Nonlinear Model Predictive Swing-Up and Stabilizing Sliding Mode Controllers
In this paper, a nonlinear model predictive swing-up
and stabilizing sliding controller is proposed for an inverted
pendulum-cart system. In the swing up phase, the nonlinear model
predictive control is formulated as a nonlinear programming problem
with energy based objective function. By solving this problem at
each sampling instant, a sequence of control inputs that optimize the
nonlinear objective function subject to various constraints over a
finite horizon are obtained. Then, this control drives the pendulum to
a predefined neighborhood of the upper equilibrium point, at where
sliding mode based model predictive control is used to stabilize the
systems with the specified constraints. It is shown by the simulations
that, due to the way of formulating the problem, short horizon
lengths are sufficient for attaining the swing up goal.
[1] R.N. Gasimov, A. Karamancioglu, and A. Yazici, "A nonlinear
programming approach for the sliding mode control design," Applied
Mathematical Modeling, vol. 29, pp. 1135-1148, 2005.
[2] K. J. Aström and K. Furuta, "Swinging up a pendulum by energy
control," Automatica, vol. 36, pp. 287-295, 2000.
[3] A. S. Shiriaev, "VSS-version of energy-based control for swinging up a
pendulum," Systems and Control Letters, vol. 44, pp. 45-56, 2001.
[4] K. Yoshida, "Swing-up control of an inverted pendulum by energybased
methods," in 1996 Proc. American Control Conference, San
Diego, California.
[5] D. Chatterjee, A. Patra, and H. K. Joglekar, "Swing-up and stabilization
of a cart-pendulum system under restricted cart track length," Systems
and Control Letters, vol. 47, pp. 355-364, 2002.
[6] N. Muskinja and B. Tovornik, "Swinging up and stabilization of a real
inverted pendulum," IEEE Trans. Industrial Electronics, vol. 53, pp.
631-639, 2006.
[7] R. Lozano, I. Fantoni, and D. J. Block, "Stabilization of the inverted
pendulum around its homoclinic orbit," Systems and Control Letters,
vol. 40, pp. 197-204, 2000.
[8] J. Yi, N. Yubazaki, and K. Hirota, "Upswing and stabilization control of
inverted pendulum system based on SIRMs dynamically connected
fuzzy inference model," Fuzzy Sets and Systems, vol. 122, pp. 139-152,
2001.
[9] E. Mosca, Optimal, Predictive and Adaptive Control, Prentice-Hall,
1994.
[10] E. F. Camacho and C. Bordons, Model Predictive Control, Springer
Verlag, 1999.
[11] J. B. Rawlings, "Tutorial overview of model predictive control," IEEE
Control Systems Magazine, pp. 38-52, June 2000.
[12] S. J. Quin and T. A. Badgwell, "A survey of industrial model predictive
control technology," Control Engineering Practice, pp. 733-764, 2003.
[13] P. Tatjewski and M. Lawrynczuk, "Soft computing in model-based
predictive control", International Journal of Applied Mathematics and
Computer Science, vol. 16, pp. 7-26, 2006.
[14] C. Onnen, R. Babushka, U. Kaymak, J. M. Sousa, H. B. Verbruggen,
and R. Isermann, "Genetic algorithms for optimization in predictive
control," Control Engineering Practice, pp. 1363-1372, 1997.
[15] K. Ogata, Modern Control Engineering, Prentice Hall, 1990.
[16] K. Sakurama, S. Hara and K. Nakano, "Swing-up and stabilization of a
cart-pendulum system via energy control and controlled lagrangian
methods," Electrical Engineering in Japan, vol. 160, pp. 24-31, 2007.
[17] R. A. DeCarlo, S. H. Zak and G. B. Matthews, "Variable structure
control of nonlinear multivariable systems: A tutorial", in 1998 Proc.
IEEE, vol. 76, pp. 212-232
[1] R.N. Gasimov, A. Karamancioglu, and A. Yazici, "A nonlinear
programming approach for the sliding mode control design," Applied
Mathematical Modeling, vol. 29, pp. 1135-1148, 2005.
[2] K. J. Aström and K. Furuta, "Swinging up a pendulum by energy
control," Automatica, vol. 36, pp. 287-295, 2000.
[3] A. S. Shiriaev, "VSS-version of energy-based control for swinging up a
pendulum," Systems and Control Letters, vol. 44, pp. 45-56, 2001.
[4] K. Yoshida, "Swing-up control of an inverted pendulum by energybased
methods," in 1996 Proc. American Control Conference, San
Diego, California.
[5] D. Chatterjee, A. Patra, and H. K. Joglekar, "Swing-up and stabilization
of a cart-pendulum system under restricted cart track length," Systems
and Control Letters, vol. 47, pp. 355-364, 2002.
[6] N. Muskinja and B. Tovornik, "Swinging up and stabilization of a real
inverted pendulum," IEEE Trans. Industrial Electronics, vol. 53, pp.
631-639, 2006.
[7] R. Lozano, I. Fantoni, and D. J. Block, "Stabilization of the inverted
pendulum around its homoclinic orbit," Systems and Control Letters,
vol. 40, pp. 197-204, 2000.
[8] J. Yi, N. Yubazaki, and K. Hirota, "Upswing and stabilization control of
inverted pendulum system based on SIRMs dynamically connected
fuzzy inference model," Fuzzy Sets and Systems, vol. 122, pp. 139-152,
2001.
[9] E. Mosca, Optimal, Predictive and Adaptive Control, Prentice-Hall,
1994.
[10] E. F. Camacho and C. Bordons, Model Predictive Control, Springer
Verlag, 1999.
[11] J. B. Rawlings, "Tutorial overview of model predictive control," IEEE
Control Systems Magazine, pp. 38-52, June 2000.
[12] S. J. Quin and T. A. Badgwell, "A survey of industrial model predictive
control technology," Control Engineering Practice, pp. 733-764, 2003.
[13] P. Tatjewski and M. Lawrynczuk, "Soft computing in model-based
predictive control", International Journal of Applied Mathematics and
Computer Science, vol. 16, pp. 7-26, 2006.
[14] C. Onnen, R. Babushka, U. Kaymak, J. M. Sousa, H. B. Verbruggen,
and R. Isermann, "Genetic algorithms for optimization in predictive
control," Control Engineering Practice, pp. 1363-1372, 1997.
[15] K. Ogata, Modern Control Engineering, Prentice Hall, 1990.
[16] K. Sakurama, S. Hara and K. Nakano, "Swing-up and stabilization of a
cart-pendulum system via energy control and controlled lagrangian
methods," Electrical Engineering in Japan, vol. 160, pp. 24-31, 2007.
[17] R. A. DeCarlo, S. H. Zak and G. B. Matthews, "Variable structure
control of nonlinear multivariable systems: A tutorial", in 1998 Proc.
IEEE, vol. 76, pp. 212-232
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49325", author = "S. Kahvecioglu and A. Karamancioglu and A. Yazici", title = "Nonlinear Model Predictive Swing-Up and Stabilizing Sliding Mode Controllers", abstract = "In this paper, a nonlinear model predictive swing-up
and stabilizing sliding controller is proposed for an inverted
pendulum-cart system. In the swing up phase, the nonlinear model
predictive control is formulated as a nonlinear programming problem
with energy based objective function. By solving this problem at
each sampling instant, a sequence of control inputs that optimize the
nonlinear objective function subject to various constraints over a
finite horizon are obtained. Then, this control drives the pendulum to
a predefined neighborhood of the upper equilibrium point, at where
sliding mode based model predictive control is used to stabilize the
systems with the specified constraints. It is shown by the simulations
that, due to the way of formulating the problem, short horizon
lengths are sufficient for attaining the swing up goal.", keywords = "Inverted pendulum, model predictive control, swingup,stabilization.", volume = "3", number = "9", pages = "1032-6", }
