To develop high-performance controllers for adaptive optics (AO) systems, it is essential to first derive sufficiently accurate state-space models of deformable mirrors (DMs). However, it is often challenging to develop realistic large-scale finite element (FE) state-space models that take into account the system damping, actuator dynamics, boundary conditions, and multi-physics phenomena affecting the system dynamics. Furthermore, it is challenging to establish a modeling framework capable of the automated and quick derivation of state-space models for different actuator configurations and system geometries. On the other hand, for accurate model-based control and system monitoring, it is often necessary to estimate state-space models from the experimental data. However, this is a challenging problem since the DM dynamics is inherently infinite-dimensional and it is characterized by a large number of eigenmodes and eigenfrequencies. In this paper, we provide modeling and estimation frameworks that address these challenges. We develop an FE state-space model of a faceplate DM that incorporates damping and actuator dynamics. We investigate the frequency and time domain responses for different model parameters. The state-space modeling process is completely automated using the LiveLink for MATLAB toolbox that is incorporated into the COMSOL Multiphysics software package. The developed state-space model is used to generate the estimation data. This data, together with a subspace identification algorithm, is used to estimate reduced-order DM models. We address the model-order selection and model validation problems. The results of this paper provide essential modeling and estimation tools to broad AO and mechatronics scientific communities. The developed Python, MATLAB, and COMSOL Multiphysics codes are available online.There are various types of DM architectures and design concepts used in AO systems. Depending on how the reflective surface is designed, we can distinguish between segmented, faceplate, and membrane DMs [1,7,8]. Due to their widespread usage, in this manuscript, we consider DMs with continuous faceplates. The results can easily be extended to other mirror concepts. A typical continuous faceplate DMs is composed of a thin faceplate that is deformed by spatially distributed actuators placed on its backside.Modeling and control problems for large-scale DMs have been considered in [5,[9][10][11][12][13][14][15][16][17][18]. Distributed control and estimation problems or problems of efficient implementation of control and estimation algorithms for large-scale DMs and AO systems have been considered in [4,[18][19][20][21][22][23]. Before these methods can be used, it is necessary to develop sufficiently accurate DM models. Furthermore, it is preferable that these models are in a state-space form that can be used for the design of advanced model-based control algorithms. Analytical mirror models that are based on the biharmonic plate equation and its modifications have been developed in [7,10,11,24,25]. Howev...