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Output feedback based sliding mode control for fuel quantity actuator system using a reduced-order GPIO

  • * Corresponding author: Shihua Li

    * Corresponding author: Shihua Li 
Abstract Full Text(HTML) Figure(8) / Table(5) Related Papers Cited by
  • In an electronically controlled VE distributive pump, the fuel quantity actuator is a significant component. It is responsible for governing the quantity of fuel being injected into diesel-type engines. The FQA system has nonlinearities and always confronts disturbances caused by the external torque and the input voltage variation in the real working condition, which can be regarded as a lumped disturbance. However, most existing results only focus on dealing with the so called constant disturbance in the FQA system which fail to remove the influence of time-varying disturbances. Therefore, to deal with the nonlinearities and reject the lumped disturbance, a reduced-order generalized proportional integral observer (GPIO) based sliding mode control approach is presented. By using a reduced-order GPIO, time-varying disturbances can be estimated accurately. In addition, a theoretical analysis of the closed-loop system is given. The proposed control scheme exhibits a satisfactory performance in terms of transient behavior and disturbance rejection. Finally, a set of experimental tests are carried out to validate the feasibility as well as efficiency of the proposed control framework.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Figure 1.  Bosch electronically controlled VE distribution pump

    Figure 2.  Structure of fuel quantity actuator

    Figure 3.  Diagram of the fuel quantity actuator under the reduced-order GPIO based output feedback sliding mode control approach

    Figure 4.  Experimental test setup

    Figure 5.  Response curves in the presence of constant disturbance under SMC+ESO controller (34) (a) angular position; (b) duty ratio

    Figure 6.  Response curves in the presence of constant disturbance under SMC+GPIO controller (18) (a) angular position; (b) duty ratio

    Figure 7.  Response curves in the presence of time-varying disturbance under SMC+ESO controller (34) (a) angular position; (b) duty ratio

    Figure 8.  Response curves in the presence of time-varying disturbance under SMC+GPIO controller (18) (a) angular position; (b) duty ratio

    Table 1.  Parameters of the fuel quantity actuator

    Parameter Symbol Value
    Nominal Input Voltage $ V_{in0} $ 12 $ V $
    Reference Output Angle $ {\theta}_{ref} $ 0.5 $ rad $
    Nominal Resistance $ R $ 0.75 $ \Omega $
     | Show Table
    DownLoad: CSV

    Table 2.  Parameters values for simplified model (5)

    Parameter Names Parameter Values
    $ a_{21} $ $ -7.1121\times10^{3} $
    $ a_{22} $ $ -41.6290 $
    $ c_{2} $ $ -36.1109 $
    $ c $ $ -2.3370\times10^{3} $
    $ b $ $ 3.7872\times10^{4} $
     | Show Table
    DownLoad: CSV

    Table 3.  Control parameters for fuel quantity actuator

    Controller Control Parameters
    $ SMC+GPIO $ $ k_1=1000, \lambda = 30, \beta=-200 $
    $ SMC+ESO $ $ k_2=1000, \lambda = 30, p=-200 $
     | Show Table
    DownLoad: CSV

    Table 4.  Comparisons of disturbance rejection performance (Case Ⅰ: Constant disturbance)

    Controller MAPR RT IAE(3-6s)
    Case Ⅰ SMC+ESO 0.0294rad 520ms 8.7119
    SMC+GPIO 0.0228rad 502ms 6.4476
     | Show Table
    DownLoad: CSV

    Table 5.  Comparisons of disturbance rejection performance (Case Ⅱ: Time-varying disturbance)

    Controller MAPR MAPD IAE(0-3s)
    Case Ⅰ SMC+ESO 0.0281rad 0.0454rad 64.3796
    SMC+GPIO 0.0149rad 0.0191rad 29.1016
     | Show Table
    DownLoad: CSV
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