱分離現象對管內水錘波之影響,”國立成功大學水利及海洋工程研究所碩士論文，1997.
64.A. Daiss and U. Kiencke, “Estimation of vehicle speed fuzzy-estimation in comparison with Kalman-filtering,” Control Applications, Proceedings of the 4th IEEE Conference, pp. 281-284, 1995.
65.Fangjun, Jiang, and Zhiqiang, Gao, “An adaptive nonlinear filter approach to the vehicle velocity estimation for ABS,” Control Applications, Proceedings of the 2000 IEEE International Conference, pp. 490-495, 2000.
66.Sergey Drakunov, Peter Dix and Behrouz Ashrah, “ABS control using optimum search via sliding modes,” IEEE Transactions on Control Systems Technology, Vol. 3, No. 1, pp. 79-85, March 1995.
67.N. Barbour, E. Brown, J. Connelly, J. Dowdle, G. Brand J. Nelson and J. Obannon, “Micro-machined, inertial sensors for vehicles,” In Proceedings of IEEE Conference on Intelligent Transportation Systems, pp. 1058-1063, 1997.
68.H. Subramanian, V. K. Varadan, V. V. Varadan and M. J. Vellekoop, “Design and fabrication of wireless remotely readable MEMS based micro-accelerometers,” Smart Material and Structure, Vol. 6, No. 6, pp. 730-738,1997.
69.L. Austin and D. Morrey, “Recent advances in antilock braking systems and traction control systems,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 214, No. 6, pp. 625-638, 2000.
70.M. Qian and P. Kachroo, “Modeling and control of electro-magnetic brakes for enhanced braking capabilities for automated highway systems,” Proc. of IEEE Conference on Intelligent Transportation Systems, pp. 391-396, 1997.