Optimal Periodic Square-Wave Forcing: A New Method

A new method of global validity is developed that determines the optimal pulsed periodic operation. This type of periodic operation is particularly attractive since it is the easiest to implement. The method is based on the Carleman approximation of the nonlinear plant equations and of a general nonlinear performance measure. An attractively simple explicit formula is derived for the general nonlinear periodic optimization problem which gives the performance measure as a function of (a) forcing frequency, (b) amplitude, and (c) wave shape. In a two-dimensional example it is shown that the optimal period depends on the wave shape and amplitude, and that periodic operation can be beneficial for a larger range of frequencies than indicated by the ¿-criterion. Finally, the effect of the order of the Carleman approximation is also investigated.