Combining Sliding Mode and Linear Quadratic Regulator to Control the Inverted Pendulum

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


The main limitation of the optimal control is the requirement of complete system   knowledge, this leads to the high sensitivity to parametric uncertainties and exogenous perturbations. A possible solution to this problem is to introduce a sliding mode control (SMC), well known for its robustness to uncertainties and disturbances, into optimal control whenever the uncertainties are present. This can make optimal control more robust and applicable to real systems. Though SMC and optimal control are two control strategies, it is possible integrate them together. In this work, combining (SMC) and linear quadratic regulator (LQR) will be analyzed, designed and applied to the so-called Inverted pendulum with and without disturbances. The simulations results will be compared to the pole placement approach. All simulations will be done using Matlab/Simulink.
Copyright © 2013 Praise Worthy Prize - All rights reserved.


Optimal Control; Sliding Mode Control (SMC); Linear Quadratic Regulator (LQR); Inverted Pendulum; Pole Placement; Ackermann’s Formula

Full Text:



W. Chen Yu, G. Jen Wang, Discrete sliding mode controller based on The suboptimal LQR approach, International mechanical Engineering DC congress, November 16-21, 2003, Washington DC.

X. Ding, A. Sinha, Sliding mode /H∞ control of a hydro-power plant, American control conference, pp 5201-5206, July 2011.

S. Rudha, Robust adaptive backstepping control of the inverted pendulum on cart system, International journal of control and automation, vol 5, n1 march 2012.pp 354-363.

P. Bhavsar, Trajectory tracking of linear inverted pendulum using integral sliding mode control, International journal intelligent systems and applications, vol 6, pp. 31-38, 2012.

H.Ngoc Nguyen,T. Dinh, Control of inverted pendulum using sliding mode technique, Proceeding of the 1st conference on sciences and technology Iss-Hutech, pp. 157-162, 2010.

H. Klee, R, Allen, Simulation of dynamic systems with Matlab and Simulink, (CRC press, Second edition , 2011).

K. Ogata, Modern control engineering, (third edition, university of Minnesota, Prentice Hall, 1997).

V. Utkin, Variable structure systems with sliding mode, IEEE trans, Auto, Con., vol 22, No 2, 1997.

J. Ackermann, V. Utkin, Sliding mode control design based on Ackermann’s formula, IEEE trans, Auto, con, Vol. 43, (No. 2, feb 1998).

S.Rotger Gritful, Modelling of an inverted pendulum, thesis, Korgens Lyngby, IMM-M.Sc, university of Denmark 2012.

H.Alwi, C.Edwards, C.Pin Tan, Fault detection and fault tolerant control using sliding modes, (Springer, 2011)


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize