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Two-degree-of-freedom $$\ell_{2}$$-optimal tracking with preview. (English) Zbl 1035.93026
Summary: A simple SISO two-degree-of-freedom pole-placement design method is presented that provides $$\ell_2$$-optimal tracking of a given reference signal. The closed-loop pole locations are first chosen by the system designer. The closed-loop zeros are then placed in an optimal fashion by a computationally inexpensive algorithm to achieve asymptotic tracking with an optimal transient response. The preview approach, which has become a common method for dealing with systems which have nonminimum phase behavior, can then optionally be used to further improve the transient behavior for both minimum phase and nonminimum phase systems. Unlike previous results based on the preview approach, the solution presented here takes into consideration the closed-loop pole dynamics and is $$\ell_2$$ optimal with respect to all other two-degree-of-freedom preview controllers with the same closed-loop poles. A simple solution to the $$H_2$$ model matching problem, where the design parameter $$Q$$ is not rational, but polynomial, is the heart of the solution method.

##### MSC:
 93B51 Design techniques (robust design, computer-aided design, etc.)
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##### References:
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