doi: 10.3934/dcdss.2021145
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Data-driven control of hydraulic servo actuator based on adaptive dynamic programming

1. 

Faculty of Mechanical and Civil Engineering, University of Kragujevac, Kraljevo, 36000, Serbia

2. 

Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi, 214122, China

3. 

School of Information Engineering, Henan University of Science and Technology, 471023, Luoyang, China

4. 

Key Laboratory of Intelligent Computing and Signal Processing (Ministry of Education), School of Electrical Engineering and Automation, Anhui University, 230601, Hefei, China

5. 

Department of Mechanical and Civil Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA

* Corresponding author: Vladimir Stojanovic (vladostojanovic@mts.rs)

Received  September 2021 Revised  October 2021 Early access December 2021

Fund Project: This research has been supported in part by the Serbian Ministry of Education, Science and Technological Development under grant 451-03-9/2021-14/200108, the National Natural Science Foundation of China under grants 61976081, 62073001, the Natural Science Fund for Excellent Young Scholars of Henan Province under grant 202300410127

The hydraulic servo actuators (HSA) are often used in the industry in tasks that request great powers, high accuracy and dynamic motion. It is well known that HSA is a highly complex nonlinear system, and that the system parameters cannot be accurately determined due to various uncertainties, inability to measure some parameters, and disturbances. This paper considers control problem of the HSA with unknown dynamics, based on adaptive dynamic programming via output feedback. Due to increasing practical application of the control algorithm, a linear discrete model of HSA is considered and an online learning data-driven controller is used, which is based on measured input and output data instead of unmeasurable states and unknown system parameters. Hence, the ADP based data-driven controller in this paper requires neither the knowledge of the HSA dynamics nor exosystem dynamics. The convergence of the ADP based control algorithm is also theoretically shown. Simulation results verify the feasibility and effectiveness of the proposed approach in solving the optimal control problem of HSA.

Citation: Vladimir Djordjevic, Vladimir Stojanovic, Hongfeng Tao, Xiaona Song, Shuping He, Weinan Gao. Data-driven control of hydraulic servo actuator based on adaptive dynamic programming. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021145
References:
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A. CavalloG. De MariaC. Natale and S. Pirozzi, Slipping detection and avoidance based on Kalman filter, Mechatronics, 24 (2014), 489-499.  doi: 10.1016/j.mechatronics.2014.05.006.  Google Scholar

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Y. H. ChangQ. Hu and C. J. Tomlin, Secure estimation based Kalman filter for cyber–physical systems against sensor attacks, Automatica, 95 (2018), 399-412.  doi: 10.1016/j.automatica.2018.06.010.  Google Scholar

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V. FilipovicN. Nedic and V. Stojanovic, Robust identification of pneumatic servo actuators in the real situations, Forschung im Ingenieurwesen - Engineering Research, 75 (2011), 183-196.  doi: 10.1007/s10010-011-0144-5.  Google Scholar

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W. GaoY. JiangZ. P. Jiang and T. Chai, Output-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programming, Automatica, 72 (2016), 37-45.  doi: 10.1016/j.automatica.2016.05.008.  Google Scholar

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[32]

N. NedicV. Stojanovic and V. Djordjevic, Optimal control of hydraulically driven parallel robot platform based on firefly algorithm, Nonlinear Dynam., 82 (2015), 1457-1473.  doi: 10.1007/s11071-015-2252-5.  Google Scholar

[33]

R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach, 2$^{nd}$ edition, John Wiley & Sons, New Jersey, 2012. Google Scholar

[34]

C. R. RojasJ. C. AgueroJ. S. WelshG. C. Goodwin and A. Feuer, Robustness in experiment design, IEEE Trans. Automat. Control, 57 (2012), 860-874.  doi: 10.1109/TAC.2011.2166294.  Google Scholar

[35]

M. RoozegarM. J. Mahjoob and M. Jahromi, Optimal motion planning and control of a nonholonomic spherical robot using dynamic programming approach: Simulation and experimental results, Mechatronics, 39 (2016), 174-184.   Google Scholar

[36]

J. L. Sun and C. S. Liu, An overview on the adaptive dynamic programming based missile guidance law, Acta Automatica Sinica, 43 (2017), 1101-1113.   Google Scholar

[37]

V. StojanovicN. NedicD. PrsicL. Dubonjic and V. Djordjevic, Application of cuckoo search algorithm to constrained control problem of a parallel robot platform, J. Advanced Manufacturing Technology, 87 (2016), 2497-2507.  doi: 10.1007/s00170-016-8627-z.  Google Scholar

[38]

V. Stojanovic and D. Prsic, Robust identification for fault detection in the presence of non-Gaussian noises: Application to hydraulic servo drives, Nonlinear Dynamics, 100 (2020), 2299-2313.  doi: 10.1007/s11071-020-05616-4.  Google Scholar

[39]

M. DavariW. GaoZ. P. Jiang and F. L. Lewis, An Optimal Primary Frequency Control Based on Adaptive Dynamic Programming for Islanded Modernized Microgrids, IEEE Transactions on Automation Science and Engineering, 18 (2021), 1109-1121.  doi: 10.1109/TASE.2020.2996160.  Google Scholar

[40]

M. Tomás-Rodríguez and S. P. Banks, Linear, Time-varying Approximations to Nonlinear Dynamical Systems: with Applications in Control and Optimization, Springer-Verlag Berlin, 2010. doi: 10.1007/978-1-84996-101-1.  Google Scholar

[41]

A. Vacca and G. Franzoni, Hydraulic Fluid Power: Fundamentals, Applications, and Circuit Design, John Wiley & Sons, USA, 2021. Google Scholar

[42]

K. G. Vamvoudakis and F. L. Lewis, Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton–Jacobi equations, Automatica, 47 (2011), 1556-1569.  doi: 10.1016/j.automatica.2011.03.005.  Google Scholar

[43]

A. van de WalleF. Naets and W. Desmet, Virtual microphone sensing through vibro-acoustic modelling and Kalman filtering, Mechanical Systems and Signal Processing, 104 (2018), 120-133.  doi: 10.1016/j.ymssp.2017.08.032.  Google Scholar

[44]

J. J. Vyas, B. Gopalsamy and H. Joshi, Electro-Hydraulic Actuation Systems: Design, Testing, Identification and Validation, Springer, Singapore, 2019. doi: 10.1007/978-981-13-2547-2.  Google Scholar

[45]

P. Werbos, Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences, Ph.D thesis, Harvard University, 1975.  Google Scholar

[46]

H. XuS. Jagannathan and F. L. Lewis, Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses, Automatica, 48 (2012), 1017-1030.  doi: 10.1016/j.automatica.2012.03.007.  Google Scholar

[47]

X. Zhang and X. Li, Input-to-state stability of non-linear systems with distributed-delayed impulses, IET Control Theory Appl., 11 (2017), 81-89.  doi: 10.1049/iet-cta.2016.0469.  Google Scholar

[48]

H. ZhangR. YeS. LiuJ. CaoA. Alsaedi and X. Li, LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays, Internat. J. Systems Sci., 49 (2018), 537-545.  doi: 10.1080/00207721.2017.1412534.  Google Scholar

show all references

References:
[1]

W. Aangenent, D. Kostic, B. de Jager, R. van de Molengraft and M. Steinbuch, Data-Based optimal control, Proceedings of the 2005 American Control Conference, (2005), 1460–1465. doi: 10.1109/ACC.2005.1470171.  Google Scholar

[2]

A. Al-TamimiF. L. Lewis and M. Abu-Khalaf, Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control, Automatica, 43 (2007), 473-481.  doi: 10.1016/j.automatica.2006.09.019.  Google Scholar

[3]

K. J. Astrom and B. Wittenmark, Adaptative Control, Addison-Wesley, Reading, 1995. Google Scholar

[4]

D. Bertsekas, Reinforcement and Optimal Control, Athena Scientific, USA, 2019. Google Scholar

[5]

D. Bertsekas, Dynamic Programming and Optimal Control Vol. 1, 4$^{th}$ edition, Athena Scientific, USA, 2012.  Google Scholar

[6]

T. Bian and Z. P. Jiang, Value iteration and adaptive dynamic programming for data-driven adaptive optimal control designs, Automatica, 71 (2016), 348-360.  doi: 10.1016/j.automatica.2016.05.003.  Google Scholar

[7]

J. F. Blackburn, G. Reethof and J. L. Shearer, Fluid Power Control, The MIT Press Cambridge, USA, 1960. Google Scholar

[8]

A. CavalloG. De MariaC. Natale and S. Pirozzi, Slipping detection and avoidance based on Kalman filter, Mechatronics, 24 (2014), 489-499.  doi: 10.1016/j.mechatronics.2014.05.006.  Google Scholar

[9]

Y. H. ChangQ. Hu and C. J. Tomlin, Secure estimation based Kalman filter for cyber–physical systems against sensor attacks, Automatica, 95 (2018), 399-412.  doi: 10.1016/j.automatica.2018.06.010.  Google Scholar

[10]

T. Chen and B. A. Francis, Optimal Sampled-data Control Systems, Springer-Verlag, London, 1996. doi: 10.1007/978-1-4471-3037-6.  Google Scholar

[11]

V. FilipovicN. Nedic and V. Stojanovic, Robust identification of pneumatic servo actuators in the real situations, Forschung im Ingenieurwesen - Engineering Research, 75 (2011), 183-196.  doi: 10.1007/s10010-011-0144-5.  Google Scholar

[12]

W. GaoY. JiangZ. P. Jiang and T. Chai, Output-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programming, Automatica, 72 (2016), 37-45.  doi: 10.1016/j.automatica.2016.05.008.  Google Scholar

[13]

W. Gao, Y. Jiang, Z. P. Jiang and T. Chai, Adaptive and optimal output feedback control of linear systems: An adaptive dynamic programming approach, Proceeding of the 11th World Congress on Intelligent Control and Automation, China, (2014), 2085–2090. Google Scholar

[14]

W. Gao and Z. P. Jiang, Learning-based adaptive optimal tracking control of strict-feedback nonlinear systems, IEEE Trans. Neural Netw. Learn. Syst., 29 (2018), 2614-2624.  doi: 10.1109/TNNLS.2017.2761718.  Google Scholar

[15]

W. GaoM. HuangZ. P. Jiang and T. Chai, Sampled-data-based adaptive optimal output-feedback control of a 2-degree-of-freedom helicopter, IET Control Theory and Applications, 10 (2016), 1440-1447.  doi: 10.1049/iet-cta.2015.0977.  Google Scholar

[16]

G. Hewer, An iterative technique for the computation of the steady state gains for the discrete optimal regulator, IEEE Transactions on Automatic Control, 16 (1971), 382-384.  doi: 10.1109/TAC.1971.1099755.  Google Scholar

[17]

Q. Hu, Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits, Nonlinear Dynamics, 55 (2009), 301-321.  doi: 10.1007/s11071-008-9363-1.  Google Scholar

[18]

P. A. Ioannou and J. Sun, Robust adaptive control, Dover Publications, New York, 2012. Google Scholar

[19]

M. Jelali and A. Kroll, Hydraulic Servo-systems: Modelling, Identification and Control, Springer-Verlag London, UK, 2012. doi: 10.1007/978-1-4471-0099-7.  Google Scholar

[20]

F. L. Lewis and D. Liu, Reinforcement Learning and Approximate Dynamic Programming for Feedback Control, John Wiley & Sons, New Jersey, USA, 2012. doi: 10.1002/9781118453988.  Google Scholar

[21]

F. L. Lewis and K. G. Vamvoudakis, Reinforcement learning for partially observable dynamic processes: Adaptive dynamic programming using measured output data, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 41 (2010), 14-25.   Google Scholar

[22]

F. L. Lewis, D. Vrabie and V. L. Syrmos, Optimal Control, 3$^{rd}$ edition, John Wiley & Sons, New Jersey, 2012. doi: 10.1002/9781118122631.  Google Scholar

[23]

X. LiJ. ShenH. Akca and R. Rakkiyappan, LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter, Appl. Math. Comput., 250 (2015), 798-804.  doi: 10.1016/j.amc.2014.10.113.  Google Scholar

[24]

X. LiX. Yang and S. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica, 103 (2019), 135-140.  doi: 10.1016/j.automatica.2019.01.031.  Google Scholar

[25]

L. Ljung, System Identification: Theory for the User, Prentice Hall, Inc., Englewood Cliffs, NJ, 1987  Google Scholar

[26]

X. Lv and X. Li, Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications, ISA Transactions, 70 (2017), 30-36.  doi: 10.1016/j.isatra.2017.07.025.  Google Scholar

[27]

K. MaesA. IliopoulosW. WeijtjensC. Devriendt and G. Lombaert, Dynamic strain estimation for fatigue assessment of an offshore monopile wind turbine using filtering and modal expansion algorithms, Mechanical Systems and Signal Processing, 76–77 (2016), 592-611.  doi: 10.1016/j.ymssp.2016.01.004.  Google Scholar

[28]

N. Manring, Fluid Power Pumps and Motors: Analysis, Design and Control, McGraw Hill Professional, USA, 2013. Google Scholar

[29]

J. J. MurrayC. J. CoxG. G. Lendaris and R. Saeks, Adaptive dynamic programming, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews, 32 (2002), 140-153.  doi: 10.1109/TSMCC.2002.801727.  Google Scholar

[30]

M. Mynuddin and W. Gao, Distributed predictive cruise control based on reinforcement learning and validation on microscopic traffic simulation, IET Intelligent Transport Systems, 14 (2020), 270-277.  doi: 10.1049/iet-its.2019.0404.  Google Scholar

[31]

M. Mynuddin, W. Gao and Z. P. Jiang, Reinforcement learning for multi-agent systems with an application to distributed predictive cruise control, 2020 American Control Conference (ACC), (2020), 315–320. doi: 10.23919/ACC45564.2020.9147968.  Google Scholar

[32]

N. NedicV. Stojanovic and V. Djordjevic, Optimal control of hydraulically driven parallel robot platform based on firefly algorithm, Nonlinear Dynam., 82 (2015), 1457-1473.  doi: 10.1007/s11071-015-2252-5.  Google Scholar

[33]

R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach, 2$^{nd}$ edition, John Wiley & Sons, New Jersey, 2012. Google Scholar

[34]

C. R. RojasJ. C. AgueroJ. S. WelshG. C. Goodwin and A. Feuer, Robustness in experiment design, IEEE Trans. Automat. Control, 57 (2012), 860-874.  doi: 10.1109/TAC.2011.2166294.  Google Scholar

[35]

M. RoozegarM. J. Mahjoob and M. Jahromi, Optimal motion planning and control of a nonholonomic spherical robot using dynamic programming approach: Simulation and experimental results, Mechatronics, 39 (2016), 174-184.   Google Scholar

[36]

J. L. Sun and C. S. Liu, An overview on the adaptive dynamic programming based missile guidance law, Acta Automatica Sinica, 43 (2017), 1101-1113.   Google Scholar

[37]

V. StojanovicN. NedicD. PrsicL. Dubonjic and V. Djordjevic, Application of cuckoo search algorithm to constrained control problem of a parallel robot platform, J. Advanced Manufacturing Technology, 87 (2016), 2497-2507.  doi: 10.1007/s00170-016-8627-z.  Google Scholar

[38]

V. Stojanovic and D. Prsic, Robust identification for fault detection in the presence of non-Gaussian noises: Application to hydraulic servo drives, Nonlinear Dynamics, 100 (2020), 2299-2313.  doi: 10.1007/s11071-020-05616-4.  Google Scholar

[39]

M. DavariW. GaoZ. P. Jiang and F. L. Lewis, An Optimal Primary Frequency Control Based on Adaptive Dynamic Programming for Islanded Modernized Microgrids, IEEE Transactions on Automation Science and Engineering, 18 (2021), 1109-1121.  doi: 10.1109/TASE.2020.2996160.  Google Scholar

[40]

M. Tomás-Rodríguez and S. P. Banks, Linear, Time-varying Approximations to Nonlinear Dynamical Systems: with Applications in Control and Optimization, Springer-Verlag Berlin, 2010. doi: 10.1007/978-1-84996-101-1.  Google Scholar

[41]

A. Vacca and G. Franzoni, Hydraulic Fluid Power: Fundamentals, Applications, and Circuit Design, John Wiley & Sons, USA, 2021. Google Scholar

[42]

K. G. Vamvoudakis and F. L. Lewis, Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton–Jacobi equations, Automatica, 47 (2011), 1556-1569.  doi: 10.1016/j.automatica.2011.03.005.  Google Scholar

[43]

A. van de WalleF. Naets and W. Desmet, Virtual microphone sensing through vibro-acoustic modelling and Kalman filtering, Mechanical Systems and Signal Processing, 104 (2018), 120-133.  doi: 10.1016/j.ymssp.2017.08.032.  Google Scholar

[44]

J. J. Vyas, B. Gopalsamy and H. Joshi, Electro-Hydraulic Actuation Systems: Design, Testing, Identification and Validation, Springer, Singapore, 2019. doi: 10.1007/978-981-13-2547-2.  Google Scholar

[45]

P. Werbos, Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences, Ph.D thesis, Harvard University, 1975.  Google Scholar

[46]

H. XuS. Jagannathan and F. L. Lewis, Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses, Automatica, 48 (2012), 1017-1030.  doi: 10.1016/j.automatica.2012.03.007.  Google Scholar

[47]

X. Zhang and X. Li, Input-to-state stability of non-linear systems with distributed-delayed impulses, IET Control Theory Appl., 11 (2017), 81-89.  doi: 10.1049/iet-cta.2016.0469.  Google Scholar

[48]

H. ZhangR. YeS. LiuJ. CaoA. Alsaedi and X. Li, LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays, Internat. J. Systems Sci., 49 (2018), 537-545.  doi: 10.1080/00207721.2017.1412534.  Google Scholar

Figure 1.  The HSA configuration
Figure 2.  ADP based control algorithm for the discretized HSA system
Figure 3.  Flowchart of ADP based controller design
Figure 4.  Hybrid nature of control signal
Figure 5.  Trajectories of the input and output of the HSA
Figure 6.  Trajectory of states
Figure 7.  Convergence of $ \bar{P}_j $ and $ \bar{K}_j $ to their optimal values $ \bar{P}^* $ and $ \bar{K}^* $ during the learning process
Figure 8.  (a) Comparison of the cost functions during learning; (b) Error between the optimal and approximated cost function
Figure 9.  (a) Comparison of the control policies during learning process; (b) Error between the optimal and approximated input signal
Table 1.  Parameters of the HSA
Notations Denotes
$ x_v $ The spool valve displacement
$ p_a $, $ p_b $ Forward and the return pressure
$ q_a $, $ q_b $ Forward and the return flows
$ y $ Piston displacement
$ L $ Piston stroke
$ K_e $ Load spring gradient
$ p_S $, $ p_0 $ Supply and tank pressure
$ m_t $, $ m_p $, $ m $ Total mass, piston mass, payload mass
$ F_f $ Friction forces
$ F_{ext} $ Disturbance forces
$ A_a $, $ A_b $ Effective areas of the head and rod piston side
$ V_a $, $ V_b $, $ V_{a0} $, $ V_{b0} $ Fluid volumes of the head and rod piston side and corresponding initial volumes
$ q_{Li} $, $ q_{Le} $ Internal and external leakage flow
$ \beta_e $ Bulk modulus of the fluid
Notations Denotes
$ x_v $ The spool valve displacement
$ p_a $, $ p_b $ Forward and the return pressure
$ q_a $, $ q_b $ Forward and the return flows
$ y $ Piston displacement
$ L $ Piston stroke
$ K_e $ Load spring gradient
$ p_S $, $ p_0 $ Supply and tank pressure
$ m_t $, $ m_p $, $ m $ Total mass, piston mass, payload mass
$ F_f $ Friction forces
$ F_{ext} $ Disturbance forces
$ A_a $, $ A_b $ Effective areas of the head and rod piston side
$ V_a $, $ V_b $, $ V_{a0} $, $ V_{b0} $ Fluid volumes of the head and rod piston side and corresponding initial volumes
$ q_{Li} $, $ q_{Le} $ Internal and external leakage flow
$ \beta_e $ Bulk modulus of the fluid
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