ABSTRACT
Control theory is an important discipline for adaptive optics systems, but it is generally not covered in optics, astronomy, or physics curricula and is not part of the typical background of adaptive optics engineers. This chapter attempts to close that gap and presents some of the elements of control theory that are essential for modern adaptive optics systems. A fast steering mirror based tilt control system is developed through examples to help reinforce concepts in the context of adaptive optics. Techniques from classical continuous time single channel control are introduced first, in both the frequency and time domains. These methods include Laplace transforms, transfer functions, state space representations, stability, and controllability and observability. The impacts of noise and uncertainty are then explored before moving on to the impacts of sampling on control loop performance and sampled data systems in general. The final three major sections of this chapter introduce multi-variable systems, optimal control theory, and robust control theory, providing an overview of modern control theory.
