Digital approximation of continuous-data control systems by point-by-point state comparison

This paper presents a point-by-point state comparison method of approximating a continuous-data system by a sampled-data system. The problem is to attempt the matching of the states of the two systems at the sampling instants. A partial matching has to be conducted if the systems have more states than controls. A weighting matrix is used to regulate the partial matching and weights placed on each state. The digital approximation is affected by use of forward gain E(T) and feedback gain G(T) in the sampled-data system. It is shown that, in general, these gains can be approximated by truncated Taylor series expansions. An illustrative example is given using the one-axis dynamics of the Skylab satellite.