Hierarchical control for drift correction in transmission electron microscopes

Electron microscopes are important tools for material science research since they can reveal accurate images (down to the atomic level) for a wide range of specimens. Moreover, a sample can be visualized while thermal processes are induced to the specimen. Such processes involve the contraction or the expansion of the specimen holder, and hence image movement. In current practice one has to wait until the image stabilizes and then analyze the sample. In this paper we propose a hierarchical control framework where at the lower levels we use local and independent PID controllers for adjusting the stage and the beam deflectors. These controllers are then coordinated by a supervisory controller such that maximum performance is achieved. The coordinating controller will solve a nonlinear optimization problem for linear stage models in the model-based predictive control (MPC) setting. Typically, this problem is NP hard and therefore difficult to solve. In this paper we propose to further improve the performance of the system by recasting the optimization problem into a mixed-integer linear programming (MILP) one. The advantage is that for MILP optimization problems solvers are available which guarantee to find the global optimum. Then the MILP solution can be used as good initial point when solving optimization problems for nonlinear stage models.