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Data-driven control of hydraulic servo actuator based on adaptive dynamic programming

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

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  • 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.

    Mathematics Subject Classification: Primary: 49M25, 76-02, 90C39.


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  • 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
     | Show Table
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