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Decoupling precompensators for multivariable, equidimensional input- output models. (English) Zbl 0653.93031

Multivariable system models having an equal number of inputs and outputs that are stable, linear, multivariable, and time-invariant, expressed in the form of a transfer matrix in the Laplace variable, are considered. The spectral form of the transfer matrix will be used to show that if the number of coupled right-hand plane zeros is less than or equal to the number of inputs to the system, then proper, stable, realizable decoupling precompensators for the system exist. Thereafter, algorithms that give the number of decoupling realizations in the set are derived, and demonstrations of the wide range of options afforded by these variations to the system designer are presented. To emphasize the flexibility and generality of the result, the decoupling precompensators for a simple multivariable system are computed together with the resulting noninteracting system/compensator combination. Selection of the “best” configuration is then made on the basis of the pole-zero pattern associated with each interfaced system. Finally, the design may be completed by way of the Nyquist array method using the preferred decoupling precompensator as a starting point in the search for a low- order realization, producing diagonal dominance rather than noninteracting characteristics.

MSC:

93C35 Multivariable systems, multidimensional control systems
93B50 Synthesis problems
93C05 Linear systems in control theory
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
93D99 Stability of control systems
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References:

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