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The valve-controlled cylinder position servo system has the advantages of large output force and large power. As characteristics of nonlinearity and uncertainty exist in the hydraulic servo system, it is difficult for the traditional PID control to meet the requirements of high precision and control. The active disturbance rejection control (ADRC) considers the uncertainty of the system and external disturbances as the total disturbance. In this paper, the valve-controlled cylinder servo system is designed based on ADRC, its working principle is described, and its mathematical model and cosimulation model based on MATLAB-AMESim are established. In the case of constant load, variable load, and long pipeline, the comparative simulation of ADRC and PID is carried out. The simulation results show that the ADRC can effectively suppress the disturbance of the internal parameter changes and external load changes of the hydraulic system and has strong robustness and high control accuracy. This study provides a reference for the application of ADRC in electrohydraulic servo systems.

The valve-controlled cylinder position servo system is a common hydraulic power execution system, with the advantages of large output force, large unit power volume ratio, and so on. It has been widely used in various fields. However, the electrohydraulic position servo control system is time-varying and nonlinear, such as nonlinearity of pressure flow and frictional force of the servo valve. It presents various features of time-varying parameters such as leakage coefficient, change of load, and change of damping ratio. Traditional PID control strategy is simple, but compared to some nonlinear, time-varying parameters of the system, it cannot achieve precise positioning control. In order to enhance the antijamming ability of electrohydraulic position servo control system while improving the precision control of the system, experts and scholars have researched a number of control strategies, including adaptive control, sliding mode control, and fuzzy control. Considering that the electrohydraulic servo system is nonlinear, Fang and Guan et al. [

In 1999, Han [

In this paper, an active disturbance rejection control strategy is developed to address those electrohydraulic position servo control systems with inherent nonlinear behaviors and modeling uncertainties. The simulation model of ADRC is established by using the MATLAB-AMESim cosimulation method in Simulink module library. The physical model of the valve-controlled cylinder position servo system was established on AMESim software. According to the simulation results, the effectiveness of the control method is verified and the influence of controller parameters on the control effect is analyzed.

The valve-controlled cylinder position servo system studied in this paper is shown in Figure

Model of valve-controlled cylinder position servo systems.

The flow equation of the servo valve is

Here,

Because the response speed of the servo amplifier is faster than that of the hydraulic system, the servo amplifier is treated as a proportional link to obtain the relationship between spool displacement (

The flow continuity equation of the hydraulic cylinder is

Here,

The force balance equation of the hydraulic cylinder and the load is

Here,

Take the state variables

The state space expression of the servo system is

The core design of ADRC is to define an extended state, take the simple cascade integral form as the standard type, treat the parts of the system dynamic that are different from the standard type (including the uncertainty and disturbance of the system) as the total disturbance (including internal disturbance and external disturbance), and define the total disturbance into the extended state. Then, by means of the extended state observer, the total disturbance is estimated and eliminated in real time, so as to restore the controlled object free of disturbance, uncertainty, and nonlinearity to the standard integral series type and realize the control of the system. ADRC makes the control system design from complex to simple, from abstract to intuitive.

The linear ADRC consists of three parts: tracking differentiator, linear extended state observer, and linear state error feedback control law, as shown in Figure

Structure of ADRC.

The design of ADRC does not need to rely on the speciﬁc mathematical model of a controlled object. It only needs to know the relative order of the system. For the design of LADRC based on generalized controlled object formula (

In this article, “Arrange transition” and “Track-Differentiator” are combined to simplify the controller structure. As shown in Figure

Schematic of the tracking differentiator.

Arrange the transition process according to the set value

Define the fast-optimal control synthesis function of equation (

The realization of fh is shown in the following equation:

Here,

The extended state observer of the system is established by tracking and estimating system state and disturbance with system output and input:

Here, it is denoted that

The real-time action of

A linear state observer is established for the extended system:

This set of parameters is “inherited” for objects of the fourth order and below and is not limited by the estimated disturbance amplitude

Linear state error feedback (LSEF) compensates the system disturbance through state error feedback. In this system, LSEF is designed as follows:

The ADRC controller has many parameters to be tuned. According to the functions of the tracking differentiator, the ESO, and the feedback control law, the parameters can be set independently according to the “separation principle”:

The parameter

The increase of

Because the electrohydraulic position servo control systems have inherent nonlinear behaviors and modeling uncertainties, it is difficult to establish an accurate mathematical model, so the cosimulation platform using MATLAB and AMESim is applied in this work. The mechanical and hydraulic parts are built in AMESim and the control part is modeled by MATLAB-Simulink. By using AMESim’s interface technology to Simulink and combining two excellent professional simulation tools, AMESim’s outstanding fluid mechanical simulation performance can be brought into play and Simulink’s powerful numerical processing capability can be utilized to achieve more perfect complementary effects.

The cosimulation principle of the valve-controlled cylinder servo system in ADRC based on MATLAB-AMESim platform is shown in Figure

Schematic diagram of cosimulation principle.

Cosimulation model. (a) Hydraulic system model in AMESim. (b) ADRC model in MATLAB.

Main parameters of the system.

Parameters | Value |
---|---|

Cylinder diameter | 45/63 mm |

Load mass | 100 kg |

Motor speed | 1500 r/min |

Pump delivery | 100 mL/r |

Relief pressure | 350 bar |

Load spring rate | 10000 N/m |

ADRC parameters are set as follows:

Observer parameters are

Controller parameters are

PID control is the most common and effective control method in engineering and its controller is designed as follows:

In order to analyze the dynamic performances of the system in ADRC, the following three simulation scenarios are designed in this section: (1) dynamic responses under constant load; (2) dynamic responses under variable load; (3) dynamic responses under long pipeline. Comparative analyses of the control characteristics of ADRC and PID are made.

When the load force is constant, step responses of the system in ADRC and PID are shown in Figure

Step responses in ADRC and PID under constant load. (a) Cylinder displacement response. (b) Spool position response.

Figure

Sinusoidal responses in ADRC and PID under constant load. (a) Cylinder displacement response. (b) Spool position response.

The step response and sinusoidal response show that ADRC has more advantages than PID and the system in ADRC has fast dynamic response and high control accuracy.

In practice, the load usually changes, so it is necessary to investigate the dynamic characteristics of the control system under variable load. In this part, the load force is variable in the simulation process. Under this condition, the parameters of PID are set as follows:

Figure

Step responses in ADRC and PID under variable load. (a) Sinusoidal load. (b) Cylinder displacement response. (c) Spool position response.

The hydraulic pipeline is one of the indispensable components of the hydraulic system and plays the role of connecting the component and the transmission medium. The characteristics of the pipeline have a great influence on the dynamic and static characteristics of the hydraulic system. When the pipeline is short, the pipeline effect can be ignored, but when the pipeline is long, the pipeline effect will cause the response to lag and the control accuracy will reduce. This section mainly discusses the dynamic characteristics of systems with long pipelines. In the simulation, the pipeline length is set to 50 m and diameter is set to 25 mm. Under this condition, the parameters of PID are set as follows:

The simulation results shown in Figure

Step responses of the hydraulic system with long pipelines. (a) Cylinder displacement response. (b) Spool position response.

A cosimulation model of the valve-controlled cylinder based on MATLAB-AMESim platform is more accurate than the mathematical model and is closer to the real system.

The structure and basic principles of active disturbance rejection control are introduced; the active disturbance rejection controller is designed, and the rule of parameter setting is clarified.

The comparative simulation with ADRC and PID is carried out in cases of constant load, variable load, and long pipeline. The simulation results show that the ADRC can effectively suppress the disturbance of the internal parameter changes and external load changes of the hydraulic system, has strong robustness and control accuracy, and has potential in electrohydraulic systems for high-performance control.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this article.

This work was supported by the Fundamental Research Funds for Central Universities (2019XKQYMS37), the Key Research and Development Program of Shanxi Province (International Cooperation) (201903D421051 and 201803D421028), and the Youth Fund Project of Shanxi Province (201901D211210).