Application of continuous dynamic programming equations to determine optimal control laws of automated systems
DOI:
https://doi.org/10.31548/Abstract
The growing shortage of energy resources necessitates the search for effective technical means of reducing the energy intensity of technological systems and industrial installations, including in the agro-industrial complex, processing and utility industries. One of these solutions is the application of optimal control laws that allow saving energy and material resources.
Among the methods of optimization of automatic systems, under certain conditions, the Bellman dynamic programming method in continuous form may be convenient for constructing closed-loop optimal control systems, which makes it possible to determine the optimal control law as a function of the initial coordinates of the control object. In this work, an electric drive loaded with a viscous friction torque is considered as a control object, which can be both the main load moment of some units and, much more often, a linear component of the motor resistance torque, which does not perform useful work, but causes energy consumption to overcome it.
The purpose of this work is to justify the use of continuous Bellman dynamic programming equations to find optimal, according to the criterion of minimum energy losses, control laws for electromechanical objects using the example of electric drives operating under the action of a viscous friction moment.
This justification is based on finding the conditions for the existence of analytical solutions to dynamic programming equations, obtaining and solving a system of differential equations of an electromechanical object in partial derivatives and solving these equations to find the optimal control law for the object as a function of its initial coordinates.
Key words: optimal control, dynamic programming, electric drive, partial derivatives, optimality criterion
References
1. Petrov, Ju. P. (1977). Variacionnye metody teorii optimal'nogo upravlenija [Variational methods of optimal control theory]. Energija, 280.
2. Krotov, V.F. (1996). Global methods in optimal control theory. New York, Basel, Hong Kong: Marcel Dekker Inc., 384.
3. Loveykin, V. S., Romasevich, Yu. O. (2010). Optimizatsiya perehidnih rezhimIv ruhu mehanichnih sistem pryamim variatsiynim metodom [Optimization of transients regim es of movement of mechanical systems with the direct variational method]. Kiyv –Nizhyn, 184.
4. Grigorov, O.V., Lovejkin, V.S. (1997). Optymalne keruvannia rukhom mekhanizmiv vantazhopidjomnykh mashyn [Optimal control of the movement of lifting machinery mechanisms]. Kyiv: IZMN, 264.
5. Loveykin, V. S., Romasevich, Yu. O. (2012). Optymizatsiya rukhu vantazhopidyomnoho krana iz traversnoyu pidviskoyu vantazhu metodom dynamichnoho prohramuvannya [Optimization of the movement of a crane with a traverse suspension of the load using the dynamic programming method]. Mechanical engineering, 10, 15-32.
6. Grigorov, O.V., Petrenko, V.S. (2005). Vantazhopidjomni mashyny [Lifting machines]. Kharkiv: NTU „KhPI”, 304.
7. LoveykIn, V. S., Romasevich, Yu. O. (2016). Dinamika i optimizatsiya rezhimiv ruhu mostovih kraniv [Dynamics and optimization of traffic overhead cranes]. Kiyv: TsP KOMPRINT, 314.
8. Shurub, Yu.V. (2012). Rozrobka systemy keruvannya tryfazno-odnofaznykh asynkhronnykh elektropryvodiv pry vypadkovykh navantazhennyakh [Working out of system of control of three-one phase induction electric drives at random loads]. Electromechanical and energy saving systems, 1, 12-15.
9. Shurub, Y., Dudnyk, A., Vasilenkov, V., Lavinskiy, D. (2020). Application of a Kalman filter in scalar form for discrete control of electromechanical systems. IEEE International Conference on Problems of Automated Electrodrive. Theory and Practice (PAEP). Kremenchuk, Ukraine, September 21-25, 2020, 1-4. https://doi.org/10.1109/PAEP49887.2020.9240805
10. Shurub, Yu. V. (2017). Statystychna optymizatsiya chastotno rehulʹovanykh asynkhronnykh elektropryvodiv pry skalyarnomu keruvanni [Statistical optimization of frequency regulated induction electric drives with scalar control]. Electrical Engineering & Electromechanics, 1, 26–30. https://doi.org/10.20998/2074-272X.2017.1.05
Published
Issue
Section
License
Relationship between right holders and users shall be governed by the terms of the license Creative Commons Attribution – non-commercial – Distribution On Same Conditions 4.0 international (CC BY-NC-SA 4.0):https://creativecommons.org/licenses/by-nc-sa/4.0/deed.uk
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
