Design of robust proportional–integral–derivative controller for generalized decoupled twin rotor multi-input-multi-output system with actuator non-linearity

Abstract

This work addresses the problem of robust stabilization of twin rotor multi-input-multi-output system in the presence of inherent actuator non-linearity and plant structured uncertainties due to parameter variation. In order to achieve so, first a generalized decoupling technique is implemented to eliminate the cross coupling effect which are present in between the input and output of main and tail rotors of twin rotor multi-input-multi-output system. Next, two proportional–integral–derivative controllers are employed to control the main and tail rotors independently. The ranges of the parameters of the controllers are evaluated based on the Kharitonov theorem so as to ensure robust stability in the presence of structured uncertainties. The values of the controller parameters are finally sought out of these robust ranges with bacterial foraging optimization technique such that satisfactory time domain criteria are met. Furthermore, the compensated system is analyzed in frequency domain with common actuator non-linearity dead-zone and saturation together. The performance of the designed controller is evaluated through both simulation and experimental results. The controllers are found to perform efficiently ensuring adequate robust stability even in the presence of uncertainty, disturbance and actuator non-linearity.

Keywords

Twin rotor multi-input-multi-output system proportional–integral–derivative controller Kharitonov’s theorem actuator non-linearity dead-zone saturation robust stability

Get full access to this article

View all access options for this article.

References

Twin rotor MIMO system, user manual (control experiments) 33-949S. Crowborough: Feedback Instruments Ltd, 1998.

Pradhan

Ghosh

. Design and implementation of decoupled compensation for a twin rotor multiple-input and multiple-output system. IET Control Theory A 2013; 7(2): 282–289.

Chelihi

Chemachema

. Model reference adaptive control for twin rotor multiple-input and multiple-output system via minimal controller synthesis. Proc IMechE, Part I: J Systems and Control Engineering 2014; 228(6): 406–418.

Ahmad

Chipperfield

Tokhi

. Dynamic modeling and open-loop control of a twin rotor multi-input multi-output system. Proc IMechE, Part I: J Systems and Control Engineering 2002; 216: 477–496.

Rahideh

Shaheed

. Mathematical dynamic modeling of a twin-rotor multiple input-multiple output system. Proc IMechE, Part I: J Systems and Control Engineering 2006; 221: 89–101.

Wen

. Decoupling control of twin rotor MIMO system using robust deadbeat control technique. IET Control Theory A 2008; 2(11): 999–1007.

Saroj

Kar

Pandey

. Sliding mode controller design for twin rotor MIMO system with a nonlinear state observer. In: Proceedings of the international multi-conference on automation, computing, communication, control and compressed sensing, Kottayam, India, 22–23 March 2013, pp.668–673. New York: IEEE.

Jahed

Farrokhi

. Robust adaptive fuzzy control of twin rotor MIMO system. Soft Comput 2013; 17(10): 1847–1860.

Wei

Grimble

. Robust MIMO control-system design using eigenstructure assignment and QFT. IEEE Proc: Control Theory Appl 2004; 151(2): 198–209.

10.

Bhattacharyya

Chapellat

Keel

. Robust control: the parametric approach. Englewood Cliffs, NJ: Prentice-Hall, 1995.

11.

Kharitonov

. Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Diff Equat 1979; 14: 1483–1485.

12.

Leena

Ray

. A set of decentralized PID controllers for n-link robot manipulator. Sadhana 2012; 37(3): 405–423.

13.

Chen

. Automatic design of robust optimal controller for interval plants using genetic programming and Kharitonov theorem. Int J Comput Int Sys 2012; 4(5): 826–836.

14.

Qiao

Luo

. Robust PID controller tuning for uncertain systems based on the constrained Kharitonov’s theorem genetic algorithm. J Comput Inform Syst 2015; 11(9): 3195–3202.

15.

Pandey

Dey

Banerjee

. Design and real-time implementation of robust PID controller for twin rotor MIMO System (TRMS) based on Kharitonov’s theorem. In: Proceedings of the 1st international conference on power electronics, intelligent control and energy systems, Delhi, India, 4–6 July 2016. New York: IEEE.

16.

Zhao

Zheng

Gao

. On model-free accommodation of actuator nonlinearities. In: Proceedings of the 10th world congress on intelligent control and automation, Beijing, China, 6–8 July 2012. New York: IEEE.

17.

Corradini

Orlando

Parlangeli

. Robust stabilization of nonlinear plants with uncertain hysteresis-like actuator nonlinearities. In: Proceedings of the European control conference, Cambridge, 1–4 September 2003. New York: IEEE.

18.

Liu

. Adaptive RBF neural network control of robot with actuator nonlinearities. J Control Theor Appl 2010; 8: 249–256.

19.

Srang

Yamakita

. Tracking control of nonlinear stochastic systems with actuator nonlinearity. In: Proceedings of the international conference on advanced intelligent mechatronics, Besancon, 8–11 July 2014. New York: IEEE.

20.

Corradini

Orlando

. Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator. IEEE T Contr Syst T 2002; 10: 158–166.

21.

Chen

Lee

Peng

et al . Composite nonlinear feedback control for linear systems with input saturation: theory and an application. IEEE T Automat Contr 2003; 48: 427–439.

22.

Zhao

Shi

Zheng

et al . Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica 2015; 60: 193–200.

23.

Wang

Chen

Liu

et al . Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE T Cybernetics 2013; 43: 2093–2104.

24.

Chen

Liu

et al . Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone. IEEE T Fuzzy Syst 2014; 22: 237–248.

25.

Zhao

Yang

Xia

et al . Adaptive fuzzy hierarchical sliding-mode control for a class of MIMO nonlinear time-delay systems with input saturation. IEEE T Fuzzy Syst 2016; 25: 1062–1077.

26.

Wang

Xiaoping

Liu

. Adaptive neural synchronization control for bilateral teleoperation systems with time delay and backlash-like hysteresis. IEEE T Cybernetics 2017; 47: 3018–3026.

27.

Veluvolu

. Multivariable control for MIMO processes, 2015, http://ncbs.knu.ac.kr/Teaching/MCS_Files/Handouts_Part4.pdf

28.

Gaing

. A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE T Energy Conver 2004; 19(2): 384–391.

29.

Dang

et al . Analysis and improvement of the bacterial foraging optimization algorithm. J Comput Sci Eng 2014; 8(1): 1–10.