Multiobjective PID controller design for active suspension system: scalarization approach

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Abstract

In this study, the PID tuning method (controller design scheme) is proposed for a linear quarter model of active suspension system installed on the vehicles. The PID tuning scheme is considered as a multiobjective problem which is solved by converting this multiobjective problem into single objective problem with the aid of scalarization approaches. In the study, three different scalarization approaches are used and compared to each other. These approaches are called linear scalarization (weighted sum), epsilon-constraint and Benson’s methods. The objectives of multiobjective optimization are selected from the time-domain properties of the transient response of the system which are overshoot, rise time, peak time and error (in total there are four objectives). The aim of each objective is to minimize the corresponding property of the time response of the system. First, these four objective is applied to the scalarization functions and then single objective problem is obtained. Finally, these single objective problems are solved with the aid of heuristic optimization algorithms. For this purpose, four optimization algorithms are selected, which are called Particle Swarm Optimization, Differential Evolution, Firefly, and Cultural Algorithms. In total,twelve implementations are evaluated with the same number of iterations. In this study, the aim is to compare the scalarization approaches and optimization algorithm on active suspension control problem. The performance of the corresponding cases (implementations) are numerically and graphically demonstrated on transient responses of the system.

Keywords

PID controller

Multiobjective

Scalarization

Particle swarm optimization

Differential evolution

Partitioned method

Conflict of interest

The authors declare they have no competing interests.

References

[1] Astrom K.J., and Hagglund T., The future of PID con- trol, Control Engineering Practice, 9, 11, 1163-1175 (2001).

[2] Arruda L.V.R, Swiech M.C.S, Delgado M.R.B, and Neves-Jr F., PID control of MIMO process based on rank niching genetic algorithm, Applied Intelligence, 29, 3, 290-305 (2008).

[3] Neath M.J., Swain A.K., Madawala U.K., and Thri- mawithana D.J., An Optimal PID Controller for a Bidirectional Inductive Power Transfer System Using Multiobjective Genetic Algorithm, IEEE Transactions on Power Electronics, 29, 3, 1523-1531 (2014).

[4] Lin C.-L., Jan H.-Y., and Shieh N.-C, GA-based mul- tiobjective PID control for a linear brushless DC mo- tor, IEEE/ASME Transactions on Mechatronics, 8, 1, 56-65 (2003).

[5] Herreros A., Baeyens E., and Pern J.R., Design of PID-type controllers using multiobjective genetic al- gorithms, ISA Transactions, 41, 4, 457-472 (2002).

[6] Reynoso-Meza G., Garcia-Nieto S., Sanchis J., and Blasco F.X., Controller Tuning by Means of Multi- Objective Optimization Algorithms: A Global Tuning Framework, IEEE Transactions on Control Systems Technology, 21, 2, 445-458 (2013).

[7] Reynoso-Meza G., Sanchis J., Blasco X., and Herrero J.M., Multiobjective evolutionary algorithms for mul- tivariable PI controller design, Expert Systems with Applications, 39, 9, 7895-7907 (2012).

[8] Zhaoa S.-Z, Willjuice Iruthayarajanb M., Baskarc S., and Suganthan P.N., Multi-objective robust PID con- troller tuning using two lbests multi-objective parti- cleswarm optimization, Information Sciences, 181, 16, 3323-3335 (2011).

[9] C.M. Seaman, A.A. Desrochers, and G.F. List, Mul- tiobjective optimization of a plastic injection molding process, IEEE Transactions on Control Systems Tech- nology, 2, 3, 157-168 (1994).

[10] Gambier A., MPC and PID control based on Multi- Objective Optimization, American Control Confer- ence, 4727-4732 (2008).

[11] Naidua K., Mokhlisa H., and Bakar A.H.A., Multiob- jective optimization using weighted sum Artiﬁcial Bee Colony algorithm for Load Frequency Control, Inter- national Journal of Electrical Power and Energy Sys- tems, 55, 657-667 (2014).

[12] Hung M.-H., Shu L.-S., Ho S.-J., and Hwang S.-F., A Novel Intelligent Multiobjective Simulated Anneal- ing Algorithm for Designing Robust PID Controllers, IEEE Transactions on Systems, Man, and Cybernetics- Part A: Systems and Humans, 38, 2, 319-330 (2008).

[13] Tseng C.-S., and Chen B.-S., Multiobjective PID con- trol design in uncertain robotic systems using neu- ral network elimination scheme, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 31, 6, 632-644 (2001).

[14] Takahashi R.H.C., Peres P.L.D., and Ferreira P.A.V.,Multiobjective H2 /H∞ guaranteed cost PID design , IEEE Control Systems, 17, 5, 37-47 (2002).

[15] Tang K.S., Man K.F., Chen G., and Kwong S., An optimal fuzzy PID controller, IEEE Transactions on Industrial Electronics, 48, 4, 757-765 (2001).

[16] Liua G.P., and Daley S., Optimal-tuning PID control for industrial systems, Control Engineering Practice, 9, 11, 1185-1194 (2001).

[17] Ayalaa H.V.H., and Coelho L.S., Tuning of PID con- troller based on a multiobjective genetic algorithm ap- plied to a robotic manipulator, Expert Systems with Applications, 49, 10, 8968-8974 (2012).

[18] Panda S., Multi-objective PID controller tuning for a FACTS-based damping stabilizer using Non- dominated Sorting Genetic Algorithm-II, Interna- tional Journal of Electrical Power and Energy Sys- tems, 33, 7, 12961308 (2011).

[19] Bourmistrova, A., Storey, I., and Subic A., Multi- objective optimisation of active and semi-active sus- pension systems with application of evolutionary al- gorithm, International Conference on Modelling and Simulation, 1217-1223 (2005).

[20] Xue X.D., Cheng K.W.E., and Xu C.D., Optimiza- tion of spring stifness in automotive and rail active suspension systems, International Conference on Elec- trical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles, International Transportation Elec- triﬁcation, 1-6 (2016).

[21] Aldair A.A., Abdalla T.Y., and Alsaedee E.B., Design of PID controller using ABC for full vehicle nonlinear active suspension system with passengerseat, Interna- tional Journal of Computer Applications, 167, 18-27 (2017).

[22] Rastegar N., and Khorram E., A combined scalariz- ing method for multiobjective programming problems, European Journal of Operational Research, 236, 1, 229237 (2014).

[23] Haimes Y., Ladson L., and Wismer D., On a bi crite- rion formulation of the problems of integrated system identiﬁcation and system optimization, IEEE Trans- actions on System, Man, and Cybernetics, 1, 296-297 (1971).

[24] Benson H.P., Existence of e伍cient solutions for vec- tor maximization problems, Journal of Optimization Theory and Applications, 26, 4, 569-580 (1978).

[25] Benson H.P., and Morin T.L., The vector maximiza- tion problem: Proper E伍ciency and Stability, SIAM Journal of Applied Mathematics, 1-18 (1974).

[26] Soleimani-Damaneh M., and Zamani M., On Ben- sons scalarization in multiobjective optimization, Op- timization Letters, Early Access, 1-6 (2016).

[27] Ehrgott M., Approximation algorithms for combinato- rial multicriteria optimization problems, International Transactions in Operational Research, 7, 531 (2000).

[28] Deb K., Multi-Objective Optimization Using Evolu- tionary Algorithms, Publisher : Chichester, UK : Wi- ley (2002).

[29] Kennedy J., and Eberhart R.C., Particle Swarm Opti- mization, Proceedings of IEEE International Confer- ence on Neural Networks, 1942-1948 (1995).

[30] Storn R., and Price K., Diferential Evolution - a simple and e伍cient adaptive scheme for global opti- mization over continuous space, International Com- puter Science Institute, Technical Report, TR-95-012 (1995).

[31] Yang X.-S., Fire丑y Algorithm, Nature Inspired Meta- heuristic Algorithms,79-90 (2008).

[32] Fister I., Yang X.-S., and Brest J., A Comprehensive Review of Fire丑y Algorithm, Swarm and Evolut,onary Computation, 13, 34-46 (2013).

[33] Yang X.-S., Fire丑y Algorithm, Stochastic Test Func- tions and Design Optimization, International Journal of Bio-Inspired Computation, 2, 78-84 (2010).

[34] Yang X.-S., Fire丑y Algorithms for Multimodal Opti- mization, Lecture Notes in Computer Science, 5792 LNCS, 169-178 (2009).

[35] Yang X.-S., Hosseini S., and Gandomi A.H., Fire- 丑y Algorithm for Solving Non-convex Economic Dis- patch Problems with Valve Loading Efect, Applied Soft Computing Journal, 12, 1180-1186 (2012).

[36] Reynolds R.G., An Adaptive Computer Model of the Evolution of Agriculture for Hunter-Gatherers in the Valley of Oaxaca Mexico, PH.D. Thesis, Department of Computer Science, University of Michigan, (1976).

[37] Reynolds R.G., and Peng B. Cultural Algorithms: Modeling of How Cultures Learn to Solve Problems, International Conference on Tools with Artiﬁcial In- telligence, 1-7 (2004).

[38] Rychtyckyj, N., Using Cultural Algorithm in Industry, IEEE Swarm Intelligence Symposium, 1-8 (2003).

[39] Chung C., and Reynolds R.G., CAEP: An Evolution- based tool for Real-Valued Function Optimization us- ing Cultural Algorithms, International Journal on Ar- tiﬁcial Intelligence Tools, 7, 239-291 (1998).

[40] Jin X., and Reynolds R.G., Using Knowledge-based Evolutionary Computation to Solve Nonlinear Con- straint Optimization Problems: A Cultural Algorithm Approach, Congress on Evolutionary Computation, 1672-1678 (1999).

[41] Reynolds R.G., and Saleem S. The Impact of Envi- ronmental Dynamics on Cultural Emergence, Oxford University Press, 1-10 (2003).

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