*Article* **Mixed Sensitivity-Based Robust** *H***∞ Control Method for Real-Time Hybrid Simulation**

**Xizhan Ning 1,2**

> 1 College of Civil Engineering, Huaqiao University, Xiamen 361021, China; xzning@hqu.edu.cn

2 Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, Huaqiao University, Xiamen 361021, China

**Abstract:** Real-time hybrid simulation (RTHS), dividing the emulated structure into numerical substructures (NS) and physical substructures (PS), is a powerful technique to obtain responses and then to assess the seismic performance of civil engineering structures. A transfer system, a servo-hydraulic actuator or shaking table, is used to apply boundary conditions between the two substructures. However, the servo-hydraulic actuator is inherently a complex system with nonlinearities and may introduce time delays into the RTHS, which will decrease the accuracy and stability of the RTHS. Moreover, there are various uncertainties in RTHS. An accurate and robust actuator control strategy is necessary to guarantee reliable simulation results. Therefore, a mixed sensitivity-based *H*∞ control method was proposed for RTHS. In *H*∞ control, the dynamics and robustness of the closed-loop transfer system are realized by performance weighting functions. A form of weighting function was given considering the requirement in RTHS. The influence of the weighting functions on the dynamics was investigated. Numerical simulations and actual RTHSs were carried out under symmetric and asymmetric dynamic loads, namely sinusoidal and earthquake excitation, respectively. Results indicated that the *H*∞ control method used for RTHS is feasible, and it exhibits an excellent tracking performance and robustness.

**Keywords:** real-time hybrid simulation; *H*∞ control; time delay; mixed sensitivity
