Nonlinear friction compensation and loading tracking control strategy for geotechnical triaxial dynamic and static loading based on iterative learning and dynamic surface inversion control

• Aiming at the problem of insufficient dynamic and static accuracy of triaxial test, based on the self-designed electro-hydraulic servo dynamic and static triaxial test platform, a composite control strategy combining dynamic inversion control (DSC) and iterative learning control (ILC) is proposed to improve the loading performance of the test. • The state space model of the electro-hydraulic servo loading system of the triaxial test platform is constructed, and the nonlinear friction model loaded by the test platform is identified and used to compensate the nonlinear friction disturbance of the system. • The system state observer and disturbance observer are built, and their stability and static and dynamic loading performance of the test platform are verified. The triaxial test platform serves as a vital instrument for determining the mechanical constitutive parameters of rock and soil materials, and its measurement accuracy directly governs the reliability of the characterized constitutive relationships. However, due to the intrinsic nonlinearity of geotechnical materials and the nonlinear friction inherent in the loading equipment, the loading accuracy of triaxial tests is often compromised. This issue becomes particularly pronounced during triaxial dynamic cyclic loading, where significant tracking hysteresis and high error rates emerge. To address the insufficiency in both dynamic and static loading accuracy, this paper proposes a composite control strategy that synergistically combines Dynamic Surface Control (DSC) with Iterative Learning Control (ILC), implemented on a self-developed electro-hydraulic servo triaxial system. The research first establishes a state-space model of the electro-hydraulic servo loading system. Subsequently, the nonlinear friction model affecting the platform is identified and compensated for to mitigate system disturbances. A state observer is then constructed, and a DSC controller is designed, with its stability and the static loading performance rigorously verified. Building upon the DSC framework, the ILC method is employed to specifically enhance the tracking performance of dynamic cyclic force loading. Experimental tests demonstrate that the proposed composite strategy delivers superior tracking performance. Comparative results indicate an approximate 43.6% improvement in static displacement tracking accuracy and about a 33.9% improvement in the accuracy of dynamic cyclic force loading.