# American Institute of Mathematical Sciences

April  2021, 14(4): 1447-1464. doi: 10.3934/dcdss.2020375

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

 1 School of Automation, Southeast University, Nanjing 210096, China 2 Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, China 3 Shenzhen Research Institute of Southeast University, Shenzhen 518057, China

* Corresponding author: Shihua Li

Received  October 2019 Revised  February 2020 Published  April 2021 Early access  May 2020

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.

Citation: Hao Sun, Shihua Li, Xuming Wang. Output feedback based sliding mode control for fuel quantity actuator system using a reduced-order GPIO. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1447-1464. doi: 10.3934/dcdss.2020375
##### References:

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##### References:
Bosch electronically controlled VE distribution pump
Structure of fuel quantity actuator
Diagram of the fuel quantity actuator under the reduced-order GPIO based output feedback sliding mode control approach
Experimental test setup
Response curves in the presence of constant disturbance under SMC+ESO controller (34) (a) angular position; (b) duty ratio
Response curves in the presence of constant disturbance under SMC+GPIO controller (18) (a) angular position; (b) duty ratio
Response curves in the presence of time-varying disturbance under SMC+ESO controller (34) (a) angular position; (b) duty ratio
Response curves in the presence of time-varying disturbance under SMC+GPIO controller (18) (a) angular position; (b) duty ratio
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 $\Omega$
 Parameter Symbol Value Nominal Input Voltage $V_{in0}$ 12 $V$ Reference Output Angle ${\theta}_{ref}$ 0.5 $rad$ Nominal Resistance $R$ 0.75 $\Omega$
Parameters values for simplified model (5)
 Parameter Names Parameter Values $a_{21}$ $-7.1121\times10^{3}$ $a_{22}$ $-41.6290$ $c_{2}$ $-36.1109$ $c$ $-2.3370\times10^{3}$ $b$ $3.7872\times10^{4}$
 Parameter Names Parameter Values $a_{21}$ $-7.1121\times10^{3}$ $a_{22}$ $-41.6290$ $c_{2}$ $-36.1109$ $c$ $-2.3370\times10^{3}$ $b$ $3.7872\times10^{4}$
Control parameters for fuel quantity actuator
 Controller Control Parameters $SMC+GPIO$ $k_1=1000, \lambda = 30, \beta=-200$ $SMC+ESO$ $k_2=1000, \lambda = 30, p=-200$
 Controller Control Parameters $SMC+GPIO$ $k_1=1000, \lambda = 30, \beta=-200$ $SMC+ESO$ $k_2=1000, \lambda = 30, p=-200$
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
 Controller MAPR RT IAE(3-6s) Case Ⅰ SMC+ESO 0.0294rad 520ms 8.7119 SMC+GPIO 0.0228rad 502ms 6.4476
Comparisons of disturbance rejection performance (Case Ⅱ: Time-varying disturbance)
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