Design of state-feedback controllers including sensitivity reduction, with applications to precision pointing

The design procedure of feedback controllers was described and the considerations for the selection of the design parameters were given. The frequency domain properties of single-input single-output systems using state feedback controllers are analyzed, and desirable phase and gain margin properties are demonstrated. Special consideration is given to the design of controllers for tracking systems, especially those designed to track polynomial commands. As an example, a controller was designed for a tracking telescope with a polynomial tracking requirement and some special features such as actuator saturation and multiple measurements, one of which is sampled. The resulting system has a tracking performance comparing favorably with a much more complicated digital aided tracker. The parameter sensitivity reduction was treated by considering the variable parameters as random variables. A performance index is defined as a weighted sum of the state and control convariances that sum from both the random system disturbances and the parameter uncertainties, and is minimized numerically by adjusting a set of free parameters.