This paper presents the experimental implementation of a gradient-based nonlinear model predictive control (NMPC) algorithm to the swing-up control of a rotary inverted pendulum. The key attribute of the NMPC algorithm used here is that it only seeks to reduce the error at the end of the prediction horizon rather than finding the optimal solution. This reduces the computation load and allows real-time implementation. We discuss the implementation strategy and experimental results. In addition to NMPC based swing-up control, we also present results from a gradient based iterative learning control, which is the basis our NMPC algorithm.
Issue Section:
Technical Briefs
1.
Kwon
, W. H.
, and Pearson
, A. E.
, 1978
, “On Feedback Stabilization of Time-Varying Discrete Linear Systems
,” IEEE Trans. Autom. Control
, 23
, pp. 479
–481
.2.
Cheng
, V. H. L.
, 1979
, “A Direct Way to Stabilize Continuous-Time and Discrete-Time Linear Time-Varying Systems
,” IEEE Trans. Autom. Control
, 24
, pp. 641
–643
.3.
Chen
, C. C.
, and Shaw
, L.
, 1982
, “On Receding Horizon Feedback Control
,” Automatica
, 18
, pp. 349
–352
.4.
Keerthi
, S. S.
, and Gilbert
, E. G.
, 1988
, “Optimal Infinite-Horizon Feedback Laws for a General Class of Constrained Discrete-Time Systems: Stability and Moving-Horizon Approximation
,” J. Optim. Theory Appl.
, 57
, pp. 265
–293
.5.
Mayne
, D. Q.
, and Michalska
, H.
, 1990
, “Receding Horizon Control of Nonlinear System
,” IEEE Trans. Autom. Control
, 35
, pp. 814
–824
.6.
Mayne
, D. Q.
, and Michalska
, H.
, 1993
, “Robust Receding Horizon Control of Constrained Nonlinear System
,” IEEE Trans. Autom. Control
, 38
, pp. 1623
–1633
.7.
Jadbabaie, A., Yu, J., and Hause, J., 1999, “Receding Horizon Control of the Caltech Ducted Fan: A Control Lyapunov Function Approach,” In Proc. 1999 IEEE Conference on Control Applications, 1999.
8.
Oliveira
, S. L.
, and Morari
, M.
, 2000
, “Contractive Model Predictive Control for Constrained Nonlinear Systems
,” IEEE Trans. Autom. Control
, 45
, pp. 1053
–1071
.9.
Lizarralde, F., Wen, J. T., and Hsu, L., 1999, “A New Model Predictive Control Strategy for Affine Nonlinear Control Systems,” in Proc. 1999 American Control Conference, San Diego, CA, June 1999, pp. 4263–4267.
10.
Divelbiss
, A.
, and Wen
, J. T.
, 1997
, “A Path Space Approach to Nonholonomic Motion Planning in the Presence of Obstacles
,” IEEE Trans. Rob. Autom.
, 13
, pp. 443
–451
.11.
Wiener, N., 1956, The Theory of Prediction Modern Mathematics for Enginners, McGraw–Hill.
12.
Wahlberg
, B.
, 1991
, “System Identification Using Laguerre Models
,” IEEE Trans. Autom. Control
, 36
, pp. 551
–562
.13.
Zervos
, C. C.
, and Dumont
, G. A.
, 1988
, “Deterministic Adaptive Control Based on Laguerre Series Representation
,” Int. J. Control
, 48
(6
), pp. 2333
–2359
.14.
Wang, L., 2001, “Discrete Time Model Predictive Control Design Using Laguerre Functions,” in Proceedings of 2001 American Control Conference, Arlington, VA, pp. 2430–2435.
15.
Polak, E., 1997, Optimization: Algorithms and Consistent Approximations, Springer-Verlag.
16.
Sontag
, E. D.
, 1995
, “Control of Systems Without Drift via Generic Loops
,” IEEE Trans. Autom. Control
, 40
, pp. 1210
–1219
.17.
Popa
, D.
, and Wen
, J. T.
, 2000
, “Singularity Computation for Iterative Control of Nonlinear Affine Systems
,” Asian J. of Control
, 2
, pp. 57
–75
.18.
Wen, J. T., and Jung, S., “Nonlinear Model Predictive Control Based on the Reduction of Predicted State Error,” in Proc. 2004 American Control Conference, Boston, MA, June 2004.
19.
Potsaid, B., and Wen, J. T., 2000, “Edubot: A Reconfigurable Kit for Control Education. Part i. Mechanical Design,” in Proc. 2000 IEEE International Conference on Control Applications, pp. 50–55.
20.
Neiling, J., 2003, “Nonlinear Model Predictive Control of a Rotary Inverted Pendulum,” Master’s thesis, Rensselaer Polytechnic Institute, Troy, NY.
Copyright © 2004
by ASME
You do not currently have access to this content.
