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The paper studies the tracking problem of linear multivariable systems using the fractional representation approach introduced by Desoer et al. (1980). This method applies not only to lumped-parameters systems, but also to some classes of distributed-parameters, time-varying and multidimensional systems. This problem has been studied before by Saeks and Murray (1981). The present paper uses a different algebraic development, and obtains what is believed to be a more “structural” result. It id proved, namely, that the necessary and sufficient compensator is a loop-stabilizer cascaded with an internal model (defined in a precise sense) of the signal to be tracked. The result applies also to the disturbance rejection problem when the signal to be rejected is applied either to the plant’s input or to the plant’s output or to the plant’s “interior”. |
