Optimal Tracking Performance: Preview Control and Exponential Signals

In this note, we study tracking performance limitation problems. Two issues are addressed, concerning how earlier results developed elsewhere may be extended to more general classes of reference signals, and how tracking performance may be further improved beyond that offered by feedback control. Toward these issues we consider exponentially increasing reference inputs and examine the use of preview control for tracking. We take an optimal interpolation approach, and our purpose is to develop analytical expressions and conceptual insight which will aid in the understanding of these issues. To this effect, we derive explicit expressions for the optimal tracking error, either as exact solutions or bounds. It is found that for the exponential signals the earlier results can be directly extended, and similar conclusive statements can be drawn. It is also shown that in general preview can be used to advantage for improving tracking performance, especially in countering the effect resulted from plant nonminimum phase zeros.