Research on electro-hydraulic position servo synchronous control system based on adaptive robust control

A control method combining adaptive robust control with cross-coupling control is designed to address the issues of model uncertainty, nonlinear friction, and external interference in electro-hydraulic servo systems. We have established a nonlinear model of the system and designed an adaptive robust controller. Further simulation studies have shown that the control method designed in this paper has better control performance and stronger anti-interference ability than PID control and still has good control performance under continuous interference.


Introduction
As a typical application in servo systems, electro-hydraulic servo systems have been applied in many departments because of their advantages, such as high power and fast response [1] .However, due to the high nonlinearity of the system and the presence of an amount of model uncertainty [2] , including parameter uncertainty and uncertainty nonlinearity [3] , these uncertainties may make controllers designed based on system calibration values unstable.In recent years, with the continuous improvement of various requirements, the inherent nonlinear characteristics and various uncertainties in electro-hydraulic servo systems make it difficult for traditional linear control strategies to meet the many requirements of the system.Therefore, there is an urgent need to design more advanced nonlinear control strategies.
To achieve better synchronous tracking performance, various control strategies have been proposed, one after another.Wang et al. [4] proposed an integral separation PID control, which improves the dynamic response and accuracy of the system by controlling the integral switch selector.Wu et al. [5] designed a fuzzy single-neuron PID control algorithm and a cross-coupling algorithm as the hydraulic synchronization control algorithm for forging machines, and the results showed that this algorithm can make the system have good robustness.Zhao et al. [6] adopted a dual hydraulic cylinder synchronous control method with a servo closed-loop, which has high synchronization accuracy.Zheng et al. [7] used a variable inertia adaptive robust synchronization control algorithm and proved the stability of the proposed control algorithm through the Lyapunov method.Simulation results showed that tracking and synchronization errors can converge to a certain domain.Wos et al. [8] conducted synchronous control on three hydraulic cylinders, taking into account feedback from shaft position and synchronization error, and achieved good simulation consequences.
This article focuses on the parameter uncertainty and uncertainty nonlinearity in the electro-hydraulic servo synchronous control system.Firstly, the system is mathematically modeled, and an adaptive robust parameter controller is designed.Finally, the cross-coupling control method is used to simulate and verify the system, and the simulation results are analyzed.where m is the equivalent total mass of the load; y is the load displacement; 1 P and 2 P are the pressures in the working chamber; 1 A and 2 A are the working area of the working chamber; B is the viscous damping coefficient; f A is the maximum value of Coulomb friction; f S is a function that approximates the shape of Coulomb friction; d is the other unmodeled interference in the system.
The pressure dynamic equation of two cavities of a hydraulic cylinder is: where d C is the flow coefficient of the orifice; w is the area gradient of the orifice; θ is the density of the liquid oil; v x is the displacement of the valve core; s P is the oil source pressure, r P is the oil return pressure.
We simplify the position of the servo valve core and the control voltage as a proportional link: vi x ku < (4) where v k is the electrical gain coefficient of the servo valve.Therefore, Formula (3) can be converted to: Formula (1), Formula (2) and Formula ( 5) are nonlinear models of systems.Based on this, the state variables of the system are defined as where ∋ ( is a mismatch interference in the system.

System control strategy
In the electro-hydraulic servo synchronous control system, there are mainly three control methods: "equivalence", "master-slave", and "cross-coupling" [9] .Among them, compared with the first two kinds of cross-coupling control strategy, each hydraulic cylinder receives its tracking error feedback and synchronization error feedback, forming a closed-loop control of synchronization error.Therefore, this control strategy has a high precision of single cylinder position control and synchronization control and is often applied to the position, speed, and force synchronous control system with high control performance requirements.Therefore, this paper adopts cross-coupling control as the synchronous control strategy of the system.The two valve-controlled cylinders are given the same displacement command signal, and the adaptive robust controller forms a feedback control system.At the same time, we compare the displacement feedback signals of the two valve controlled cylinders and compensate for the deviation of the two to the forward channel to eliminate errors as much as possible.To enhance the control effect of the compensation signal, a PID controller has been added to the channel, and Figure 2 shows its schematic diagram.
At the same time, the interference term d is smooth and bounded, the first and second derivatives exist and are bounded: We let the estimated value of the unknown parameter π be π , and the parameter estimation error be π ∃ , π ππ <, ∃ .To ensure the validity of Hypothesis 3.2, the following parameter adaptive discontinuous mapping is defined: where i =1, ⋯, 4. Given the following controlled parameter adaptive law:

Controller design
First, we define the error variable: .According to Formula (18), 22 s  can be designed to be suitable for stabilization conditions: δ is a controller parameter that can be arbitrarily small, 1 0 δ = .A robust control law 22 s  that meets the above requirements can be designed as follows: % , it can be seen that it includes a computable partial differential part and an uncomputable part, so the two are classified as 2c  % and 2u % respectively.According to Formula (22), we design an adaptive robust controller u :

Conclusion
This article focuses on a series of problems in the electro-hydraulic position servo synchronization control system and designs a dual channel electro-hydraulic servo synchronization control method that combines adaptive robust control and cross-coupling control strategy.Simulation research is conducted in MATLAB/Simulink.The conclusion is as follows: (1) Adaptive robust control can reduce the impact of interference, and its control effect is improved by about 92.5% compared to the PID controller, with good signal tracking ability.
(2) Compared with PID controllers, adaptive robust control based on cross-coupling control has better synchronization control accuracy, shorter adjustment time, and stronger anti-interference ability, laying a theoretical foundation for the future application of adaptive robust control in electro-hydraulic position servo synchronization control systems.
Afterward, this project will conduct testing experiments after the completion of the experimental platform to verify the performance of the controller.

Figure 1 .
Figure 1.System structure diagram.Due to the consistent and symmetrical structure of the two hydraulic cylinders, only one of them is used as an example for mathematical modeling analysis.The system dynamic equation is: ∋( 11 22 ff m yP A P A B yA Sy d < , , ,, % % %%

3. 2 Hypothesis 3 . 2 :
Parameter adaptive rate design We define system unknown parameter vectors as Ζ ∴ T T 1234 ,,, ft B, A ,d,C π ππππ  <<  .The following assumptions are listed: Hypothesis 3.1: The reference instruction signal 1 ()dxt is third-order continuous differentiable, and the reference instruction and its first to third derivatives are bounded.The pressure of both chambers must The size range of the uncertainty π of system parameters and the nonlinearity d ∃ of the uncertainty is known:

4 .
Simulation analysisTo verify the control method designed in this article, it was simulated in MATLAB/Simulink.R e l a t e d h y d r a u l i c a n d c o n t r o l p a r a m e t e r s o f t h e s y s t e m a r to make a comparative analysis, the traditional PID control algorithm is introduced for comparison.The comparison diagram is shown in Figures3-6.

Figure 5 .
Figure 5.Comparison of cylinder 2 error.Figure 6.Comparison of synchronization errors.It can be seen that the adaptive robust controller has improved the average level of synchronization error and tracking error by about 90.3% and 92.5%, respectively, compared to PID, and the degree of error dispersion has also been improved.Moreover, due to the smaller value of ITAE E , it indicates that the adaptive robust controller has better robustness, effectively improving position accuracy and synchronization accuracy.

Figure 6 .
Figure 5.Comparison of cylinder 2 error.Figure 6.Comparison of synchronization errors.It can be seen that the adaptive robust controller has improved the average level of synchronization error and tracking error by about 90.3% and 92.5%, respectively, compared to PID, and the degree of error dispersion has also been improved.Moreover, due to the smaller value of ITAE E , it indicates that the adaptive robust controller has better robustness, effectively improving position accuracy and synchronization accuracy.