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

Hao Sun; Shihua Li; Xuming Wang

doi:10.3934/dcdss.2020375

Article Contents

2021, Volume 14, Issue 4: 1447-1464. Doi: 10.3934/dcdss.2020375

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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
^* Corresponding author: Shihua Li

Received: October 2019

Revised: February 2020

Early access: May 2020

Published: April 2021

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Abstract

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.

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

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Figure 1. Bosch electronically controlled VE distribution pump

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Figure 2. Structure of fuel quantity actuator

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

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Figure 4. Experimental test setup

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

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

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

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

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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 $

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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} $

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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 $

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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

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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

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