Abstract
The algorithms of model reference parametric adaptation are considered, providing the astaticism and disturbances estimation. The structure of the control system is suggested allowing to design multivariable controllers providing the movement along the specified trajectories for an object described by kinematics and dynamics of mechanical systems in three-dimensional space. The asymptotic stability of a closed-loop adaptive system including a loop to provide astaticism is proved by the method of Lyapunov functions. The errors analysis is carried out of disturbances estimation by asymptotic observer. The boundaries of the estimation error are shown, and the relations are given to adjust the observer parameters. The results of the numerical investigations are given.
Similar content being viewed by others
References
Rutkovskii, V. Yu Nonsearching Adaptive Systems and Space Control Systems: Research and Development Projects at the Institute of Control Sciences. Autom. Remote Control 60(no. 6), 791–796 (1999).
Zemlyakov, S. D. & Rutkovskii, V. Yu Some Results of the Theory of Nonsearching Adaptive Systems and Their Application. Autom. Remote Control 62(no. 7), 1115–1131 (2001).
Kleiman, E. G. Identification of Time-Varying Systems. Autom. Remote Control 60(no. 10, part 1), 1371–1402 (1999).
Kleiman, E. G. Identification of Input Signals in Dynamical Systems. Autom. Remote Control 60, 1675–1685 (1999).
Rutkovskii, V.Yu. and Krutova, I.N.A Class of Self-adjusting Systems with Model: Principles of Design and Some Problems of the Theory, 1st All-Union Conf. on Theory and Practice of Self-Adjusting Systems (December 10-14, 1963), Moscow: Nauka, 1965, pp. 46–63.
Rutkovskii, V.Yu. and Ssorin-Chaikov, V.N.Self-tuning Systems with a Test Signal, Proc. I All-Union Conf. on Theory and Practice of Self-Tuning Systems, Moscow, 1965, pp. 93–111.
Zemlyakov, S.D.Some Problem of Analytical Synthesis in Model Reference Control Systems by the Direct Method of Lyapunov. Theory of Self Adaptive Control System, 2nd IFAC Symp. on the Theory of Self-Adaptive Control Systems, England, Teddington, 1965, New York: Hummon Plenum, 1966, pp. 175–179.
Zhang, Dan & Wei, Bin A Review on Model Reference Adaptive Control of Robotic Manipulators. Ann. Rev. Control 43, 188–198 (2017).
Druzhinina, M. V., Nikiforov, V. O. & Fradkov, A. L. Methods of Nonlinear Adaptive Control with Respect to Output. Autom. Remote Control 57, 153–176 (1996).
Andrievsky, B. R. & Fradkov, A. L. Adaptive Flight Control Based on Parameter Identification Procedure Simultaneously with Sliding Mode Motion. Upravlen. Bolash. Sist. no. 26, 113–144 (2009).
Bushmanova, Yu. A. Combined Control of Scalar Non-Stationary Plants in Systems with an Unobvious Standard. Informat. Sist. Upravlen. no. 2, 165–172 (2007).
Rutkovskii, V. Yu & Glumov, V. M. Dynamics Peculiarities of an Adaptive Control System with Nonlinear Reference Model. I. Autom. Remote Control 78(no. 4), 654–665 (2017).
Rutkovskii, V. Yu & Glumov, V. M. Dynamics Peculiarities of an Adaptive Control System with Nonlinear Reference Model. II. Autom. Remote Control 78(no. 5), 836–846 (2017).
Dadenkov, D. A. & Kazantsev, V. P. Synthesis of Electromechanical Control Systems with Nonlinear Adaptive Reference Model. Fundament. Issled. no. 11, 1466–1471 (2014).
Eremin, E. L. A Modified Adaptive System for Controlling the Singlechannel Plant with Inlet Saturation. Informat. Sist. Upravlen. no. 3(49), 119–131 (2016).
Eremin, E. L., Pikul, Z. D. & Telichenko, D. A. Adaptive Control System of Structural-Parametric Uncertain Objects of One Class in a Scheme with Explicit and Implicit Reference Models. Informat. Sist. Upravlen. no. 1(43), 105–114 (2015).
Furtat, I. B. & Tsykunov, A. M. Adaptive Control of Plants of Unknown Relative Degree. Autom. Remote Control 71(no. 6), 1076–1084 (2010).
Pshikhopov, V. Kh, Medvedev, M. Yu & Krukhmalev, V. A. Base Algorithms of the Direct Adaptive Position-Path Control for Mobile Objects Positioning. Mekhatr. Avtomatiz. Upravlen. no. 4(16), 219–225 (2015).
Pshikhopov, V. Kh, Medvedev, M. Yu & Gurenko, B. V. The Basic Algorithms of Adaptive Position-Trajectory Control System of Mobile Objects. Probl. Upravlen. no. 4, 66–74 (2015).
Medvedev, M. Yu, Rogov, V. A. & Medvedeva, T. N. Position-Path Control of Vehicles with Multiple Loop Adaptation. Izv. YuFU, Tekhn. Nauki no. 7, 101–114 (2016).
Isidori, A. Nonlinear Control Systems. (Springer, London, 1999).
Burdakov, S. F., Miroshnik, I. V. & Stel’makov, R. E. Sistemy upravleniya dvizheniem kolesnykh robotov (Control Systems of Wheeled Robot Motion). (Nauka, St. Petersburg, 2001).
Byushgens, G. S. & Studnev, R. V. Dinamika samoleta. Prostranstvennoe dvizhenie (Aircraft Dynamics. Spatial Motion). (Mashinostroenie, Moscow, 1983).
Pshikhopov, V. H., Medvedev, M. Yu & Gajduk., A. R. et al. Position-Trajectory Control System for Robot on Base of Airship: Control Algorithms. Mekhatron., Avtomatiz., Upravlen. no. 7, 13–20 (2013).
Bessekerskii, V. A. & Popov, E. P. Teoriya sistem avtomaticheskogo regulirovaniya (Theory of Automatic Control Systems). (Nauka, Moscow, 1972).
Alexandrov, A. G. Optimalanyye i adaptivnyye sistemy: uchebnoye posobie (Optimal and Adaptive Systems. Textbook). (Vysshaya Shkola, Moscow, 1989).
Piskunov, N.S.Differentsial’noe i integral’noe ischisleniya dlya vtuzov (Differential and Integral Calculus Technical Colleges), Moscow: Nauka, 1985, vol. 2, 13th ed.
Medvedev, M. Yu Algorithms of an Adaptive Control of Actuating Motors. Mekhatron., Avtomatiz., Upravlen no. 6, 17–22 (2006).
Bucy, R. Nonlinear filtering Theory. IEEE Trans. Automat. Control AC-1(no. 2), 198 (1965).
Krasovskii, A. A. Cyclic Estimation in Primary Filtering of Sensor Signals. Autom. Remote Control 49(no. 6), 729–735 (1988).
Gantmakher, F.R.Teoriya matrits (Theory of Matrices), Moscow: Fizmatlit, 2004, 5th ed. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.
Babakov, N.A., Voronov, A.A., et al.Teoriya avtomaticheskogo upravleniya: uchebnik dlya vuzov, chast’ I: Teoriya lineinykh sistem avtomaticheskogo upravleniya (Automatic Control Theory: Textbook for Higher Education, vol. I: Theory of Linear Systems for Automatic Control), Voronov, A.A., Ed., Moscow: Vysshaya Shkola, 1986, 2nd ed.
Sedov, L. I. Ploskie zadachi gidrodinamiki i aerodinamiki. (Nauka, Moscow, 1980). Translated under the title Two-dimensional Problems in Hydrodynamics and Aerodynamics, New York: Wiley, 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pshikhopov, V., Medvedev, M. Multi-Loop Adaptive Control of Mobile Objects in Solving Trajectory Tracking Tasks. Autom Remote Control 81, 2078–2093 (2020). https://doi.org/10.1134/S0005117920110090
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117920110090