APSO Based Weighting Matrices Selection of LQR Applied to Tracking Control of SIMO System

  • S. Karthick
  • Jovitha Jerome
  • E Vinodh Kumar
  • G Raaja
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 43)

Abstract

This paper employs an adaptive particle swarm optimization (APSO) algorithm to solve the weighting matrices selection problem of linear quadratic regulator (LQR). One of the important challenges in the design of LQR for real time applications is the optimal choice state and input weighting matrices (Q and R), which play a vital role in determining the performance and optimality of the controller. Commonly, trial and error approach is employed for selecting the weighting matrices, which not only burdens the design but also results in non-optimal response. Hence, to choose the elements of Q and R matrices optimally, an APSO algorithm is formulated and applied for tracking control of inverted pendulum. One of the notable changes introduced in the APSO over conventional PSO is that an adaptive inertia weight parameter (AIWP) is incorporated in the velocity update equation of PSO to increase the convergence rate of PSO. The efficacy of the APSO tuned LQR is compared with that of the PSO tuned LQR. Statistical measures computed for the optimization algorithms to assess the consistency and accuracy prove that the precision and repeatability of APSO is better than those of the conventional PSO.

Keywords

APSO LQR Inverted pendulum Riccati equation Tracking control 

References

  1. 1.
    Wang, L., Ni, H., Zhou, W., Pardalos, P.M., Fang, J., Fei, M.: MBPOA-based LQR controller and its application to the double-parallel inverted pendulum system. Eng. Appl. Artif. Intell. 36, 262–268 (2014)CrossRefGoogle Scholar
  2. 2.
    Ang, K.K., Wang, S.Y., Quek, S.T.: Weighted energy linear quadratic regulator vibration control of piezoelectric composite plates. J. Smart Mater. Struct. 11(1), 98–106 (2002)CrossRefGoogle Scholar
  3. 3.
    Niknezhadi, A., Miguel, A.F., Kunusch, C., Carlos, O.M.: Design and implementation of LQR/LQG strategies for oxygen stoichiometry control in PEM fuel cells based systems. J. Power Sources 196(9), 4277–4282 (2011)CrossRefGoogle Scholar
  4. 4.
    Usta, M.A., Akyazi, O., Akpinar, A.S.: Aircraft roll control system using LQR and fuzzy logic controller. In: IEEE Conference on Innovations in Intelligent Systems and Applications (INISTA), pp. 223–227. Istanbul (2011)Google Scholar
  5. 5.
    Solihin, M.I., Akmeliawati, R.: Particle swam optimization for stabilizing controller of a self-erecting linear inverted pendulum. Int. J. Electr. Electron. Syst. Res. 3, 410–415 (2010)Google Scholar
  6. 6.
    Panda, S., Padhy, N.P.: Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design. Appl. Soft Comput. 8(4), 1418–1427 (2008)CrossRefGoogle Scholar
  7. 7.
    Tsai, S.J., Huo, C.L., Yang, Y.K., Sun, T.Y.: Variable feedback gain control design based on particle swarm optimizer for automatic fighter tracking problems. Appl. Soft Comput. 13, 58–75 (2013)CrossRefGoogle Scholar
  8. 8.
    Lim, W.H., Isa, N.A.M.: Teaching and peer-learning particle swarm optimization. Appl. Soft Comput. 18, 39–58 (2014)CrossRefGoogle Scholar
  9. 9.
    Nickabadi, A., Ebadzadeh, M.M., Safabakhsh, R.: A novel particle swarm optimization algorithm with adaptive inertia weight. Appl. Soft Comput. 11, 3658–3670 (2011)CrossRefGoogle Scholar
  10. 10.
    Vinodh Kumar, E., Jovitha, J.: Stabilizing controller design for self erecting single inverted pendulum using robust LQR. Aust. J. Basic Appl. Sci. 7(7), 494–504 (2013)Google Scholar

Copyright information

© Springer India 2016

Authors and Affiliations

  • S. Karthick
    • 1
  • Jovitha Jerome
    • 1
  • E Vinodh Kumar
    • 2
  • G Raaja
    • 1
  1. 1.Department of Instrumentation and Control Systems EngineeringPSG College of TechnologyCoimbatoreIndia
  2. 2.School of Electrical EngineeringVIT UniversityVelloreIndia

Personalised recommendations