In this article, an adaptive control logic is proposed to serve as a supervisory control system sufficient to curb the adverse effects due to modelling uncertainties and external disturbances. The control logic belongs to the class of adaptive control methodologies. The attractive attribute of this technique is that only the superior features of each individual candidate controller are obtained by applying appropriate weight to these controllers. In order to prove its effectiveness and applicability, the benchmark problem for stabilization of cart-inverted pendulum system is carried out using this technique. The system performance is tried against that with each individual candidate controllers existing techniques. In addition, the simulation-based analysis is strengthened by analysing the performance of a real-time cart-inverted pendulum system setup, stabilized using the proposed control logic.
WhitakerHPYamronJKezerA.Design of model-reference adaptive control systems for aircraft. Technical Report, MIT Instrumentation Laboratory, Cambridge, MA, 1958.
6.
KalmanRE.Design of a self-optimizing control systems. Trans ASME1958; 80(1): 468–478.
7.
MiddletonRHGoodwinGCHillDJet al. Design issues in adaptive control. IEEE T Automat Contr1988; 33(1): 50–58.
8.
KoutsoukosXDAntsaklisPJStiverJAet al. Supervisory control of hybrid systems. P IEEE2000; 88(7): 1026–1049.
9.
IoannouPAFidanB.Adaptive control tutorial. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2006.
10.
SaridisGNMendelJMNikolicZZ.Report on definitions of self-organizing control processes and learning systems. IEEE Contr Syst Soc Newsl1973.
11.
RughWJShammaJS.Research on gain scheduling. Automatica2000; 36(10): 1401–1425.
12.
ShammaJAthansM.Analysis of gain scheduled control for nonlinear plants. IEEE T Automat Contr1990; 35(8): 898–907.
13.
ÅströmKHägglundT.The future of PID control. Control Eng Pract2001; 9(11): 1163–1175.
14.
FurutaKYamakitaMKobayashiS.Swing-up control of inverted pendulum using pseudo-state feedback. Proc IMechE, Part I: J Systems and Control Engineering1992; 206(4): 263–269.
15.
OgataK.Modern control engineering. Upper Saddle River, NJ: Prentice Hall, 2010.
16.
YuHLiuYYangT.Closed-loop tracking control of a pendulum-driven cart-pole underactuated system. Proc IMechE, Part I: J Systems and Control Engineering2008; 222(2): 109–125.
17.
IshitobiMOhtaYNishiokaYet al. Swing-up of a cartpendulum system with friction by energy control. Proc IMechE, Part I: J Systems and Control Engineering2004; 218(5): 411–415.
18.
BoubakerO.The inverted pendulum benchmark in nonlinear control theory: a survey. Int J Adv Robot Syst2013; 10(5): 233–242.
19.
AdhikaryNMahantaC.Integral backstepping sliding mode control for under-actuated systems: swing-up and stabilization of the Cart-Pendulum System. ISA T2013; 52(6): 870–880.
20.
SahnehsaraeiMAMahmoodabadiMBagheriA.Pareto optimum control of a 2-DOF inverted pendulum using approximate feedback linearization and sliding mode control. T I Meas Control2014; 36(4): 496–505.
21.
LiM.Digital double-loop PID controller for inverted pendulum. Sens Transducer2013; 156(9): 324–329.
22.
MishraSKChandraD.Stabilization of inverted cart-pendulum system using PID controller: a frequency-domain approach. Chinese J Eng2013; 2013: 962401.
23.
MishraSKChandraD.Stabilization and tracking control of inverted pendulum using fractional order PID controllers. J Eng Hindawi2014; 2014: 752918.
24.
TeixeiraMZakS.Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE T Fuzzy Syst1999; 7(2): 133–142.
25.
BhushanBKValluruSSinghM.Takagi-Sugeno fuzzy system based stable direct adaptive control of nonlinear systems. Int J Comput Appl2013; 68(15): 30–36.
26.
Aguilar-IbáñezCMendoza-MendozaJDávilaJ.Stabilization of the cart pole system: by sliding mode control. Nonlinear Dynam2014; 78(4): 2769–2777.
PatnaikABeheraL. Evolutionary multiobjective optimization based control strategies for an inverted pendulum on a cart. In: 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence), Hong Kong, China, 1–6June2008, pp.3141–3147. New York: IEEE.
29.
YuLFeiSQianW.Robust adaptive control for single input/single output discrete systems via multi-model switching. Proc IMechE, Part I: J Systems and Control Engineering2014; 228(1): 42–48.
30.
AngeliDMoscaE.Adaptive switching supervisory control of nonlinear systems with no prior knowledge of noise bounds. Automatica2004; 40(3): 449–457.
31.
BattistelliGHespanhaJPMoscaEet al. Model-free adaptive switching control of time-varying plants. IEEE T Automat Contr2013; 58(5): 1208–1220.
32.
XiangZRWangRHChenQW.Robust stabilization of uncertain stochastic switched non-linear systems under asynchronous switching. Proc IMechE, Part I: J Systems and Control Engineering2011; 225(1): 8–20.
33.
DoustiMBaslamsliSCOnderETet al. Design of a multiple-model switching controller for ABS braking dynamics. T I Meas Control2015; 37(5): 582–595.
KoshkoueiAJNowakL.Stabilisation of ship roll motion via switched controllers. Ocean Eng2012; 49: 66–75.
36.
ChaoITuKLinSet al. Design and implementation of a switching controller for transient improvement in a time synchronization system. IEEE T Instrum Meas2011; 60(7): 2184–2190.
37.
SaikrishnaPSPasumarthyR.Multi-objective switching controller for cloud computing systems. Control Eng Pract2016; 57: 72–83.
38.
ChiuC.The design and implementation of a wheeled inverted pendulum using an adaptive output recurrent cerebellar model articulation controller. IEEE T Ind Electron2010; 57(5): 1814–1822.
39.
HanwateSHoteYVSaxenaS.Adaptive policy for load frequency control. IEEE T Power Syst2018; 33(1): 1142–1144.
40.
XieW.H∞ performance realisation and switching controller design for linear time-invariant plant. IET Control Theory A2016; 10(4): 424–430.
41.
ValluruSKSinghM.Stabilization of nonlinear inverted pendulum system using MOGA and APSO tuned nonlinear PID controller. Cogent Eng2017; 4(1): 1357314.
42.
GhoshAKrishnanTRSubudhiB.Robust proportional-integral-derivative compensation of an inverted cart-pendulum system: an experimental study. IET Control Theory A2012; 6(8): 1145–1152.
43.
TanNKayaIYerogluCet al. Computation of stabilizing PI and PID controllers using the stability boundary locus. Energ Convers Manage2006; 47(1819): 3045–3058.
44.
HanwateSDHoteYV.Relative stability analysis of perturbed cart inverted pendulum: an experimental approach. IETE Tech Rev2018; 38(6): 640–655.
45.
Digital Pendulum Control Experiments Manual. Crowborough: Feedback Instruments Ltd, 2002.
RajputJWeiguoZ.Fundamental methodologies for control of nonlinear nonminimum-phase systems: an overview. Proc IMechE, Part I: J Systems and Control Engineering2014; 228(8): 553–564.
