Technical Communique: Linear Multivariable Servomechanisms Revisited: System Type and Accuracy Trade-offs

  • Authors:

  • BERNARDO A. LEÓN DE LA BARRA;ABBAS EMAMI-NAEINI;EUGENIO R. CHINCHÓN

  • Affiliations:

  • Department of Electrical Engineering, Universidad de Chile, P.O. Box 412-3, Santiago, Chile.;SC Solutions, Inc., 3211 Scott Blvd., Santa Clara, CA 95054, USA;Department of Electrical Engineering, Universidad de Chile, P.O. Box 412-3, Santiago, Chile.

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1998

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Abstract

It is shown that every scalar closed-loop output of a linear multivariable type m servomechanism, where m is larger than one, will always track its corresponding reference trajectory with an instantaneous tracking error whose integral over time identically vanishes. This is true for all polynomial reference signals of up to order m-2. The simplest implication of this result is that the step responses of a multivariable servomechanism, which is capable of asymptotically following ramp signals, must all display overshoot. This is analogous to the familiar classical control result. New insight into tracking of dependent signals is also provided using the notion of ''generalized'' system type.