## Abstract

This study has developed adaptive synergetic control (ASC) algorithm to control the angular position of moving plate in the electronic throttle valve (ETV) system. This control approach is inspired by synergetic control theory. The adaptive controller has addressed the problem of variation in systems parameters. The control design includes two elements: the control law and adaptive law. The adaptive law is developed based on Lyupunov stability analysis of the controlled system, and it is responsible for estimating the potential uncertainties in the system. The effectiveness of the proposed adaptive synergetic control has been verified by numerical simulation using MATLAB/Simulink. The results showed that the ASC algorithm could give good tracking performance in the presence of uncertainty perturbations. In addition, a comparison study has been made to compare the tracking performance of ASC and that based on conventional synergetic control (CSC) for the ETV system. The simulated results showed that the performance of ASC outperforms that based on CSC. Moreover, the results showed that the estimation errors between the actual and estimated uncertainties are bounded and there is no drift in the developed adaptive law of ASC.

## 1 Introduction

The electronic throttle valve device is a modern technology in recent industrial and automotive applications. It serves to manage the air flow in gasoline-powered engines to achieve optimal air-fuel mixtures, to minimize emissions and to maximize fuel economy [1]. Due to complex nonlinearities, it is difficult to find exact and reliable physical models. Therefore, the control of throttle valve system is a challenging problem and a robust controller is required to cope with built-in uncertainties. The valve of ETV must be regulated rapidly without overshoot to ensure bounded position errors. The electronic throttle valve consists of servo motor, motor pinion gear, valve plates, dynamic spring, and position sensor (see Fig. 1).

Synergetic controls take advantage of the potential of open systems to self-organize. The theory implies a holistic philosophy of regulated dynamic interactions between energy, matter, and information, which is executed by means of both positive and negative feedback. The philosophy of synergetic control design is founded on the notion of dynamic expansion and contraction of the controlled system's state space. The extension of the state space enriches the system dynamics by supplying more information that is essential for enhancing the efficiency of the closed-loop system. In contrast to expansion, constriction of the state space accomplished by the control action eliminates undesirable system dynamics or reduces excessive degrees of freedom. At the stage of control design, these undesirable dynamics are eliminated by inserting dynamic constraints represented as invariant manifolds in the system's state space. In what follows, a brief review of previous works that are most recent and relevant will be presented. Yuan et al. [2] proposed a support vector machine (SVM)-based approximate model control for the electronic throttle. Based on an input-output approximation method, the Taylor expansion is used to develop the nonlinear control law such as to avoid complexity in control design, reduction in computation effort, and to perform online adjustment and learning. With a new input–output approximation introduced for the general NARMA model, the approximate control law is defined straightly, and its design by using the SVM is direct without additional training. Honek et al. [3] address a problem with electronic throttle control. The suggested approach method is a discrete PI controller with a feedforward controller and parameters scheduling working together. Dulau and Oltean [4] describe the mathematical modeling of the throttle valve of internal combustion engines. The model is used to create reliable controllers using H2 and H(inf) synthesis All of the simulation scenarios focus attention on the closed-loop system's rightness stability characteristics, even when the plant model is influenced by disturbances. Horn et al. [5] presented controllers for electronic throttle valves, using concepts of sliding-mode control to be applied. Standard integrating sliding-mode controllers are in opposition to super-twisting algorithms, which are higher order concepts. Zeng & Wan [6] designed a nonlinear PID controller for the position control of the throttle valve. With the changing system error, it continuously modifies the controller's proportional gain P, integral gain I, and differential gain D. Son Tran & Ngoc Anh Dang [7] suggested a control strategy using a Model Reference Adaptive System-based Learning Feed-Forward Controller technique to combine a PD controller with a traditional PID controller to replace it. Combining these techniques will allow the PD controller to manage the valve plate's position while tracking the reference signal by overcoming the nonlinearities in the system. Mercorelli [8] demonstrated how an approximated proportional derivative (PD) regulator may be self-tuned in real time to compensate for tracking error induced by inexact feedback linearization. It is worth noting that the structure of the estimated PD regulator is identical to that of the velocity estimator. The suggested loop control achieves robustness. Thanok et al. [9] developed adaptive cruise control and created an AIT intelligent car. Drive-by-wire technology replaces the mechanical throttle valve control. The position of the throttle valve is controlled by a dc servo motor in the drive-by-wire system. The throttle valve is controlled by a proportional and derivative control algorithm. Loh et al. [10] used the input-output feedback linearization technique to create nonlinear control action for Electronic Throttle Valve system, they compared simulation and real-time implementation output and achieved good outcomes for this specific ETC system. Shibly Ahmed Al-Samarraie et al. [11] developed controller (slide mode) including an estimated perturbation term with a negative sign (to negate it) and a stabilizing term to stabilize the nominal system model. The perturbation term includes unknown external input and nonlinear throttle valve model uncertainty. Humaidi & Hameed [12] developed two adaptive control algorithms for the sliding mode and adaptive backstepping based control of the angular position of the electronic throttle valve plate. Comparison of the two approaches. the establishment of the adaptive law by the utilization of a smoothly switching feature. The Lyapunov theory is utilized to analyze the stability of closed-loop system based on adaptive controller. The control law and adaptive laws of adaptive controller are developed based on Lyapunov stability analysis to guarantee asymptotic stability of adaptive controlled-system.

In the work, design of classic and adaptive synergetic control schemes have been developed to control the position of throttle plate. The following points address the contributions of this study:

Design of classic and adaptive control schemes based on synergetic control theory to control the plate angular position of ETV system.

Conducting a comparison study in performance between adaptive synergetic control and classic synergetic control.

Designing the adaptive law of ASC which ensures boundness of estimated states or to avoid the drift of adaptive gains.

The rest of the article is organized in five sections. The second section presents the state representation of ETV system. The control design for both adaptive and classical synergetic schemes are developed in the third section. The fourth section conducts numerical simulation to validate and assess the performance of both controllers. In the fifth part, the discussion has been conducted. The conclusion and future work has been highlighted in the sixth section.

## 2 The dynamic model for electronic throttle valve

Figure 2 shows the details of ETV system. The DC motor is represented by electric circuits. The shaft of DC is linked by gear box, which is used to actuate the plate of the ETV system.

Circuit diagram of ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Circuit diagram of ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Circuit diagram of ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

## 3 Control design for electronic throttle valve system

In this part, the control design is developed based on synergetic control theory. Two versions of synergetic controllers are presented: the classical synergetic control (CSC) and adaptive synergetic control (ASC). The latter is developed to cope with the uncertainties in the system parameters [14–21].

### 3.1 Synergetic controller (CSC)

*T*has positive real constant and it represents the converging ratio of

### 3.2 Adaptive synergetic control design

The suggested synergetic and adaptive synergetic control strategy is shown in the form of a schematic in Fig. 3.

The proposed adaptive synergetic control scheme for the ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

The proposed adaptive synergetic control scheme for the ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

The proposed adaptive synergetic control scheme for the ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

## 4 Computer simulation

The MATLAB/Simulink is used for modelling and simulation of the ETV system controlled by ASC and CSC. The numerical simulation has been conducted to verify the effectiveness of both controllers (ASC and CSC). The proposed control techniques have been numerically simulated and implemented within an environment of MATLAB software [27]. The Simulink model shown in Fig. 4 simulates the adaptive synergetic controlled ETV system using Simulink library. The model is made up of a total of five components: two subsystems and three MATLAB function blocks. Table 1 lists the parameter settings for the throttle valve system (TVS) [28].

Simulation modeling of ASC-based ETV system using MATLAB/Simulink

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Simulation modeling of ASC-based ETV system using MATLAB/Simulink

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Simulation modeling of ASC-based ETV system using MATLAB/Simulink

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

The parameters' values of the ETV system

Parameter | Value | Parameter | Value |

0.0017 H | 0.02 Kg. | ||

2.1 Ω | 0.072 N m A^{−1} | ||

0.075 | 4 | ||

0.006 N. m. s | 0.32 N m^{−1} | ||

0.03 N. m. s | 0.004 N. m. s | ||

0.01 kg. | 0.007 N. m. s |

The design parameters *T* value has been set to ^{−1} frequency.

### 4.1 Case I: excitation by sinusoidal waveform

The simulation of controlled system has been conducted by exerting desired sinusoidal trajectory, which oscillates at 0.5 rad s^{−1} and swings between 0.1745 and 0.723 rad in the angular range. Furthermore, the conditions of 0.4363 rad start the sinusoidal desired trajectory. In Fig. 5, the open-loop response shows that the system is unstable and cannot reach the desired trajectory. The throttle valve response angle for synergetic control (CSC) and adaptive synergetic control (ASC) is shown in Fig. 6. The adaptive synergetic controller shows better transient responsiveness and resilience than the synergetic controller.

Open-loop response for ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Open-loop response for ETV system

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Open-loop response for ETV system

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Tracking performance for ETV angular position based on CSC and ASC

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Tracking performance for ETV angular position based on CSC and ASC

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Tracking performance for ETV angular position based on CSC and ASC

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

The tracking error for the ASC is demonstrated, taking into account the uncertainty in the parameter and external disturbance. In this case, the ASC controller yields a root mean square error (RMSE) value of 0.1164 rad, while the CSC gives 0.1321 rad. One can conclude that the ASC exhibits better tracking performance compared to its counterpart.

Figure 7 depicts the throttle plate's angular speed response, where the adaptive synergetic controller has better transient characteristics than the synergetic controller. Figure 8 displays the behaviors of control efforts for both controllers. The figure shows that the height of spike in cases of adaptive synergetic controller is lower than that based on classical synergetic controller. In addition, the RMS of control effort for ASC is lower than that based on CSC.

Angular velocity of plate based on CSC and ASC

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Angular velocity of plate based on CSC and ASC

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Angular velocity of plate based on CSC and ASC

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Control action response based on CSC and ASC

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Control action response based on CSC and ASC

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Control action response based on CSC and ASC

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Figures 9–11 illustrate, the actual and estimated values of parameters a1, a2, and w, respectively. The boundness of estimate errors for unknown parameters is one of the most important aspects to consider when assessing the performance of adaptive designs for the vast majority of adaptive controllers. If specific limits are exceeded, the regulated system's stability may be compromised. According to Figs 9–11, one can conclude that the ASC could successfully produce bounded estimated gains and it was able to prevent these gains from growing without bound. However, if the designed adaptive controller lacks the ability to confine these gains within certain bound, instability problem can occur and the controller will be infeasible in control of the electronic throttle valve.

Actual and estimated parameter a1

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Actual and estimated parameter a1

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Actual and estimated parameter a1

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Actual and estimated parameter a2

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Actual and estimated parameter a2

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Actual and estimated parameter a2

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Actual and estimated parameter w

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Actual and estimated parameter w

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Actual and estimated parameter w

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### 4.2 Case II: excitation by random desired trajectory

Figure 12 depicts the angle position behavior based on CSC and ASC. It is evident from the zoomed-in image of the figure that the ASC performs tracking faster than that based on CSC.

Tracking performance for angular position the ETV system based on CSC and ASC with random desired

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Tracking performance for angular position the ETV system based on CSC and ASC with random desired

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Tracking performance for angular position the ETV system based on CSC and ASC with random desired

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

The tracking error between the synergetic and adaptive controlled electronic throttle valve is shown in Fig. 13. In terms of numbers, the ASC's RMSE value is equivalent to 0.1176 rad, while the RMSE provided by CSC is equal to 0.2035 rad. This shows that the tracking performance and error variance provided by the ASC are superior to those provided by a trial-and-error method. The velocity behaviors for CSC and ASC are shown in Fig. 14. However, it is clear that CSC's peak velocity response is a little bit higher than ASC's peak velocity response. Figure 15 depicts the CSC and ASC control actions. However, the peak of the CSC control signal is slightly higher than that of the ASC signal.

Error response of plate angular position based on CSC and ASC (with random desired)

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Error response of plate angular position based on CSC and ASC (with random desired)

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Error response of plate angular position based on CSC and ASC (with random desired)

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Angular speed response depending on (CSC) and (ASC) with random desired

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Angular speed response depending on (CSC) and (ASC) with random desired

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Angular speed response depending on (CSC) and (ASC) with random desired

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Response of control action based on (CSC) and (ASC) with random desired trajectory

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Response of control action based on (CSC) and (ASC) with random desired trajectory

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

Response of control action based on (CSC) and (ASC) with random desired trajectory

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00706

## 5 Discussion

This study made a comparison in performance between classical synergetic control (CSC) and adaptive synergetic control (ASC) in controlling the angular position of throttle valve. The ASC controller shows superior transient responsiveness and resilience compared to the CSC. The tracking error for ASC is 0.1164 Rad, indicating superior tracking performance and error variance. The angular speed response of the throttle plate is slightly better for ASC. The ASC requires almost the same control effort during transients, but with a lower RMSE. When tested the system with random desired wave, the tracking error of ACS is 0.1176 rad, while the CSC's RMSE is 0.2035 rad. The CSC's peak velocity response is slightly higher than the ASC's. Table 2 show RMSE value for CSC and ASC for both desired specific sinusoidal and random wave. The percentage difference in the RMSE values of the ASC was slightly less than that of the CSC, but when using the (ASC) it showed greater resistance to changes in the random wave and gave a value of MSMS less than CSC.

The improvements in performance

Desired Input | Controller | Improvement | |

CSC | ASC | ||

RMSE | |||

Sinusoidal desired input | 0.1321 | 0.1164 | 13.48% |

Random desired input | 0.2035 | 0.1176 | 11.88% |

## 6 Conclusions

This paper presented a synergetic and adaptive synergetic control (ASC) design for electronic throttle valve system to achieve angular position tracking control. The ASC has been developed to cope with inherited uncertainty and unknown parameters. The stability analysis has been conducted to derive the control laws and adaptive laws. Two scenarios with two desired trajectories have been presented to verify the effectiveness of the proposed controllers. According to simulation results, it has been shown that the adaptive controlled system (ASC) has better tracking performance than the CSC. In case of sinusoidal waveform, the ASC shows an improvement 13.43%, while the ASC gives 11.88% improvement in the case of random desired input. Furthermore, the ASC can effectively constrain the estimation errors of uncertain parameters within defined bound to avoid the drifting problem in estimation errors, which may lead to instability of the controlled system. This study can be extended by suggesting another control scheme in the literature and a comparison study can be made with proposed controllers for the electronic throttle valve system [29–41].

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