Position Control of a Flexible Joint via Explicit Model Predictive Control: An Experimental Implementation

Massoud Hemmasian Ettefagh, Mahyar Naraghi, Farzad Towhidkhah


This paper experimentally controls a flexible joint via explicit model predictive control (Explicit MPC) method. The scheme divides the state space into different partitions, then solves the associated multi parametric optimization in off-line computations. The result stores in a look-up table to be used in on-line algorithm. First, the state space equations of the flexible joint are derived and linearized around the working point. Then, in order to meet the plant’s specifications, desired performance and the limitation of processor/memory, the constraints, weights, sampling time and prediction horizon are determined for the system. Finally, the algorithm is applied on the experimental plant. Numerous simulations, the result of the experiment and comparison with other methods confirmed that the method was able to control the vibrations of the constrained flexible joint.


Flexible Joint; Explicit Model Predictive Control; Multi-Parametric Optimization; Discrete Linear Time Invariant System.


Dwivedy, Santosha Kumar, and Peter Eberhard. “Dynamic Analysis of Flexible Manipulators, a Literature Review.” Mechanism and Machine Theory 41, no. 7 (July 2006): 749–777. doi:10.1016/j.mechmachtheory.2006.01.014.

Shigang, Yue. “Redundant Robot Manipulators with Joint and Link flexibility—I. Dynamic Motion Planning for Minimum End Effector Deformation.” Mechanism and Machine Theory 33, no. 1–2 (January 1998): 103–113. doi:10.1016/s0094-114x(97)00028-1.

Morari, Manfred, and Jay H. Lee. “Model Predictive Control: Past, Present and Future.” Computers & Chemical Engineering 23, no. 4–5 (May 1999): 667–682. doi:10.1016/s0098-1354(98)00301-9.

Qin, S.Joe, and Thomas A. Badgwell. “A Survey of Industrial Model Predictive Control Technology.” Control Engineering Practice 11, no. 7 (July 2003): 733–764. doi:10.1016/s0967-0661(02)00186-7.

Wang, Yang, and Stephen Boyd. “Fast Model Predictive Control Using Online Optimization.” IEEE Transactions on Control Systems Technology 18, no. 2 (March 2010): 267–278. doi:10.1109/tcst.2009.2017934.

Wang, Liuping. “Discrete Model Predictive Controller Design Using Laguerre Functions.” Journal of Process Control 14, no. 2 (March 2004): 131–142. doi:10.1016/s0959-1524(03)00028-3.

Ettefagh, Massoud Hemmasian, Mahyar Naraghi, Farzad Towhidkhah, and Jose De Dona. “Model Predictive Control of Linear Time Varying Systems Using Laguerre Functions.” 2016 Australian Control Conference (AuCC) (November 2016). doi:10.1109/aucc.2016.7868014.

Bemporad, Alberto, Manfred Morari, Vivek Dua, and Efstratios N. Pistikopoulos. “The Explicit Linear Quadratic Regulator for Constrained Systems.” Automatica 38, no. 1 (January 2002): 3–20. doi:10.1016/s0005-1098(01)00174-1.

Hrovat, D., S. Di Cairano, H.E. Tseng, and I.V. Kolmanovsky. “The Development of Model Predictive Control in Automotive Industry: A Survey.” 2012 IEEE International Conference on Control Applications (October 2012). doi:10.1109/cca.2012.6402735.

Alessio, Alessandro, and Alberto Bemporad. “A Survey on Explicit Model Predictive Control.” Lecture Notes in Control and Information Sciences (2009): 345–369. doi:10.1007/978-3-642-01094-1_29..

Quanser Inc. (2011). SRV02 rotary servo base unit. User Manual.

Ettefagh, Massoud Hemmasian, José De Doná, Mahyar Naraghi, and Farzad Towhidkhah. “Control of Constrained Linear-Time Varying Systems via Kautz Parametrization of Model Predictive Control Scheme.” Emerging Science Journal 1, no. 2 (September 19, 2017): 65. doi:10.28991/esj-2017-01117.

Bazaraa, M. S., Sherali, H. D., & Shetty, C. M., Nonlinear programming: theory and algorithms. (2013), John Wiley & Sons.

Mayne, D.Q., J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert. “Constrained Model Predictive Control: Stability and Optimality.” Automatica 36, no. 6 (June 2000): 789–814. doi:10.1016/s0005-1098(99)00214-9.

Baotić, Mato, Francesco Borrelli, Alberto Bemporad, and Manfred Morari. “Efficient On-Line Computation of Constrained Optimal Control.” SIAM Journal on Control and Optimization 47, no. 5 (January 2008): 2470–2489. doi:10.1137/060659314.

Geyer, Tobias, Fabio D. Torrisi, and Manfred Morari. “Optimal Complexity Reduction of Polyhedral Piecewise Affine Systems.” Automatica 44, no. 7 (July 2008): 1728–1740. doi:10.1016/j.automatica.2007.11.027.

Bemporad, A., and C. Filippi. “Suboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming.” Journal of Optimization Theory and Applications 117, no. 1 (April 2003): 9–38. doi:10.1023/a:1023696221899.

Lofberg, J. “YALMIP : a Toolbox for Modeling and Optimization in MATLAB.” 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) (2004). doi:10.1109/cacsd.2004.1393890.

Kvasnica, Michal, Pascal Grieder, Mato Baotić, and Manfred Morari. “Multi-Parametric Toolbox (MPT).” Lecture Notes in Computer Science (2004): 448–462. doi:10.1007/978-3-540-24743-2_30.

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DOI: 10.28991/esj-2019-01177


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