A novel multi-objective optimization algorithm for Pareto design of a fuzzy full state feedback linearization controller applied on a ball and wheel system
Restricted accessResearch articleFirst published online April, 2022
A novel multi-objective optimization algorithm for Pareto design of a fuzzy full state feedback linearization controller applied on a ball and wheel system
The control and stabilization of a ball and wheel system around the equilibrium point are challenging tasks because it is an underactuated, nonlinear, and open-loop unstable plant. In this paper, Pareto design of a Fuzzy Full State Feedback Linearization Controller (FFSFLC) for the ball and wheel system based upon a novel multi-objective optimization algorithm is introduced. To this end, at first, a full state feedback linearization approach is employed to stabilize the dynamics of the system. Next, appropriate fuzzy systems are determined to tune the control gains. Then, a new multi-objective optimization algorithm is utilized to promote the proposed control scheme. This optimization algorithm is a combination of Simulated Annealing (SA) and Artificial Bee Colony (ABC) approaches benefiting advantages of the non-dominated Pareto solutions. To evaluate the capabilities of the suggested algorithm, its optimal solutions of several standard test functions are compared with those of five renowned multi-objective optimization algorithms. The results confirm that the proposed hybrid algorithm yields closer non-dominated Pareto solutions to the true optimal Pareto front with shorter runtimes than other algorithms. After selecting proper objective functions, multi-objective optimization of FFSFLC for the ball and wheel system is performed, and the results are compared with previous works. Simulations illustrate that the proposed strategies can accurately converge the system states to the desired conditions and yield superior robustness against disturbance signals in comparison with former studies.
AhrariAAtaiAA (2010) Grenade explosion method: A novel tool for optimization of multimodal functions. Applied Soft Computing10(4): 1132–1140.
2.
AmmarA (2019) Performance improvement of direct torque control for induction motor drive via fuzzy logic-feedback linearization: Simulation and experimental assessment. The International Journal for Computation and Mathematics in Electrical and Electronic Engineering38(2): 672–692.
3.
AroraSSinghS (2017) An effective hybrid butterfly optimization algorithm with artificial bee colony for numerical optimization. International Journal of Interactive Multimedia and Artificial Intelligence4(4): 14–21.
4.
AskarzadehA (2016) A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm. Computers & Structures169: 1–12.
5.
AtashkariKNariman-ZadehNGölcüM, et al. (2007) Modelling and multi-objective optimization of a variable valve-timing spark-ignition engine using polynomial neural networks and evolutionary algorithms. Energy Conversion and Management48(3): 1029–1041.
6.
BouarroudjNBoukhetalaDBoudjemaF (2015) A hybrid fuzzy fractional order PID sliding-mode controller design using PSO algorithm for interconnected nonlinear systems. Journal of Control Engineering and Applied17(1): 41–51.
7.
BrajevicITubaM (2013) An upgraded artificial bee colony (ABC) algorithm for constrained optimization problems. Journal of Intelligent Manufacturing24: 729–740.
8.
CaiJWenCSuH, et al. (2017) Adaptive backstepping control for a class of nonlinear systems with non-triangular uncertainties. IEEE Transactions on Automatic Control62(10): 5220–5226.
9.
ChangW-D (2007) A multi-crossover genetic approach to multivariable PID controllers tuning. Expert Systems with Applications33(3): 620–626.
10.
ChenB-STsengC-SUangH-J (1999) Robustness design of nonlinear dynamic systems via fuzzy linear control. IEEE Transactions on Fuzzy Systems7(5): 571–585.
11.
ChienT-LChenC-CTsaiM-C, et al. (2010) Control of AMIRA’s ball and beam system via improved fuzzy feedback linearization approach. Applied Mathematical Modelling34(12): 3791–3804.
12.
Chun-FengWKuiLPei-PingS (2014) Hybrid artificial bee colony algorithm and particle swarm search for global optimization. Mathematical Problems in Engineering2014: 1–8.
13.
DebKPratapAAgarwalS, et al. (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation6(2): 182–197.
14.
DelavariHGhaderiRRanjbarA, et al. (2010) Fuzzy fractional order sliding mode controller for nonlinear systems. Communications in Nonlinear Sciences and Numerical Simulation15(4): 963–978.
15.
DhimanGKumarV (2017) Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications. Advances in Engineering Software114: 48–70.
16.
DingMLiuBWangL (2019) Position control for ball and beam system based on active disturbance rejection control. Systems Science & Control Engineering7(1): 97–108.
17.
DorigoMManiezzoVColorniA (1996) Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)26(1): 29–41.
18.
DuT-SKeX-TLiaoJ-G, et al. (2018) DSLC-FOA: Improved fruit fly optimization algorithm for application to structural engineering design optimization problems. Applied Mathematical Modelling55: 314–339.
19.
EberhartRKennedyJ (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, Nagoya, Japan, 4–6 October, pp. 39–43. Piscataway, NJ: IEEE.
20.
EjazMChenM (2018) Optimal backstepping control for a ship using firefly optimization algorithm and disturbance observer. Transactions of the Institute of Measurement and Control40(6): 1983–1998.
21.
El-BardiniMEl-NagarAM (2014) Inverted type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system. ISA Transactions53(3): 732–743.
22.
GaidhanePJNigamMJ (2018) A hybrid grey wolf optimizer and artificial bee colony algorithm for enhancing the performance of complex systems. Journal of Computational Science27: 284–302.
23.
GaoHZhaoYChenT (2009) H∞ fuzzy control of nonlinear systems under unreliable communication. IEEE Transactions on Fuzzy Systems17(2): 265–278.
24.
GargH (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Applied Mathematics and Computation274: 292–305.
25.
GheisarnejadM (2018) An effective hybrid harmony search and cuckoo optimization algorithm based fuzzy PID controller for load frequency control. Applied Soft Computing65: 121–138.
26.
HeSRelfKUnbehauenR (1998) A neural approach for control of nonlinear systems with feedback linearization. IEEE Transactions on Neural Networks9(6): 1409–1421.
27.
HoM-TLuJ-M (2005) H∞ PID controller design for Lur’e systems and its application to a ball and wheel apparatus. International Journal of Control78(1): 53–64.
28.
HoM-TTuY-WLinH-S (2009) Controlling a ball and wheel system using full-state-feedback linearization. IEEE Control Systems Magazine29(5): 93–101.
HuangC-JLiT-HSChenC-C (2009) Fuzzy feedback linearization control for MIMO nonlinear system and its application to full-vehicle suspension system. Circuits, Systems and Signal Processing28: 959–991.
31.
IncremonaGPRubagottiMFerraraA (2017) Sliding mode control of constrained nonlinear systems. IEEE Transactions on Automatic Control62(6): 2965–2972.
32.
JainMSinghVRaniA (2019) A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm and Evolutionary Computation44: 148–175.
33.
KarabogaD (2005) An idea based on honey bee swarm for numerical optimization. Report for the Department of Computer Engineering report no. TR06, October. Kayseri: Erciyes University.
34.
KarabogaDBasturkB (2007) A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. Journal of Global Optimization39(3): 459–471.
35.
KavehADadrasA (2017) A novel meta-heuristic optimization algorithm: Thermal exchange optimization. Advances in Engineering Software110: 69–84.
36.
KirkpatrickSGelattCDJrVecchiMP (1983) Optimization by simulated annealing. Science220(4598): 671–680.
37.
LeiJKhalilHK (2016) Feedback linearization for nonlinear systems with time-varying input and output delays by using high-gain predictors. IEEE Transactions on Automatic Control61(8): 2262–2268.
38.
LiPJinF-J (2010) Adaptive fuzzy control for unknown nonlinear systems with perturbed dead-zone inputs. Acta Automatica Sinica36(4): 573–579.
39.
LiT-HSHuangC-JChenC-C (2010) Novel fuzzy feedback linearization strategy for control via differential geometry approach. ISA Transactions49(3): 348–357.
40.
LiuY-JTongS (2015) Adaptive fuzzy control for a class of unknown nonlinear dynamical systems. Fuzzy Sets and Systems263: 49–70.
41.
LongWJiaoJLiangX, et al. (2018) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Engineering Applications of Artificial Intelligence68: 63–80.
42.
LongWWuTLiangX, et al. (2019) Solving high-dimensional global optimization problems using an improved sine cosine algorithm. Expert Systems with Applications123: 108–126.
43.
LoucifFKechidaSSebbaghA (2019) Whale optimizer algorithm to tune PID controller for the trajectory tracking control of robot manipulator. Journal of the Brazilian Society of Mechanical Sciences and Engineering42(1): 1–11.
44.
MafarjaMMMirjaliliS (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing260: 302–312.
45.
MahmoodabadiMJAbedzadeh MaafiRTaherkhorsandiM (2017) An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems. Applied Soft Computing52: 1191–1199.
46.
MahmoodabadiMJAbedzadeh MaafiREtemadi HaghighiS, et al. (2020) Pareto design of decoupled fuzzy sliding mode controller for nonlinear and underactuated systems using a hybrid optimization algorithm. SAIEE Africa Research Journal111(1): 4–21.
47.
MahmoodabadiMJBagheriAAbedzadeh MaafiR, et al. (2013) Pareto optimal design of square cyclone separators using a novel multi-objective optimization algorithm. Transactions of the Institute of Measurement and Control35(3): 289–300.
48.
MahmoodabadiMJBagheriANariman-zadehN, et al. (2012) Pareto design of decoupled sliding-mode controllers for nonlinear systems based on a multiobjective genetic algorithm. Journal of Applied Mathematics2012: 1–22.
49.
MahmoodabadiMJRasekhMZohariT (2018) TGA: Team game algorithm. Future Computing and Informatics Journal3(2): 191–199.
50.
MahmoodabadiMJTaherkhorsandiMAbedzadeh MaafiR, et al. (2015) A novel multi objective optimisation algorithm: Artificial bee colony in conjunction with bacterial foraging. International Journal of Intelligent Engineering Informatics3(4): 369–386.
51.
MengJChenQHeR (2014) Research on optimal control for the vehicle suspension based on the simulated annealing algorithm. Journal of Applied Mathematics2014: 1–5.
52.
MetropolisNRosenbluthAWRosenbluthMN, et al. (1953) Equation of state calculations by fast computing machines. The Journal of Chemical Physics21(6): 1087–1092.
53.
MirjaliliSLewisA (2016) The whale optimization algorithm. Advance in Engineering Software95: 51–67.
54.
MirjaliliSMirjaliliSMHatamlouA (2016) Multi-verse optimizer: A nature-inspired algorithm for global optimization. Neural Computing and Applications27: 495–513.
55.
MirjaliliSMirjaliliSMLewisA (2014a) Grey wolf optimizer. Advance in Engineering Software69: 46–61.
56.
MirjaliliSWangG-GCoelhoLS (2014b) Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Computing and Applications25: 1423–1435.
57.
MishraRNMohantyKB (2018) Design and implementation of a feedback linearization controlled IM drive via simplified neuro-fuzzy approach. IETE Journal of Research64(2): 209–2302018.
58.
MoeziSAZakeriEEghtesadM (2019) Optimal adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control method for some classes of nonlinear systems. ISA Transactions93: 23–39.
59.
MohanVChhabraHRaniA, et al. (2019) An expert 2DOF fractional order fuzzy PID controller for nonlinear systems. Neural Computing and Applications31: 4253–4270.
60.
Montazeri-GhMPoursamadAGhalichiB (2006) Application of genetic algorithm for optimization of control strategy in parallel hybrid electric vehicle. Journal of the Franklin Institute343(4–5): 420–435.
61.
MostaghimSTeichJ (2003) Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of the 2003 IEEE swarm intelligence symposium, Indianapolis, IN, 26 April, pp. 26–33. New York: IEEE.
62.
NematiSBasiriMHGhasem-AghaeeN, et al. (2009) A novel ACO-GA hybrid algorithm for feature selection in protein prediction. Expert Systems with Applications36(10): 12086–12094.
63.
NobahariHNasrollahiS (2019) A non-linear estimation and model predictive control algorithm based on ant colony optimization. Transactions of the Institute of Measurement and Control41(4): 1123–1138.
64.
NocedalJWrightS (2006) Numerical Optimization (2nd edn). New York: Springer.
65.
OgataK (1997) Modern Control Engineering (3rd edn). Upper Saddle River, NJ: Prentice-Hall.
66.
PanW-T (2012) A new fruit fly optimization algorithm: Taking the financial distress model as an example. Knowledge-based Systems26: 69–74.
67.
ParkC-W (2004) Robust stable fuzzy control via fuzzy modeling and feedback linearization with its applications to controlling uncertain single-link flexible joint manipulators. Journal of Intelligent and Robotic Systems39: 131–147.
68.
PassinoKM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Systems Magazine22(3): 52–67.
69.
PiltanFYarmahmoudiMHMirzaieM, et al. (2013) Design novel fuzzy robust feedback linearization control with application to robot manipulator. International Journal of Intelligent Systems and Applications5: 1–10.
70.
RaoSS (1996) Engineering Optimization: Theory and Practice (3rd edn). Chichester: John Wiley & Sons.
71.
RashediENezamabadi-PourHSaryazdiS (2009) GSA: A gravitational search algorithm. Information Sciences179(13): 2232–2248.
72.
SandgrenE (1990) Nonlinear integer and discrete programming in mechanical design. Journal of Mechanical Design112(2): 223–229.
73.
SharkawyABEl-AwadyHMoustafaKAF (2003) Stable fuzzy control for a class of nonlinear systems. Transactions of the Institute of Measurement and Control25(3): 265–278.
SunXHuCLeiG, et al. (2020) State feedback control for a PM hub motor based on gray wolf optimization algorithm. IEEE Transactions on Power Electronics35(1): 1136–1146.
76.
TongSC (2019) Adaptive fuzzy control for uncertain nonlinear systems. Journal of Control and Decision6(1): 30–40.
77.
TsaiS-JSunT-YLiuC-C, et al. (2010) An improved multi-objective particle swarm optimizer for multi-objective problems. Expert Systems with Applications37(8): 5872–5886.
78.
VasantP (2010) Hybrid simulated annealing and genetic algorithms for industrial production management problems. International Journal of Computational Methods7(2): 279–2972010.
79.
WangBJinXPChengB (2012) Lion pride optimizer: An optimization algorithm inspired by lion pride behavior. Science China Information Sciences55(10): 2369–2389.
80.
WangL-X (1997) A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall.
81.
WangYCaoLZhangS, et al. (2016) Command filtered adaptive fuzzy backstepping control method of uncertain non-linear systems. IET Control Theory & Applications10(10): 1134–1141.
82.
WuT-SKarkoubMChenC-T, et al. (2013) Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed. International Journal of Control, Automation and Systems11(6): 1300–1313.
83.
Yazdani BejarbanehEHosseinian AhangarnejadABagheriA, et al. (2020) Optimal design of adaptive and proportional integral derivative controllers using a novel hybrid particle swarm optimization algorithm. Transactions of the Institute of Measurement and Control42(8): 1492–1510.
84.
YiJYubazakiN (2000) Stabilization fuzzy control of inverted pendulum systems. Artificial Intelligence in Engineering14(2): 153–163.
85.
YuJJQLiVOK (2015) A social spider algorithm for global optimization. Applied Soft Computing30: 614–627.
86.
YuXZhihongM (2002) Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications49(2): 261–264.
87.
ZadehLA (1965) Fuzzy sets. Information and Control8(3): 338–353.
88.
ZhangZDingSJiaW (2019) A hybrid optimization algorithm based on cuckoo search and differential evolution for solving constrained engineering problems. Engineering Applications of Artificial Intelligence85: 254–268.
89.
ZhaoFLeiWMaW, et al. (2016) An Improved SPEA2 algorithm with adaptive selection of evolutionary operators scheme for multiobjevtive optimization problems. Mathematical Problems in Engineering2016: 1–20.
