In this paper, a combination of approximate feedback linearization and sliding mode control approaches is applied to stabilize a class of fourth-order nonlinear systems. In order to improve the performance of the proposed controller, design parameters of the sliding surface are adjusted using the adaptation laws, based on the gradient descent technique. Eventually, a new version of particle swarm optimization is implemented to optimize the control gains with respect to the integral of time-weighted absolute errors as the objective function, and a constraint on the maximum control effort value. The introduced idea is put into practice for the under-actuated inverted pendulum system, and the procedure is described with details step by step. The time responses of cart position, pendulum angle, and control effort of the proposed method is then compared with those of several recently published references so as to evaluate the effectiveness of this scenario.
AkayBKarabogaD (2012) A modified artificial bee colony algorithm for real-parameter optimization. Information Sciences192(1): 120–142.
2.
Andalib SahnehsaraeiMMahmoodabadiMBagheriA (2014) Pareto optimum control of a 2-DOF inverted pendulum using approximate feedback linearization and sliding mode control. Transactions of the Institute of Measurement and Control36(4): 496–505.
BayramogluHKomurcugilH (2014) Time-varying sliding-coefficient-based decoupled terminal sliding-mode control for a class of fourth-order systems. ISA Transactions53(4): 1044–1053.
CermanOHušekP (2012) Adaptive fuzzy sliding mode control for electro-hydraulic servo mechanism. Expert Systems with Applications39(11): 10269–10277.
7.
ChenYWenC (2010) Design of controller for inverted pendulum. In: Proceedings of IEEE International Symposium on Computer, Communication, Control and Automation, Tainan, Taiwan, 5–7 May 2010, pp. 231–233. IEEE.
8.
CoelhoLDSSouzaRCTMarianiVC (2009) Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems. Mathematics and Computers in Simulation79(10): 3136–3147.
9.
CuiRGuoJMaoZ (2015) Adaptive backstepping control of wheeled inverted pendulums models. Nonlinear Dynamics79(1): 501–511.
10.
DadrasSMomeniHR (2012) Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty. Communications in Nonlinear Science and Numerical Simulation17(1): 367–377.
11.
EberhartRCKennedyJ (1995) A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, Japan, 4–6 October 1995, pp. 39–43. New York, NY: IEEE.
12.
GaoSDongHNingBChenL (2015b) Neural adaptive control for uncertain nonlinear system with input saturation: State transformation based output feedback. Neurocomputing159(1): 117–125.
13.
GaoXZLuoWCHouZX (2009) Application of an improved PSO algorithm in solving constrained optimization problem. Computer Simulation10(1): 1–10.
14.
GaoYWangHLiuYJ (2015a) Adaptive fuzzy control with minimal leaning parameters for electric induction motors. Neurocomputing156(1): 143–150.
15.
HamidaMAGlumineauALeonJDLoronL (2014) Robust adaptive high order sliding-mode optimum controller for sensorless interior permanent magnet synchronous motors. Mathematics and Computers in Simulation105(1): 79–104.
16.
HarrisonRF (2003) Asymptotically optimal stabilising quadratic control of an inverted pendulum. IEE Proceedings - Control Theory and Applications150(1): 7–16.
17.
HollandJH (1968) Hierarchical descriptions of universal spaces and adaptive systems. Technical Report ORA Projects, Ann Arbor University of Michigan, Department of Computer and Communication Sciences.
18.
HuangSHuangC (2000) Control of an inverted pendulum using gray prediction model. IEEE Transactions on Industry Applications36(2): 452–458.
19.
KalmanRE (1958) Design of a self-optimizing control system, Transactions of the American Society of Mechanical Engineers80(2): 468–478.
20.
KarabogaD (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department.
21.
KhalilHKGrizzleJ (1996) Nonlinear Systems. vol. 3. New Jersey: Prentice Hall.
22.
LeeDKimHJSastryS (2009) Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. International Journal of Control, Automation and Systems7(3): 419–428.
MahmoodabadiMJArabani MostaghimSBagheriANariman-ZadehN (2013) Pareto optimal design of the decoupled sliding mode controller for an inverted pendulum system and its stability simulation via Java programming. Mathematical and Computer Modelling57(5–6): 1070–1082.
25.
MahmoodabadiMJSalahshoor MottaghiZBagheriA (2014) HEPSO: High exploration particle swarm optimization. Information Sciences273(1): 101–111.
26.
MahmoodabadiMJTaherkhorsandiMTalebipourMCastillo-VillarK (2015) Adaptive robust PID control subject to supervisory decoupled sliding mode control based upon genetic algorithm optimization. Transactions of the Institute of Measurement and Control37(4): 505–514.
27.
MaitiDAcharyaAChakrabortyM, et al. (2008) Tuning PID and PIλDδ controllers using the integral time absolute error criterion. In: Proceedings of IEEE 4th International Conference on Information and Automation for Sustainability, Colombo, Sri Lanka, USA, 4–9 May 1998, pp. 457–462. IEEE.
28.
MatasJVicunaLGDMiretJGuerreroJMCastillaM (2008) Feedback linearization of a single-phase active power filter via sliding mode control. IEEE Transactions on Power Electronics23(1): 116–125.
29.
MobayenSMajdVJSojoodiM (2012) An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems. Mathematics and Computers in Simulation85(1): 1–10.
30.
OrioloGLucaADVendittelliM (2002) WMR control via dynamic feedback linearization: Design, implementation, and experimental validation. IEEE Transactions on Control Systems Technology10(6): 835–852.
31.
RatnaweeraAHalgamugeSKWatsonHC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficient. IEEE Transactions on Evolutionary Computation8(3): 240–255.
32.
RincónAPiarpuzánDAnguloF (2015) A new adaptive controller for bio-reactors with unknown kinetics and biomass concentration: Guarantees for the boundedness and convergence properties. Mathematics and Computers in Simulation112(1): 1–13.
33.
ShiW (2015) Adaptive fuzzy control for multi-input multi-output nonlinear systems with unknown dead-zone inputs. Applied Soft Computing30(1): 36–47.
34.
ShiYEberhartR (1998) A modified particle swarm optimizer. In: Proceedings of IEEE World Congress on Computational Intelligence, Anchorage, AK, USA, USA, 12–14 December 2008, pp. 69–73. IEEE.
35.
ShinSYLeeJJ (2010) Fuzzy sliding mode control for an under-actuated system with mismatched uncertainties. Artificial Life and Robotics15(3): 355–358.
SuXXiaFLiuJWuL (2018) Event-triggered fuzzy control of nonlinear systems with its application to inverted pendulum systems. Automatica94(1): 236–248.
38.
TaherkhorsandiMMahmoodabadiMJTalebipourMCastillo-VillarK (2014) Pareto design of an adaptive robust hybrid of PID and sliding control for a biped robot via genetic algorithm optimization. Nonlinear Dynamics79(1): 251–263.
39.
UtkinVI (1978) Sliding Modes and their Application in Variable Structure Systems. Moscow: Mir Publishers.
40.
WangJJ (2011) Simulation studies of inverted pendulum based on PID controllers. Simulation Modelling Practice and Theory19(1): 440–449.
41.
WangJJ (2012) Stabilization and tracking control of X -Z inverted pendulum with sliding-mode control. ISA Transactions51: 763–770.
42.
WhitakerHPYamronJKezerA (1958) Design of model-reference adaptive control systems for aircraft. Massachusetts Institute of Technology, Instrumentation Laboratory, Jackson & Moreland.
43.
XiaYZhuZLiC, et al. (2010) Robust adaptive sliding mode control for uncertain discrete-time systems with time delay. Journal of the Franklin Institute347(1): 339–357.
44.
YamadaKNittaKYuzawaA (2003) A Nonlinear Control Design for the Pendubot. In: Proceedings of the 22nd IASTED International Conference on Modelling, Identification, and Control, Innsbruck, Austria.
45.
ZhongWRockH (2001) Energy and passivity based control of the double inverted pendulum on a cart. In: Proceedings of the 2001 IEEE International Conference on Control Applications, Mexico City, Mexico, 7 September 2001, pp. 896–901. IEEE.
