UC San Diego

The purpose of this thesis is the computation of optimal input signals for output tracking of a dynamic system. The starting point is a non-optimal input signal given in the form of a simple step input and the measurement of the resulting output. The data is used to formulate a (linear) dynamic model from which the optimal input signal is computed via “input shaping”. This paper presents a summary of the method to obtain a dynamic model from the step response data, and compares various “input shaping” methods to compute (sub)optimal input signals to achieve a desired output signal. The method to estimate a dynamic model is based on the realization algorithm; the optimal input shaping techniques compared in this paper include zero vibration (ZV), finite impulse response (FIR) filtering and a convex optimization formulation using linear programming (LP). It is shown that the linear programming solution for input shaping can also be generalized to find optimal input signals with a fixed resolution using a mixed integer linear programming formulation. The approach of dynamic modeling and input shaping is illustrated on a simulation example of a two-mass system as well as experimental data obtained from a class IV LASER system characterized by varying the pulse length of the low power used to seed it.