Observer-Based Intensity-Feedback Control for Laser Beam Pointing and Tracking

This paper presents an investigation of the control problem of aiming a laser beam under dynamic disturbances, using light intensity for feedback only. The idea is to steer the beam with a biaxial microelectromechanical mirror, which is driven by a control signal generated by processing the beam intensity sensed by a single photodiode. Since the pointing location of the beam is assumed to be unavailable for real-time control, a static nonlinear mapping from the 2-D beam location to the photodiode sensor measurement output is estimated with the use of the least-squares algorithm, treating data from a biaxial optical position sensor as inputs to the static mapping. This formulation results in a nonlinear Wiener-Hammerstein system composed of a linear subsystem connected in series to a nonlinear static output mapping. Conceptually, the controller design problem is addressed with the integration of an observer and a pair of linear time-invariant single-input/single-output controllers into one system. This approach motivates two research questions that are considered independently in this paper. The first is about the multiple-experiment observability of the considered nonlinear optical system. The second is about the search of an heuristic method, based on the extended Kalman filter (EKF) algorithm, for estimating the state of the linear subsystem, necessary for implementing the proposed control approach. Here, we present a compelling answer for the first question and we propose a methodology to tackle the second. It is important to state that the problem considered in this article is very challenging, because the nonlinear static output map of the system is not one-to-one. In order to address this issue, we introduce the idea of integrating stable output disturbance models into the design of the proposed EKF-based observer. This is the main contribution of the paper, which could have an impact in the way other nonlinear control problems are addressed in the future. Evidence of the suitability of the proposed method is provided through experimental results from a case relevant to free-space optics for communications and directed energy applications.