## Abstract

The Electronic Throttle Valve (ETV) is the core part of automotive engines which are recently used in control-by-wire cars. The estimation of its states and uncertainty is instructive for control applications. This study presents the design of Extended State Observer (ESO) for estimating the states and uncertainties of Electronic Throttle Valve (ETV). Two versions of ESOs have been proposed for estimation: Linear ESO (LESO) and Nonlinear ESO (NESO). The model of ETV is firstly developed and extended in state variable form such that the extended state stands for the uncertainty in system parameters. The design of both structures of ESOs are developed and a comparison study has been conducted to show the effectiveness of the proposed observers. Numerical simulation has been conducted to assess the performance of observers in estimating the states and uncertainties of ETV. The simulated results showed that both full order and reduced order models of ETV have the same transient characteristics. Moreover, the effectiveness of two versions of observers has been examined based on Root Mean Square of Error (RMSE) indicator. The results showed that the NESO has less estimation errors for both states and uncertainties than LESO.

## 1 Introduction

The throttle valve part is one of the important parts in automobile engines. By changing the opening angle of the valve plate, the air–fuel ratio is adjusted during the combustion process. In conventional engines of cars, the driver controls the valve plate directly by connecting the valve plate to the accelerator pedal via a wire connection. In this classical technology, external and internal conditions like weather conditions, road conditions, fuel efficiency, emission performance of vehicles, fuel economy are not taken into consideration. This has an adverse effect on the whole efficiency of the engine and the accuracy of the car system; especially there are high complexities and nonlinearity in dynamics of the throttle valve due to variable stiffness and mechanical hysteresis. In recent technologies of the automotive industry, the ETV has appeared to solve the problems due to conventional throttle valve in the previous era. The key of using ETV is that its plate angle is controlled by an electronic unit. Instead of using direct connection between the valve plate and the acceleration pedal to control the air flow, the level of the gas pedal is firstly measured via a special sensor which gives feedback to control algorithm. The control algorithm is responsible for generating the required control signals to actuate the DC motor for moving the throttle plate at the required angle [1–3].

The throttle valve system is characterized by high and non-smooth nonlinearities such as gear backlash, stick–slip friction, and a nonlinear spring. This makes control design difficult and sophisticated. Moreover, another control difficulty arises due to variation in system parameters and the inexact modeling of these non-smooth nonlinearities. In addition, unmatched parameter uncertainties inherently exist, which can further complicate the design of controller. Therefore, robust controller is required to cope with all the above model problems [4–6].

In some control applications, it is not possible to measure all states of the systems. Therefore, state-feedback control techniques are difficult to apply unless another tool is used to estimate the unmeasurable states. This problem can be solved by using state observer, which makes the estimation of all states possible with only measuring the output of the system. The Luenberger observer (LO) was the conventional technique to estimate the states of linear systems. The LO could give quicker convergence of system states when its gain is set at high values. High gain of LO may lead to peaking phenomenon which results in amplification of estimation errors. This difficulty can be overcome by introducing other nonlinear high-gain observers, which can give quick convergence of estimation errors with high suppressing of peaking phenomenon. One effective and successive observer is the sliding mode-observer. This observer gives good robustness characteristics, but it suffers from some problems like anti-chattering, adaptability, and uncertainty estimation [7, 8]. To address these issues, Extended State Observer (ESO) is presented, which estimates the state vector, as well as the uncertainties in an integrated manner.

The ESO plays a vital role in feedback control design of nonlinear systems like active disturbance rejection control (ADRC). The ESO could not only estimate the unmeasured states in real time, but it can also estimate the total disturbance due to external disturbance, unknown coefficient of control, unmodeled system dynamics, or those parts which are hard to be described by the practitioner. In general, the ESO can deal with uncertainties which are either coming from external disturbance or coming from the system itself. However, the high gain nature of ESO is considered a challenge in conditions where the output measurement is contaminated by high-frequency and non-negligible noise [9–13].

In the literature, there are many researchers who have used different structures of observers to estimate the states of ETV. In [14], S. A. Al-Samarraie et al. used Sliding Mode Perturbation Estimator to control the angular position of plate in ETV. In [15], Li Y applied ESO to observe the opening angle of plate in ETV under intelligent double integral sliding mode controller. In [16], J. Xue et al. utilized ESO in control of ETV to compensate the total disturbances due to uncertainties of system parameters and nonlinearities of return spring and frictions. In [17], Y. Li et al. presented the design of ESO based on dynamic model of ETV to estimate the total disturbance and the opening angle change of throttle valve plate. The ESO is the main element of the controller based on double-loop integral sliding-mode control. In [18], B. Yang et al. used Luenberger-sliding mode observer (LSMO) to estimate the change of throttle valve opening. In addition, the total uncertainties, like gear backlash torque and external disturbance, are approximated based on fuzzy logic system. The LSMO is the essential part in output feedback control based on double loop integral sliding mode control. In [19], Zheng et al. have designed ESO to estimate the opening angle of throttle valve plate to satisfy control accuracy of plate angle. The designed ESO is used in output feedback control based on sliding mode control approach. In [20], R. Gzam et al. presented two versions of observers to estimate the state of valve angular position, to detect the faults in sensors and system, and to compensate for the external disturbances. The proposed observers are Luenberger Observer (LO) and Unknown Input Observer (UIO). The observers have supported the robustness of the proposed PID controller against unknown input disturbances and faults of sensors. In [21], T. Agbaje et al. have designed global finite-time observer to estimate the total disturbances and to estimate the derivatives of ET system output. Based on the designed observer, the proposed terminal SMC can achieve finite-time control of plate motion for ETV system.

In this study, ESO has been proposed to estimate the states of ETV systems including the lumped uncertainties of the system. This observer is different from observers addressed in the above literature. The estimated states include the angular position and velocity of the throttle plate. In addition, the observer also estimates the total uncertainties inherited in the ETV system due to external disturbance and nonlinearities of spring characteristics. Two versions of ESO have been considered; one version is based on linear structure of ESO and the other is based on Nonlinear structure of ESO. The contribution of this work can be summarized as follows:

To design the Linear Extended State Observer (LESO) and Nonlinear Extended State Observer (NESO) for estimating the states and uncertainties of ETV system.

To conduct a comparison study in performance between LESO and NESO.

The article is organized in four parts. The first part has addresses the mathematical modeling of ETV for both full and reduced order dynamic models. The second part presents the design of ESO based on reduced-order model of the ETV. The third section conducts numerical simulations to verify the effectiveness of both versions of ESO, represented by LESO and NESO. The fourth part highlights the concluded points obtained by the computer simulation.

## 2 Model of electronic throttle valve system

As shown in Fig. 1, the ETV consists of DC motor, motor pinion gear, an intermediate gear, a sector gear, a valve plate, and a nonlinear spring.

## 3 Extended state observer design

### Assumption

For the system described by state variable of Eq. (5), the extended state variable can be satisfied if there is a new bounded and differentiable state variable

The parameters

## 4 Computer simulation

In order to verify the effectiveness of proposed versions of extended state observers in estimating the actual states and uncertainties of EVT, the numerical simulation based on MATLAB/SIMULINK has been conducted. This programming tool is efficient in control design of different control applications. It is supported by robust numerical solvers which can cope with complex differential equations. It also provides flexibility in programming. The control engineers can develop their control algorithms either with matlab files, blocks within SIMULINK environment, or hybridization of both Simulink tools with matlab functions. The control designer can code the control laws or represent the differential equations of dynamic system using general instructions which are devoted to these purposes. The physical parameters of ETV are listed in Table 1.

The parameter setting of ETV

Parameter symbol | Setting value |

1/18 | |

In the first scenario, the open-loop test of ETV has been simulated based on full dynamic model, Eq. (2), and reduced dynamic model, Eq. (3). In Figs 2 and 3, the open-loop tests have been conducted for both reduced order and full order models, respectively, under zero test input with initial values

Open loop response (reduce model)

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Open loop response (reduce model)

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Open loop response (reduce model)

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Open loop response (full model)

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Open loop response (full model)

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Open loop response (full model)

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

In this open-loop test scenario, it is interesting to investigate the convergence of states in phase plane portrait. Figures 4 and 5 show the trace of trajectories with different initial conditions (

Phase portrait (

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Phase portrait (

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Phase portrait (

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Phase portrait (

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Phase portrait (

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Phase portrait (

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

In the second scenario, the numerical simulation has been implemented for estimating the states and uncertainties of the ETV system. Figure 6 shows the validation of linear ESO, where

The performance of linear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The performance of linear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The performance of linear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The responses of estimation errors due to linear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The responses of estimation errors due to linear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The responses of estimation errors due to linear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

In the next simulation, the performance of nonlinear ESO has been verified and assessed. Figure 8 shows the behavior of estimated states due to nonlinear ESO. Again, the nonlinear ESO could successfully estimate the actual states and the state representing the total uncertainty of the ETV system. Figure 9 shows the behaviors of both actual states and estimated states due to both linear and nonlinear ESO.

The performance of nonlinear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The performance of nonlinear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The performance of nonlinear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The behaviors of actual and estimated states due to both linear and nonlinear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The behaviors of actual and estimated states due to both linear and nonlinear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

The behaviors of actual and estimated states due to both linear and nonlinear ESO

Citation: International Review of Applied Sciences and Engineering 2023; 10.1556/1848.2023.00662

Table 2 gives the evaluation report based on two types of ESO. The Root Mean Square of Error (RMSE) has been used as index of evaluation. The table shows that the LESO gives less RMSE for estimation errors of angular position and angular error velocity. Moreover, the LESO outperforms NESO in terms of uncertainty estimation. The LESO gives better estimation accuracy of uncertainty as compared to that based on NESO.

Performance evaluation of ESOs

Type of Estimation Error | RMSE | |

LESO | NESO | |

Tracking estimation error of angle | ||

Tracking estimation error of angular velocity | 1.098 | 1.724 |

Uncertainty estimation error | 5.200 | 7.01 |

## 5 Conclusion

In this study, two versions of ESOs are proposed to estimate the actual states and uncertainties of the ETV system. These observers are LESO and NESO. The extension of the system model is a prerequisition in application of ESO. The extended state represents all uncertainties and external loads in the applied system. The performances of LESO and NESO have been verified using numerical simulations, which showed that both observers could estimate the actual states and uncertainties of throttle valve in a good manner. The performances of the proposed ESOs are evaluated based on the index RMSE. According to Table 2, it has been concluded that LESO gives less RMSE for estimation errors of angular position and angular error velocity. Moreover, the LESO outperforms NESO in terms of uncertainty estimation. Based on these results, one can conclude that the LESO has better estimation performance than NESO in terms of estimation errors.

In order to extend this study to future work, other observer techniques can be suggested to estimate the states of ETV such as adaptive observer, backstepping observer, nonlinear disturbance observer, perturbation observer, sliding mode observer [22–27]. One can conduct a comparison study between one of the suggested observers and the proposed observer in this study. Other suggestion for future work is to use optimization techniques such as Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Butterfly Optimization Algorithm (BOA), and Gray Wolf Optimization (GWO) to tune the design parameters of the proposed observer for further improvement [28–32].

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