CHAPTER 6 FUTURE WORK:
6.4 Stability and adaptation algorithm
Then the friction model is parameterized as
( ) ( ) ( )
f d d f f
F l =Y l θ +Y l θ (6.32)
Subsequently, a complete dynamic model in parametric form with consideration of friction forces is developed
[ ]
Rewrite the parametric model in compact form with separated dynamic and frictionforce
where compact friction model is combined as
( ) ( )
,( )
1 ,( )
6.4 Stability and adaptation algorithm
For adaptive control strategy, the stability of system, which contains minimal joint error and variation of parameter values, must be confirmed. Craig [3], proposed Lyapunov function candidate to ensure the stabilization of error of joints and
parameters, and then develop adaptive law. For funding Lyapunov function, the
dynamics function should be requested
(
a, a, d, d, d)
f( )
fF Y q q q q q= θ+Y l θ (6.39)
and estimated dynamics is proposed
( )
ˆˆ a, a, d, d, d
F Y q q q q q= θ +Y lf
( )
θˆf (6.40), hat ^ means estimation.
Then, the liberalized dynamic of entire system in state-space form is given by [3]
x Ax BF
As a result, the error of joint is defined as difference between estimated length and real length
ˆ
e x x= - (6.42)
And the estimated parameter error is given by - ˆ
φ θ θ= , φf =θ θf - ˆf (6.43)
Afterward, introduce estimated error to dynamic equation e Ae BF
The positive definite and diagonal matrices P,M are available
T
-A P P-A Q
PB C
+ =
= (6.45)
For deriving adaptation law, a Lyapunov candidate function is chosen
(
, , f)
12(
T T -1 fT f-1 f)
V eφ φ = e Pe+ Γ +φ φ φ Γ φ (6.46)
Then, differentiation to time leads the candidate function to
( )
For guaranteeing stability of system, the differential should be smaller than zero.
Consequently, adaptation law is set - Y ET , f - fY EfT
φ= Γ φ = Γ (6.48)
, and the differential Lyapunov function is obtained in negative form
- T 0
V = e Qe ≤ (6.49)
which guarantees the system globally stable, and deviation of parameter f and trajectory error e to go to zero. Sinceφ θ θ= - ˆ ,φf =θ θf - ˆf, the ˆθ φ= , θˆf =φ and f adaptive rule for adapting parameter vector with updating by time
ˆ - Y ET
θ= Γ , -θˆf = ΓfY EfT
(6.50) With dynamic model, the robot system can be controlled more precisely and
rapidly. It needs available computational model and resolve subtle deviation of model occurred by external disturbance. On the other hand, adaptive controlling law helps us modifying the systemic parameters and improving control effectiveness. Thus,
implementing the MCCPM system in the dynamic control system will validate the hydraulic manipulator well performing in trajectory tracking. The structure of
hydraulic manipulator system with adaptive controller and MCCPM system is shown in Fig. 6.4.
Fig. 6.4. Control flow chart with adaptive control and MCCPM system
REFERENCES
[1] C. Canudas de Wit, Olsson H., K.J. Astrom, and P. Lischinsky, “A new model for control of systems with friction,” IEEE, Trans. Automat. Contr., Vol. 40, No. 3, Mar. 1995, pp. 419-425.
[2] Zheng Li, Y. S. Chiou, and Steven Y. Liang, “Three dimensional cutting force analysis in end milling,” Int. J. Mech. Sci., Vol. 38, No. 3, 1996, pp. 259-269.
[3] P. Lischinsky, C. Canudas-de-Wit, and G. Morel, “Friction compensation for an industrial hydraulic robot,” Control Systems Mag, IEEE, Vol. 19, Issue 1, Feb.
1999 pp. 25 – 32.
[4] Herbert E. Merrit. “Hydraulic control systems,” John Wiley & Sons, Inc., 1967 [5] J. Zhou, “Experimental Evaluations of a Kinematic compensation control method
for hydraulic robot manipulators,” Control Eng. Practice, Vol. 3, No. 5, 1995, pp.
675-684.
[6] K. Kosuge, K. Takeo, T. Fukuda, H. Kitayama, N. Takeuchi, and H. Murakami,
“Force control of parallel link manipulator with hydraulic actuators,” Int. Conf.
Robotics and Automation, 1996, pp. 305-310.
[7] Yuan-Ming Cheng, Jih-Hua Chin, “Machining contour errors as ensembles of cutting, feeding and machine structure effects,” Int. J. Mach. Tools Manuf. 43 (2003), pp. 1001-1014.
[8] 陳昱丞, “基因演算法對複合式運動平台協同運動之最佳化,” Dep. Mech. Eng.
NCTU, Taiwan, ROC., Master Thesis, 2004.
[9] Jih-Hua Chin, Her-Chyi Tsai, “A path algorithm for robotic machining,”
Robotics & Computer-Integrated Manuf, Vol. 10, No. 3, 1993, pp. 195-198.
[10] Chih-Wei Lue, Yuan-Ming Cheng, and Jih-Hua Chin “System structure and contour tracking for a hybrid motion platform”, Int. J. Adv. Manuf. Tech., DOI.
10.1007/s00170-004-211-2., 2004
[11] Honegger, M., “Adaptive control of the Hexaglide, a 6 DOF parallel manipulator,” Proc. IEEE ICRA, Albuquerque NM,USA, 1997.
[12] Rolf Johansson, “Adaptive control of robot manipulator motion,” IEEE Trans. on robotics and automation, Vol. 6, No. 4, Aug. 1990, pp. 483-490.
[13] Michael W. Walker, Liang-Boon Wee, “An adaptive control strategy for space based robot manipulators,” Proc. IEEE ICRA, Sacramento CA, USA, Apr. 1991.
[14] A. Benallegue, “Adaptive control for flexible-joint robots using a passive
systems approach,” Control Eng. Practice, Vol. 3, No. 10, 1995, pp.1393-1400.
[15] Gang Feng, “A new adaptive control algorithm for robot manipulators in task space,” IEEE Trans. on robotics and automation, Vol. 11, No. 3, Jun. 1990, pp.
457-462.
[16] B. Dasguptaa, T.S. Mruthyunjaya, “The Stewart platform manipulator: a review,” Mech. Mach. Theory, Vol. 35, No.1, 2000, pp. 15-40.
[17] Geng, Z., Haynes, L. S., Lee, J. D. and Carroll, R. L., “On the dynamic model and kinematics analysis of a class of Stewart platforms,” Robotics and
Autonomous Syst. 9, 1992, pp. 237-254.
[18] Lung-Wen Tsai, “Robot analysis – The mechanics of serial and parallel manipulators,” Wiley & Sons, Inc., 1999.
[19] Lung-Wen Tsai, “Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work,” J. of Mechanical Design, ASME, Vol. 122, Mar.
2000, pp. 3-9.
[20] B. Dasgupta, T. S.Mruthyunjaya, “A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator,” Mech. Mach. Theory, Vol. 33, No. 8, 1998, pp. 1135-1152.
[21] K. Harib, K Srinivasan., “Kinematic and dynamic analysis of Stewart
platform-based machine tool structures,” Robotica, Vol. 21, 2003, pp. 541-554.
[22] B. Dasgupta, T. S. Mruthyunjaya, “Closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach,” Mech. Mach.
Theory, Vol. 33, No. 7, 1998, pp. 993-1012.
[23] Jih-Hua Chin, Xiang-En Peng, 2004, “A tracking simulation for a hybrid Stewart platform manipulator”, Proc. IASTED International Conf. on Modelling and Simulation, Cancun, Mexico, May 18-21, 2005.
[24] L. Sciavicco, B. Siliano, “Modeling and control of robot manipulators,”
McGraw-Hill, Inc., 1996.
[25] G. P. Liu, S. Daley, “Optimal-tuning nonlinear PID control of hydraulic systems,” Control Eng. Practice, Vol. 8, 2000, pp. 1045-1053.
[26] M. R. Sirouspour, S. E. Salcudean, “Nonlinear control of a hydraulic parallel manipulator,” IEEE Trans. Robotics and Automation, vol. 17, no. 2, Apr. 2001, pp. 173-182.
[27] Jih-Hua Chin, H. W. Lin, “The algorithms of the cross-coupled pre-compensation method for generation the involute-type scrolls,” ASME J. Dynamic Systems, Measurement, and Control, March, Vol.121, 1999, pp.96-104.
[28] Kunwoo Lee, “Principles of CAD/CAM/CAE system,” Addison Wesley, 1999 [29] B. Siciliano, L. Villani, “Adaptive compliant control of robot manipulators,”
Control Eng. Practice, Vol. 4, No. 5, 1996, pp. 705-712.
[30] F. Alonge, F. D’Ippolito, F.M. Raimondi, “Globally convergent adaptive and robust control of robotic manipulators for trajectory tracking,” Control Eng.
Practice, Vol. 12, Apr. 2004, pp. 1091-1100.
[31] Lung-Wen Tsai, “Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work,” J. of Mechanical Design, ASME, Vol. 122, Mar.
2000, pp. 3-9.
[32] J. Tlusty, ”Dynamics of cutting forces in end milling,” Annals of the CIRP, Vol. 24, No. 1, 1975, pp. 433-436.
[33] M. Y. Yang, T. M. Lee, “Hybrid adaptive control based on the characteristics of CNC end milling,” Int. J. Mach. Tools Manuf., Vol. 42, 2002, pp. 489-499.
[34] T. Y. Kim, J. W. Kim, “Adaptive cutting force control for a machining center by using indirect cutting force measurements,” Int. J. Mach. Tools Manuf., Vol. 36, No. 8, 1996, pp. 925-937.
[35] D. S. Kwon, S. M. Babcock, and et al, “Tracking control on the hydraulically actuated flexible manipulator,” IEEE Int. Conf. on Robotics and Automation, vol.3, 1995, pp 2200 – 2205.
簡介
姓名：孫晏晞 (Sun, Yen-Hsi) 生日：1981 年 11 月 5 日 學歷：
高雄市立小港國小 1988.9 – 1994.6 高雄市立小港國中 1994.9 – 1997.6 高雄市私立道明中學 1997.9 – 2000.6 國立交通大學機械工程系學士班 2000.9 – 2004.1 國立交通大學機械工程系碩士班 2004.2 – 2005.6 通訊錄：高雄市小港區中船二村十七號 07-831-4850 E-Mail: [email protected]
Vita
Full Name: Sun, Yen-His
Date of Birth: 1981/11/05
Educational Background:
Kaohsiung Hsiao-Kang
Elementary School 1988.9 – 1994.6 Kaohsiung Hsiao-Kang
Senior High School 1994.9 – 1997.6 St. Dominic High School 1997.9 – 2000.6 National ChiaoTung University - 2000.9 – 2004.1 Department of Mechanical Engineering 2004.2 – 2005.6 Address: No.17, Jhong-Chuan 2nd Village, Siaogang District
Kaohsiung, 812, Taiwan (R.O.C) 886-7-8314850 E-Mail: [email protected]