###### Abstract
They used support systems for the installation, positioning, and detection of large-diameter or thin mirrors by improving traditional mechanisms, designing new support systems, and optimizing the mechanism parameters of the support systems. However, only a few scholars applied the FSS to the optical mirror processing stage and conducted in-depth research on the FSS. Therefore, it is necessary to further study the application of the FSS in the processing stage of large-aperture optical mirrors. The FSS is uncertain, non-linear, and susceptible to external disturbances, so it is relatively difficult to control and easily produces errors [15; 16]. To ensure the stability of the support stiffness, support height, and output force accuracy of the FSS, it is necessary to analyze the degree of influence of the FSS on the external environment. Several scholars have done a lot of research on the influence of external environmental disturbances on nonlinear hydraulic systems. [PERSON] et al. analyzed the number of air bubbles entrained in hydraulic oil, the size and distribution of these bubbles, and the influence of the compressibility of the mixture on the effective bulk modulus and proposed a new theoretical model [17]. To study the low-pressure effective volume of hydraulic oil, [PERSON] et al. calculated the effective bulk elastic modulus by three different methods: mass change, volume change, and sound speed method, and determined the relationship between the release pressure of dissolved air in the oil and the variable gas constant with the rate of volume change [18]. Through the combination of experimental and mathematical model methods, [PERSON] et al. determined the undissolved air content in hydraulic oil and calculated the bulk modulus of hydraulic oil considering the hydraulic oil system in a pipeline [19]. [PERSON] et al. addresses the problem of bubble evolution arising from gas cavitation in hydraulic oils, including the interphase mass transfer represented by air release and absorption phenomena and different thermodynamic considerations, and three new models in a progressive relationship were proposed on the basis of the Rayleigh-Plesset equation which describes bubble dynamics [20]. [PERSON] et al. designed a robust controller for uncertain systems with time-varying uncertainties, nonlinearities, and external disturbances to reduce the influence of external disturbances on the system and improve system stability [21; 22]. Based on an improvement of [PERSON]'s law and the polytropic process equation for gases, [PERSON] et al. proposed a modified model for the dynamic bulk modulus of gas-containing hydraulic oil. Through the analysis of parameter influence, the influence of initial gas content and pressure on the dynamic bulk modulus of gas-containing hydraulic oil during compression and expansion was discussed [23]. Based on a modified effective bulk modulus model of hydraulic oil built upon the IFAS model (developed at the Institute fur Fluidtechnische Antriebe and Steuerungen, Rheinisch-Westfalische Technische Hochschule Aachen university), [PERSON] et al. developed an empirical non-linear model for a servo-hydraulic uni-axial shaking table [24]. The above scholars have analyzed the elastic modulus and the change in stiffness of hydraulic oil with the air content and temperature. The theoretical models for different working conditions were respectively established, and the mode accuracy was verified. However, there is little research on the influence of the ambient temperature and working medium on the support pressure, support stiffness, and support height of the FSS used for large-scale optical mirror processing support. To achieve adjustable support stiffness, a flexible support system for an optical mirror is proposed, which uses hydraulic oil as the working medium. It could unload the impact force exerted by robots on the mirror to be machined effectively.