臺灣博碩士論文加值系統

本學位論文針對一創新的腳踏動力自我平衡獨輪車進行動態、打滑現象分析，並提供相應的平衡控制策略。此獨輪車(Legway)裝載一顆直流無刷馬達做以實現自我平衡的機制，但同時保留了腳踩踏板作為主要的前進動力來源。在轉向與維持側向平衡方面，Legway的轉向機構使騎乘者能以龍頭操控Lwgway的轉向與維持側向平衡。為了使Legway自我平衡、轉向等功能得以實現並保證一定的行車安全性，本論文提出了三個議題並加以探討。首先，Legway在縱方向上的平衡採用一個具重心適應能力的平衡控制器。此控制器的設計採用線性矩陣不等式(LMI)。此控制器可自動將騎乘者與車身的重心旋轉至輪軸正上方，如此一來可大幅減小馬達力矩與腳踏力矩的衝突，使Legway可具有如傳統腳踏車般的騎乘方式。第二，為了實現Legway的轉向與側向平衡，描述Legway轉向與側向平衡的動態模型被建立並分析。此分析說明了Legway的轉彎特性並提供對關鍵系統參數的調整方向以改善轉彎性能。最後，為了確保Legway的行車安全，本論文提出一針對倒單擺車設計的防滑穩定器。此防滑穩定器可與平衡控制器協同運作：透過對平衡控制器提供適當的補償，平衡控制器在Legway打滑時仍維持正常運作，並確保整體系統的穩定。此研究的關鍵在於防滑穩定器須適應各種不同的路面情況。由於不同路面狀況有不同的磨擦係數函數，防滑穩定器須具備足夠的強健性以應對此非線性且時變之系統。因此，本研究提出此防滑穩定器的合成方法，可設計防滑穩定器的增益矩陣並分析整體系統在不同路面狀況下的穩定性。本論文中提出之設計與控制概念均已模擬或實驗驗證。此學位論文中的研究成果可促進智慧與綠能車輛的發展。

In this thesis, modeling, design, and control issues associated with a pedaled and self-balanced personal mobility vehicle are studied. The vehicle, named Legway, is structurally similar to a pedaled unicycle but uses a brushless DC (BLDC) hub motor as its main driving wheel. The lateral balance and steering of the vehicle is controlled manually by the rider via a passive steering mechanism including a handle, a rotational joint, cables, pulleys, and so on. In order to balance, to steer, and to safely drive Legway on slippery road, three research issues are studied. First of all, to longitudinally balance Legway, a balancing controller with center of gravity (COG) adaptation capability is proposed, and the associated control synthesis method utilizing linear matrix inequality (LMI) is developed. Using this controller, Legway can automatically place COG of the rider plus the vehicle frame right above wheel axle so as to minimize the interference between the balancing motor torque and the rider’s pedaling torque. Secondly, to maintain lateral balance and steer Legway, the dynamics of the passive steering mechanism of Legway is modeled. Simulations on the dynamic model allow one to select crucial design parameters to enhance steering performance. Finally, to drive Legway safely on slippery road, an anti-slip compensator is proposed to cooperate with the balancing controller. Such a compensator provides appropriate compensating action to the balancing controller so that it can maintain its stability in the presence of tire slip. A synthesis method is proposed to design the gain matrix in the compensator and to analyze the stability of the overall system. The design and control concepts presented are verified by simulations or experiments. The work of the thesis can greatly facilitate the development of intelligent and green personal mobility vehicles.

List of Figures x
List of Tables xiv
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Balancing Control in Pitch Direction for Better Human-Machine
Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Steering Mechanism Design and Optimization . . . . . . . . . 8
1.2.3 Stabilization Control under Tire Slip . . . . . . . . . . . . . . 13
1.3 Scope of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 System Dynamics Modeling 17
2.1 Wheeled Inverted Pendulum Dynamics with Tire Slip . . . . . . . . . 17
2.1.1 WIP Model with a Free-rolling Wheel . . . . . . . . . . . . . . 19
2.1.2 Slip Ratio and Tire Friction . . . . . . . . . . . . . . . . . . . 20
2.2 No-slip Model for Balancing Control . . . . . . . . . . . . . . . . . . 23
2.2.1 WIP Model with No-slip Constraint . . . . . . . . . . . . . . . 23
2.2.2 Simple Model for Motor . . . . . . . . . . . . . . . . . . . . . 26
2.2.3 Plant for Balancing Control Design . . . . . . . . . . . . . . . 27
3 Balancing Control 29
3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Performance Optimization . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Numerical Analysis and Simulation . . . . . . . . . . . . . . . . . . . 38
3.4.1 Optimization Design procedure . . . . . . . . . . . . . . . . . 40
3.4.2 Time Response . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.3 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.4 Region of Attraction for the Non-linear plant . . . . . . . . . . 50
3.5 Experimental Verications . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5.1 Adaptation Test . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5.2 Pedaling Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.3 Electric Throttling Test . . . . . . . . . . . . . . . . . . . . . 57
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Analysis and Design on Steering Mechanism of Legway 59
4.1 System Conguration . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Dynamic Model for Legway II . . . . . . . . . . . . . . . . . . . . . . 61
4.2.1 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.2 Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.3 Dynamic Equation . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2.4 Linearized Dynamics . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Simulation and Design Analysis . . . . . . . . . . . . . . . . . . . . . 71
4.4 Experimental Evaluation of the Steering Performance . . . . . . . . . 76
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5 Anti-slip Control 80
5.1 Derivation of the Anti-slip Compensator . . . . . . . . . . . . . . . . 80
5.2 Generalized Version of Anti-slip Compensator . . . . . . . . . . . . . 84
5.3 Generalized Stabilizer Design and Stability Analysis . . . . . . . . . . 86
5.3.1 Closed-loop Dynamics . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 Robust Stabilizer Design . . . . . . . . . . . . . . . . . . . . . 88
5.4 Simulation of the WIP with Anti-slip Control . . . . . . . . . . . . . 93
5.4.1 Design of the Anti-slip Compensator . . . . . . . . . . . . . . 93
5.4.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6 Conclusions and Potential Applications 102
A Control Hardware of the Legway System 104
B The Components of Matrices in Chapter 4 108
C Lemmas and Theorems Required in Chapter 3 and Chapter 5 110
D Anti-slip Compensator Design for Legway 113
Bibliography 115

Bibliography
[1] Segway. [Online]. Available: http://www.segway.com/
[2] Enicycle. [Online]. Available: http://enicycle.com/
[3] U3X. [Online]. Available: http://asimo.honda.com/innovations/U3-X-Personal-
Mobility/
[4] I. Inc, \Solowheel." [Online]. Available: http://solowheel.com/
[5] J. Yi, D. Song, J. Zhang, and Z. Goodwin, \Adaptive trajectory tracking control
of skid-steered mobile robots," in Proceedings 2007 IEEE International Confer-
ence on Robotics and Automation, April 2007, pp. 2605{2610.
[6] Winglet. [Online]. Available: http://www.toyota.co.jp/
[7] Y. Ha and S. Yuta, \Trajectory tracking control for navigation of self-
contained mobile inverse pendulum," in Intelligent Robots and Systems '94.
'Advanced Robotic Systems and the Real World', IROS '94. Proceedings of the
IEEE/RSJ/GI International Conference on, vol. 3, Sep 1994, pp. 1875{1882
vol.3.
[8] F. Grasser, A. D'Arrigo, S. Colombi, and A. C. Rufer, \Joe: a mobile, inverted
pendulum," IEEE Transactions on Industrial Electronics, vol. 49, no. 1, pp. 107{
114, Feb 2002.
[9] A. Salerno and J. Angeles, \The control of semi-autonomous two-wheeled robots
undergoing large payload-variations," in Robotics and Automation, 2004. Pro-
ceedings. ICRA '04. 2004 IEEE International Conference on, vol. 2, April 2004,
pp. 1740{1745 Vol.2.
[10] K. Pathak, J. Franch, and S. K. Agrawal, \Velocity and position control of a
wheeled inverted pendulum by partial feedback linearization," IEEE Transac-
tions on Robotics, vol. 21, no. 3, pp. 505{513, June 2005.
[11] M. A. Karkoub and M. Parent, \Modelling and non-linear feedback stabilization
of a two-wheel vehicle," Proceedings of the Institution of Mechanical Engineers,
Part I: Journal of Systems and Control Engineering, vol. 218, no. 8, pp. 675{686,
2004. [Online]. Available: http://pii.sagepub.com/content/218/8/675.abstract
[12] Z. Li and C. Yang, \Neural-adaptive output feedback control of a class of trans-
portation vehicles based on wheeled inverted pendulum models," IEEE Transac-
tions on Control Systems Technology, vol. 20, no. 6, pp. 1583{1591, Nov 2012.
[13] C. C. Tsai, H. C. Huang, and S. C. Lin, \Adaptive neural network control of a self-
balancing two-wheeled scooter," IEEE Transactions on Industrial Electronics,
vol. 57, no. 4, pp. 1420{1428, April 2010.
[14] J. Huang, F. Ding, T. Fukuda, and T. Matsuno, \Modeling and velocity control
for a novel narrow vehicle based on mobile wheeled inverted pendulum," IEEE
Transactions on Control Systems Technology, vol. 21, no. 5, pp. 1607{1617, Sept
2013.
[15] Y. Naveh, P. Z. Bar-Yoseph, and Y. Halevi, \Nonlinear modeling and control of
a unicycle," Dynamics and Control, vol. 9, no. 4, pp. 279{296, 1999. [Online].
Available: http://dx.doi.org/10.1023/A:1026481216262
[16] Z. Sheng and K. Yamafuji, \Postural stability of a human riding a unicycle and its
emulation by a robot," IEEE Transactions on Robotics and Automation, vol. 13,
no. 5, pp. 709{720, Oct 1997.
[17] S. N. Kadam and B. Seth, \Lqr controller of one wheel robot stabilized by reaction
wheel principle," in Instrumentation Control and Automation (ICA), 2011 2nd
International Conference on, Nov 2011, pp. 299{303.
[18] L. Murata Manufacturing Co., \Murata girl." [Online]. Available:
http://www.murata.com/en-global/about/mboymgirl/mgirl
[19] X. Ruan, Q. Wang, and N. Yu, \Dual-loop adaptive decoupling control for single
wheeled robot: Based on neural pid controller," in Control Automation Robotics
Vision (ICARCV), 2010 11th International Conference on, Dec 2010, pp. 2349{
2354.
[20] Z. Shao and D. Liu, \Balancing control of a unicycle riding," in Proceedings of
the 29th Chinese Control Conference, July 2010, pp. 3250{3254.
[21] J. Lee, S. Han, and J. Lee, \Decoupled dynamic control for pitch and roll axes of
the unicycle robot," IEEE Transactions on Industrial Electronics, vol. 60, no. 9,
pp. 3814{3822, Sept 2013.
[22] H. Jin, J. Zhao, J. Fan, and J. Lee, \Gain-scheduling control of a 6-dof single-
wheeled pendulum robot based on dit parameterization," in Robotics and Au-
tomation (ICRA), 2011 IEEE International Conference on, May 2011, pp. 3511{
3516.
[23] M. Ha, Y. G. Bae, and S. Jung, \Synchronization of two
ywheels for stable
balancing control of one-wheel transportation vehicle: Gyrocycle," in Ubiquitous
Robots and Ambient Intelligence (URAI), 2013 10th International Conference
on, Oct 2013, pp. 499{502.
[24] M. Ha and S. Jung, \Balancing control of a one-wheel transportation vehicle:
Gyrocycle," in Robotics (ISR), 2013 44th International Symposium on, Oct 2013,
pp. 1{4.
[25] Y. Xu and S. K. W. Au, \Stabilization and path following of a single wheel
robot," IEEE/ASME Transactions on Mechatronics, vol. 9, no. 2, pp. 407{419,
June 2004.
[26] J. H. Park and S. Jung, \Experimental studies of balancing and driving control
of a single wheeled mobile robot: Gyrobo ii," in Control Conference (ASCC),
2011 8th Asian, May 2011, pp. 96{100.
[27] T. B. Lauwers, G. A. Kantor, and R. L. Hollis, \A dynamically stable single-
wheeled mobile robot with inverse mouse-ball drive," in Proceedings 2006 IEEE
International Conference on Robotics and Automation, 2006. ICRA 2006., May
2006, pp. 2884{2889.
[28] C. Rui and N. H. McClamroch, \Stabilization and asymptotic path tracking of
a rolling disk," in Decision and Control, 1995., Proceedings of the 34th IEEE
Conference on, vol. 4, Dec 1995, pp. 4294{4299 vol.4.
[29] J.-C. Ryu and S. K. Agrawal, \Differential
atness-based robust control
of mobile robots in the presence of slip," The International Journal of
Robotics Research, vol. 30, no. 4, pp. 463{475, 2011. [Online]. Available:
http://ijr.sagepub.com/content/30/4/463.abstract
[30] N. Hamzah, M. K. Aripin, Y. M. Sam, H. Selamat, and R. Ghazali, \Second order
sliding mode controller for longitudinal wheel slip control," in Signal Processing
and its Applications (CSPA), 2012 IEEE 8th International Colloquium on, March
2012, pp. 138{143.
[31] D. Hong, P. Yoon, H.-J. Kang, I. Hwang, and K. Huh, \Wheel slip control systems
utilizing the estimated tire force," in 2006 American Control Conference, June
2006, pp. 6{11.
[32] S. Muller, M. Uchanski, and K. Hedrick, \Estimation of the maximum tire-road
friction coefficient," Journal of Dynamic Systems, Measurement, and Control,
vol. 125, no. 125(4), pp. 607{617, 2004.
[33] K. Ohishi, Y. Ogawa, I. Miyashita, and S. Yasukawa, \Anti-slip re-adhesion
control of electric motor coach based on force control using disturbance observer,"
in Industry Applications Conference, 2000. Conference Record of the 2000 IEEE,
vol. 2, 2000, pp. 1001{1007 vol.2.
[34] S.-T. Peng, J.-J. Sheu, and C.-C. Chang, \On one approach to constraining wheel
slip for the autonomous control of a 4ws/4wd vehicle," in Control Applications,
2004. Proceedings of the 2004 IEEE International Conference on, vol. 2, Sept
2004, pp. 1254{1259 Vol.2.
[35] G. Baffet, A. Charara, and J. Stephant, \Sideslip angle, lateral tire force and road
friction estimation in simulations and experiments," in 2006 IEEE Conference on
Computer Aided Control System Design, 2006 IEEE International Conference on
Control Applications, 2006 IEEE International Symposium on Intelligent Con-
trol, Oct 2006, pp. 903{908.
[36] B. R. Liang and W. S. Lin, \A new slip ratio observer and its application in
electric vehicle wheel slip control," in 2012 IEEE International Conference on
Systems, Man, and Cybernetics (SMC), Oct 2012, pp. 41{46.
[37] H. Jing, Z. Liu, and J. Liu, \Wheel slip control for hybrid braking system of elec-
tric vehicle," in Transportation, Mechanical, and Electrical Engineering (TMEE),
2011 International Conference on, Dec 2011, pp. 743{746.
[38] R. T. Ramamoorthy, B. Larimore, and M. Bhardwaj, Sensored Field
Oriented Control of 3-Phase Permanent Magnet Synchronous Motors
Using TMS320F2837x, Taxas Instruments, 2016. [Online]. Available:
http://www.ti.com/lit/an/sprabz0/sprabz0.pdf
[39] F.-K. Wu, T.-J. Yeh, and C.-F. Huang, \Motor control and torque coordination
of an electric vehicle actuated by two in-wheel motors," Mechatronics, vol. 23,
no. 1, pp. 46{60, Feb. 2013.
[40] H. L. Trentelman, A. A. Stoorvogel, and M. Hautus, Control Theory for Linear
Systems. Springer-Verlag London, 2001.
[41] S. H. Zak, Systems and Control. Oxford University Press, 2003.
[42] A. M. LYAPUNOV, \The general problem of the stability of motion,"
International Journal of Control, vol. 55, no. 3, pp. 531{534, 1992. [Online].
Available: http://dx.doi.org/10.1080/00207179208934253
[43] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities
in System and Control Theory. Society for Industrial and Applied Mathematics
(SIAM), 1994.
[44] C. Scherer and S. Weiland, Linear Matrix Inequalities in Control, Nov. 2004.
[45] J. H. Ginsberg, Advanced Engineering Dynamics, 2nd Edition, 2nd ed. Cam-
bridge University Press, Nov. 1998.
[46] I. The MathWorks, \Matlab and symbolic math toolbox release 2014b."
[47] L. Zaccarian and A. R. Teel, \A common framework for anti-windup, bumpless
transfer and reliable designs," Automatica, vol. 38, no. 10, p. 17351744, Oct.
2002.
[48] Y. Qi and W. Bao, \Dynamic bumpless transfer: An exact model matching
approach," in Control Conference (CCC), 2011 30th Chinese, July 2011, pp.
1795{1799.
[49] K. Zheng, T. Basar, and J. Bentsman, \H1 bumpless transfer under controller
uncertainty," IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1718{
1723, July 2009.
[50] P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox
Users Guide, The MathWorks, Inc., 1995.
[51] A. Damen and S. Weiland, Robust Control, 2002.
[52] J.-J. Slotine and W. Li, Applied Nonlinear Control, 1st Edition. Pearson, Pren-
tice Hall, 1991.
[53] STMicroelectronics. [Online]. Available: http://www.st.com/
[54] Microchip, \Microchip technology inc." [Online]. Available:
http://www.microchip.com/
[55] I. Schur, \Schur complement." [Online]. Available: https://en.wikipedia.org
[56] F. Zhang, Ed., The Schur Complement and Its Applications. Springer US, 2005.
122