Performance Index Selection in Machinery Dynamics Instruction

Authors

DOI:

https://doi.org/10.7250/ecce-2026-0002

Keywords:

control engineering education, control nonlinearities, dynamics, key performance indicator, machine control, mechatronics, motion analysis, optimal control

Abstract

The practical need for an effective student-centric organisation of active study by Bachelor’s and Master’s students of technical specialties at universities of the course on the fundamentals of optimal control theory determines the relevance of the author’s methodological approach presented in this paper. The approach is associated with the development of a comprehensive individual student assignment on computational multi-criteria nonlinear optimisation modelling of various optimal controls of linear one-dimensional motion of a controlled material point within the framework of the computational visualisation of the sequential nonlinear influence of the algebraic construct of each of the minimized functionals (A1)-(A20). They were mathematically constructed from systems engineering considerations on the completely non-obvious nonlinear dynamic features of each corresponding geometric profile of the desired optimal control signal. Most of the nonlinear formulas for the minimized functionals (A3)-(A20) proposed by the author of this study are original and principally new applied scientific results for the multidisciplinary field of engineering teaching of optimal control. The calculated results of nonlinear optimisation modelling presented in this study were obtained using the computing capabilities of JModelica-{1.17; 2.14} with the Optimica extension. The study can find wide engineering and pedagogical application in teaching university disciplines in automation, cybernetic, mechanical, electromechanical, information technology and computational optimisation cycles.

References

J. Åkesson, K.-E. Årzén, M. Gäfvert, T. Bergdahl, and H. Tummescheit, “Modeling and optimisation with Optimica and JModelica.org – Languages and tools for solving large-scale dynamic optimisation problems”, Computers & Chemical Engineering, vol. 34, no. 11, pp. 1737–1749, Nov. 2010. https://doi.org/10.1016/j.compchemeng.2009.11.011

S. D. Bencomo, “Control learning: present and future”, Annual Reviews in Control, vol. 28, no. 1, pp. 115–136, Jan. 2004. https://doi.org/10.1016/j.arcontrol.2003.12.002

F. Biral, E. Bertolazzi, and P. Bosetti, “Notes on numerical methods for solving optimal control problems”, IEEJ Journal of Industry Applications, vol. 5, no. 2, pp. 154–166, 2016. https://doi.org/10.1541/ieejjia.5.154

J.-B. Caillau et al., OptimalControl.jl: a Julia package to model and solve optimal control problems with ODE’s. (Oct. 31, 2025). Zenodo. [Online]. Available: https://doi.org/10.5281/zenodo.17491943

O. Cots and J. Gergaud, “Numerical tools for geometric optimal control and the Julia control-toolbox package”, in IVAN KUPKA LEGACY: A Tour Through Controlled Dynamics, 1st ed. B. Bonnard, M. Chyba, D. Holcman, and E. Trélat, Eds. AIMS Sciences, 2024, pp. 209–243. [Online]. Available: https://hal.science/hal-04578955

Y. A. Davizón, J. Sánchez-Leal, and E. D. Smith, “The role of optimal control theory in the curricular proposal for dynamic supply chains in industrial engineering education”, Frontiers in Education, vol. 11, Mar. 2026, Art. no.1747320. https://doi.org/10.3389/feduc.2026.1747320

J. Doyle et al., “Teaching control theory in high school”, in 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, USA, Dec. 2016, pp. 5925–5949. https://doi.org/10.1109/CDC.2016.7799181

L. C. Evans, “Lecture notes: Version 0.2 for an old undergraduate course “An Introduction to Mathematical Optimal Control Theory”. Department of Mathematics, University of California, Berkeley, Spring 2024. https://math.berkeley.edu/~evans/control.course.pdf

S. Gros and M. Diehl. Numerical Optimal Control. Oct. 2024. [Online]. Available: https://www.syscop.de/files/2024ws/NOC/book-NOCSE.pdf

K. Hauser. Robotic Systems. UIUC, 2024. [Online]. Available: https://motion.cs.illinois.edu/RoboticSystems/

I. Horvath and G. Ábrahám, “Transdisciplinary shifts in system paradigm-driven disciplines: Mechatronics as an example”, Transdisciplinary Journal of Engineering and Science, vol. 16, May 2025. https://doi.org/10.22545/2025/00276

R. N. Jazar, “Time optimal control”, in Theory of Applied Robotics: Kinematics, Dynamics, and Control, R. N. Jazar, Ed. Cham: Springer, 2022, pp. 731–757. https://doi.org/10.1007/978-3-030-93220-6_13

U. Jönsson et al., “Lectures on “Optimal control”. KTH Royal Institute of Technology, February 6, 2002. [Online]. Available: https://www.user.tu-berlin.de/mtoussai/08-optimal-control/jonsson-lectureNotes.pdf

S. S. Kia, “Lecture notes for the UCI course MAE 274 “Optimal Control”. University of California Irvine, 2019-04-10. [Online]. Available: https://solmaz.eng.uci.edu/Teaching/MAE274/MAE274-Notes.pdf

D. E. Kirk, Optimal Control Theory: An Introduction. New Jersey: Prentice-Hall, 1970. http://e.guigon.free.fr/rsc/book/Kirk04.pdf

I. Kocsis, S Hajdu, S. Mikuska, and P. Korondi, “Introduction to the mathematics of control education in calculus for engineering students”, IEEE Transactions on Education, vol. 68, no. 1, pp. 163–172, Feb. 2025. https://doi.org/10.1109/TE.2024.3520590

J. Kong, J. Feng, Q. Zhang, T. Su, and X. Jin, “Design and practice of new engineering innovation education for automation majors”, ICCK Transactions on Education and Learning Technologies, vol. 1, no. 1, pp. 1–13, May 2025. https://doi.org/10.62762/TELT.2025.700195

R. W. Krauss, A. Ali, and A. L. Lenz, “Teaching dynamic systems and control without dynamics”, in 2017 ASEE Annual Conference & Exposition, Columbus, Ohio, USA, Jun. 2017. [Online]. Available: https://peer.asee.org/28911

H. T. M. Kussaba et al., “Learning optimal controllers: a dynamical motion primitive approach”, IFAC-PapersOnLine, vol. 56, no. 2, pp. 4776–4782, Jan. 2023. https://doi.org/10.1016/j.ifacol.2023.10.1242

D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton, New Jersey, USA: Princeton Univ. Press, 2012. https://liberzon.csl.illinois.edu/teaching/cvoc.pdf

Z. Manchester et al., “Lecture Notebooks from the course 16-745 “Optimal Control and Reinforcement Learning”. Carnegie Mellon University, Spring 2025. [Online]. Available: https://optimalcontrol.ri.cmu.edu/

H. Maurer, “Tutorial on control and state constrained optimal control problems”, SADCO Summer School 2011 – Optimal Control, Sep. 2011, London, United Kingdom. [Online]. Available: https://inria.hal.science/inria-00629518/

T. Miquel, “Introduction to optimal control”, CEL: Open Access Courses, Oct. 2022. [Online]. Available: https://cel.hal.science/hal-02987731v2

M. R. Mojallizadeh, B. Brogliato, and C. Prieur, “Modeling and control of overhead cranes: A tutorial overview and perspectives”, Annual Reviews in Control, vol. 56, Art. no. 100877, Jan. 2023. https://doi.org/10.1016/j.arcontrol.2023.03.002

R. M. Murray, “Optimisation-based control”, Version v2.3h. California Institute of Technology, Mar. 2023. [Online]. Available: https://www.cds.caltech.edu/~murray/books/AM05/pdf/obc-complete_12Mar2023.pdf

B. K. Negash and N. Boizot, “Consumption minimization for a car-like robot with quadratic drag”, IFAC-PapersOnLine, vol. 59, no. 19, pp. 638–643, Jan. 2025. https://doi.org/10.1016/j.ifacol.2025.11.107

V. Nezhadali, L. Eriksson, and A. Fröberg, “Modeling and optimal control of a wheel loader in the lift-transport section of the short loading cycle”, IFAC Proceedings Volumes, vol. 46, no. 21, pp. 195–200, Jan. 2013. https://doi.org/10.3182/20130904-4-JP-2042.00083

H. Niemann, J. C. Andersen, and O. Ravn, “Towards a modern concept for teaching control engineering”, IFAC Proceedings Volumes, vol. 42, no. 24, pp. 71–76, Jan. 2010. https://doi.org/10.3182/20091021-3-JP-2009.00015

J. E. Normey-Rico and M. M. Morato, “Teaching control with basic maths: Introduction to process control course as a novel educational approach for undergraduate engineering programs”, Journal of Control, Automation and Electrical Systems, vol. 35, no. 1, pp. 41–63, Feb. 2024. https://doi.org/10.1007/s40313-023-01063-9

M. A. Pastrana et al., “A novel approach to teaching theory control: Integrating STEM education, mobile robot simulation, and bio-inspired optimisation”, Operations Research Forum, vol. 6, no. 3, Jun. 2025, Art. no. 85. https://doi.org/10.1007/s43069-025-00489-y

M. Pavone et al., “Lecture Notes from the course AA 203 “Optimal and Learning-Based Control”. Stanford University, Spring 2024. [Online]. Available: https://stanfordasl.github.io//aa203/sp2324/

A. V. Perig, A. N. Stadnik, A. A. Kostikov, and S. V. Podlesny, “Research into 2D dynamics and control of small oscillations of a cross-beam during transportation by two overhead cranes”, Shock and Vibration, vol. 2017, 2017, Art. no.9605657. https://doi.org/10.1155/2017/9605657

A. V. Perig et al., “Engineering pedagogy course mapping”, Acta Metallurgica Slovaca, vol. 28, no. 1, pp. 49–67, Mar. 2022. https://doi.org/10.36547/ams.28.1.1411

O. V. Perig, “DataSet for Perig’s manuscript on performance index selection teaching – ver Nov 2025”, Nov. 2025, [Online]. Available: https://doi.org/10.13140/RG.2.2.29913.38245

L. S. Pontryagin, The Mathematical Theory of Optimal Processes, 1st ed. Montreux, Switzerland: Gordon and Breach Science Publishers, 1986. https://doi.org/10.1201/9780203749319

C. V. Rojas-Palacio, E. I. Arango-Zuluaga, and H. A. Botero-Castro, “Teaching control theory: A selection of methodology based on learning styles”, DYNA, vol. 89, no. 222, pp. 9–17, Jul. 2022. https://doi.org/10.15446/dyna.v89n222.100547

S. P. Sethi, Optimal Control Theory: Applications to Management Science and Economics. Cham: Springer Nature Switzerland, 2021. https://doi.org/10.1007/978-3-030-91745-6

S. V. Sokolov, Optymalni ta adaptyvni systemy [Optimal and adaptive systems]. Sumy: Sumy State University, 2018. [Online]. Available: http://essuir.sumdu.edu.ua/handle/123456789/68042 [in Ukrainian].

O. A. Stenin et al., Optymalni systemy upravlinnia [Optimal control systems]. Kyiv: NTUU KPI (National Technical University of Ukraine). Available: https://library.kpi.kharkov.ua/uk/math_physics_Optsiu [in Ukrainian].

J. Tar et al., “Abstraction in teaching ways of control engineering to support the understanding of mathematics behind Industry 4.0 – a Hungarian approach”, IFAC-PapersOnLine, vol. 55, no. 17, pp. 230–235, Jan. 2022. https://doi.org/10.1016/j.ifacol.2022.09.284

R. Tedrake, “Underactuated robotics: Algorithms for walking, running, swimming, flying, and manipulation”, (Course Notes for MIT 6.832). [Online]. Available: https://underactuated.csail.mit.edu/

K. L. Teo, B. Li, C. Yu, and V. Rehbock, Applied and Computational Optimal Control: A Control Parametrization Approach. Cham: Springer Nature Switzerland, 2022. https://doi.org/10.1007/978-3-030-69913-0

T. Vámos, B. Ruth, L. Keviczky, and D. Sík, “Methodology of teaching the first control course”, Opus et Educatio, vol. 7, no. 2, Jan. 2020. https://doi.org/10.3311/ope.375

R. Weber, “Lecture notes for the course “Optimisation and Control”. University of Cambridge, Lent Term 2016. [Online]. Available: https://www.dpmms.cam.ac.uk/~rrw1/oc/index.html

D. Wu et al., “Graduate course “Optimal Control 2023”. Department of Automatic Control, Lund University, Lund, Sweden, 2023. [Online]. Available: https://www.control.lth.se/education/doctorate-program/optimal-control/optimal-control-2023/

Z. Yang, “Operation control of visualization VR teaching platform for mechanical manufacturing professional course under iterative learning PID algorithm”, Discover Computing, vol. 29, no. 1, Jan. 2026, Art. no. 22. https://doi.org/10.1007/s10791-025-09879-6

K. Zenger, “Control engineering, system theory and mathematics: the teacher’s challenge”, European Journal of Engineering Education, vol. 32, no. 6, pp. 687–694, Dec. 2007. https://doi.org/10.1080/03043790701520719

Downloads

Published

2026-04-28

How to Cite

Perig, O. V. (2026). Performance Index Selection in Machinery Dynamics Instruction. Electrical, Control and Communication Engineering, 22(1), 17-30. https://doi.org/10.7250/ecce-2026-0002