Skip to main content
Log in

Synthesis and Implementation of a Robust Fixed Low-Order Controller for Uncertain Systems

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Advancements in microelectronics and software allow the use of embedded systems in the implementation of some control laws. In this work, the STM32 microcontroller is exploited in order to implement a robust fixed low-order controller on an electronic system. Parametric uncertainty model is employed to describe the system behavior, and the controller objective is to guarantee some time response specifications in the presence of model uncertainties. The controller design is expressed as a min-max non-convex optimization problem while taking into account the desired closed-loop performances and uncertainties. Accordingly, with the aim of obtaining an optimal solution and then an optimal control law, the application of a global optimization method is recommended. In this work, the exploited global optimization method is the generalized geometric programming. The implementation of a proportional integral controller, a proportional integral derivative controller and the fixed low-order controller shows the efficiency of the latter one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hongyan G., Hong C., Fang X., Fei W., Geyu L.: Implementation of EKF for vehicle velocities estimation on FPGA. IEEE Trans. Ind. Electron. 60(9), 645–658 (2013)

    Google Scholar 

  2. Nascimento P.S.B., DeSouza H.E.P., Neves F.A.S., Limongi L.R.: FPGA Implementation of the generalized delayed signal cancelation phase locked loop method for detecting harmonic sequence components in three-phase signals. IEEE Trans. Ind. Electron. 60(2), 645–658 (2013)

    Article  Google Scholar 

  3. Ling, K.V.; Yue, S.P.; Maciejowski, J.M.: A FPGA implementation of model predictive control. In: IEEE Proceedings of the American Control Conference, pp. 1930–1935 (2006)

  4. Jayaraman Y., Ravindran U.: FPGA implementation of predictive control strategy for power factor correction. World Acad. Sci. Eng. Technol. 15(1), 199–204 (2008)

    Google Scholar 

  5. Ling, K.; Wu, B.; Maciejowski, J.: Embedded model predictive control (MPC) using a FPGA. In: Proceedings of the 17th World Congress the International Federation of Automatic Control, pp. 15250–15255, IFAC (2008)

  6. Curkovic M., Karel J., Horvat R.: FPGA-Based Predictive Sliding Mode Controller of a Three-Phase Inverter. IEEE Trans. Ind. Electron. 60(2), 637–644 (2013)

    Article  Google Scholar 

  7. Zhen, Z.; Yan, G.: Design of the fuzzy PID controller for the hot runner temperature control system. In: IEEE Proceedings of the 32nd Chinese Control Conference, pp. 3464–3469 (2013)

  8. Lian J.: The Design of Gas Drainage Holes’ Opening Parameters Intelligent Measurement and Control System for Coal Mine. Proc. Earth Planet. Sci. 3(1), 331–337 (2011)

    Article  Google Scholar 

  9. Wang K., Li P., Liu J., Ning D.: Application of \({\mu}\) c/os-II in the Design of Mine dc Electrical Prospecting Instrument. Proc. Earth Planet. Sci. 3(1), 485–492 (2011)

    Article  Google Scholar 

  10. Zhang H., Kang W.: Design of the data acquisition system based on STM32. Proc. Comput. Sci. 17(1), 222–228 (2013)

    Article  Google Scholar 

  11. Zhang, H.; Zhao, J.: The design of RF data acquisition system based on STM32 and FPGA. In: IEEE Proceedings of the International Conference on Multimedia Technology, pp. 832–834 (2011)

  12. Ben Hariz, M.; Bouani, F.; Ksouri, M.: Design of a Controller with Time Response Specifications on STM32 Microcontroller, Azar, A.T.; Vaidyanathan, S.; Handbook of Research on Advanced Intelligent Control Engineering and Automation. Advances in Computational Intelligence and Robotics (ACIR) Book Series, pp. 624–650, IGI Global, USA (2015)

  13. Toksari M.D.: Minimizing the multimodal functions with Ant Colony Optimization approach. Expert Syst. Appl. 36(3), 6030–6035 (2009)

    Article  MathSciNet  Google Scholar 

  14. Liu C.H., Hsu Y.Y.: Design of a self-tuning PI controller for a STATCOM using particle swarm optimization. IEEE Trans. Ind. Electron. 57(2), 702–715 (2010)

    Article  Google Scholar 

  15. Toledo C.F.M., Oliveira L., Frana P.M.: Global optimization using a genetic algorithm with hierarchically structured population. J. Comput. Appl. Math. 261(1), 341–351 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mamdoohi G., Abas A.F., Samsudin K., Ibrahim N.H., Hidayat A., Mahdi M.A.: Implementation of genetic algorithm in an embedded microcontroller based polarization control system. Eng. Appl. Artif. Intel. 25(4), 869–873 (2012)

    Article  Google Scholar 

  17. El-Said, M.H.F.: Application of genetic algorithms for the estimation of ultrasonic parameters. In: Azar, A.T.; Vaidyanathan, S. (eds.) Computational Intelligence applications in Modeling and Control. Studies in Computational Intelligence, pp. 55–72. Springer, Germany (2015)

  18. Valdez F., Melin P., Castillo O.: Modular neural networks architecture optimization with a new nature inspired method using a fuzzy combination of particle swarm optimization and genetic algorithms. Inform. Sci. 270(20), 143–153 (2014)

    Article  Google Scholar 

  19. Taherkhorsandi, M.; Castillo-Villar, K.K.; Mahmoodabadi, M.J.; Janaghaei, F.; Mortazavi Yazdi, S.M.: Optimal sliding and decoupled sliding mode tracking control by multi-objective particle swarm optimization and genetic algorithms. In: Azar, A.T.; Zhu, Q. (eds.) Advances and Applications in Sliding Mode Control systems. Studies in Computational Intelligence, pp. 43–78. Springer, Germany (2015)

  20. Andalib Sahnehsaraei, M.; Mahmoodabadi, M.J.; Taherkhorsandi, M.; Castillo-Villar, K.K.; Mortazavi Yazdi, S.M.: A hybrid global optimization algorithm: particle swarm optimization in association with a genetic algorithm. In: Zhu, Q.; Azar, A.T. (eds.) Complex System Modelling and Control Through Intelligent Soft Computations. Studies in Fuzziness and Soft Computing., pp. 45–86. Springer, Germany (2015)

  21. Boulkroune, A.; Bouzeriba, A.; Hamel, S.: Projective synchronization scheme based on Fuzzy controller for uncertain multivariable chaotic systems. In: Azar, A.T.; Vaidyanathan, S. (eds.) Chaos Modeling and Control Systems Design, Studies in Computational Intelligence., pp. 73–93. Springer, Berlin (2015)

  22. Ramirez D.R., Arahal M.R., Camacho E.F.: Minmax predictive control of a heat exchanger using a neural network solver. IEEE Trans. Control Syst. Technol. 12(5), 776–786 (2004)

    Article  Google Scholar 

  23. Zafiriou E.: Robust model predictive control of processes with hard constraints. Comput. Chem. Eng. 14(4), 359–371 (1990)

    Article  Google Scholar 

  24. Wu C., Teo K.L., Wu S.: Minmax optimal control of linear systems with uncertainty and terminal state constraints. Automatica 49(6), 1809–1815 (2013)

    Article  MathSciNet  Google Scholar 

  25. Azar A.T., Serrano F.E.: Robust IMCPID tuning for cascade control systems with gain and phase margin specifications. Neural Comput. Appl. 25(5), 983–995 (2014)

    Article  Google Scholar 

  26. Gao Y., Chong K.T.: The explicit constrained min–max model predictive control of a discrete-time linear system with uncertain disturbances. IEEE Trans. Automat. Control 57(9), 2373–2378 (2012)

    Article  MathSciNet  Google Scholar 

  27. Jin L., Kim Y.C.: Fixed, low-order controller design with time response specifications using non-convex optimization. ISA Trans. 47(4), 429–438 (2008)

    Article  MathSciNet  Google Scholar 

  28. Ben Hariz M., Bouani F., Ksouri M.: Robust controller for uncertain parameters systems. ISA Trans. 51(5), 632–640 (2012)

    Article  Google Scholar 

  29. Ben Hariz, M.; Chagra, W.; Bouani, F.: Controllers design for MIMO systems with time response specifications. In: IEEE Proceedings of the International Conference on Control, Decision and Information Technologies (CoDIT), pp. 573–578 (2013)

  30. Ben Hariz M., Chagra W., Bouani F.: Synthesis of Controllers for MIMO Systems with Time Response Specifications. Int. J. Syst. Dyn. Appl. 3(3), 25–52 (2014)

    Google Scholar 

  31. Ben Hariz, M.; Bouani, F.: Design of controllers for decoupled TITO systems using different decoupling techniques. In: IEEE Proceedings of the 20th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 1116–1121 (2015)

  32. Kim Y.C., Keel L.H., Bhattacharyya S.P.: Transient response control via characteristic ratio assignment. IEEE Trans. Automat. Control 48(12), 2238–2244 (2003)

    Article  MathSciNet  Google Scholar 

  33. Kim, Y.; Kim, K.; Manabe, S.: Sensitivity of time response to characteristic ratios. In: IEEE Proceedings of the American Control Conference, pp. 2723–2728 (2004)

  34. Nand K.: Geometric programming based robot control design. Comput. Indust. Eng. 29(1), 631–635 (1995)

    Google Scholar 

  35. Choi J.C., Dennis L.: Effectiveness of a geometric programming algorithm for optimization of machining economics models. Comput. Oper. Res. 23(10), 957–961 (1996)

    Article  MATH  Google Scholar 

  36. Maranas C.D., Floudas C.A.: Global optimization in generalized geometric programming. Comput. Chem. Eng. 21(4), 351–369 (1997)

    Article  MathSciNet  Google Scholar 

  37. Porn R., Bjork K.M., Westerlund T.: Global solution of optimization problems with signomial parts. Discrete Optim. 5(1), 108–120 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. Tsai J.: Treating free variables in generalized geometric programming problems. Comput. Chem. Eng. 33(1), 239–243 (2009)

    Article  Google Scholar 

  39. Tsai J.F., Lin M.H., Hu Y.C.: On generalized geometric programming problems with non-positive variables. Eur. J. Oper. Res. 178(1), 10–19 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  40. Bjork K.M., Lindberg P.O., Westerlund T.: Some convexifications in global optimization of problems containing signomial terms. Comput. Chem. Eng. 27(5), 669–679 (2003)

    Article  Google Scholar 

  41. STMicroelectronics, Datasheet stm32f100x4, stm32f100x6, stm32f100x8, stm32f100xb Doc ID 16455 Rev 7, 2012, http://www.st.com

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maher Ben Hariz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ben Hariz, M., Bouani, F. Synthesis and Implementation of a Robust Fixed Low-Order Controller for Uncertain Systems. Arab J Sci Eng 41, 3645–3654 (2016). https://doi.org/10.1007/s13369-016-2247-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-016-2247-7

Keywords

Navigation