Design of Experiments for Multivariable Systems Subject to Integral Controllability
Mark Darby, Department of Chemical and Biomolecular Engineering, University of Houston, 4800 Calhoun Ave., Houston, TX 77204-4004 and Michael Nikolaou, Chemical and Biomolecular Engineering, University of Houston, 4800 Calhoun Ave., Hoston, TX 77204-4004.
In this work we develop an upper bound for the integral controllability condition and show how this bound can be incorporated into various optimization problems for the design of experiments. Previously known literature designs, based on the use of uncorrelated rotated inputs reciprocally proportional to an ill-conditioned system's singular values, are in agreement with the proposed framework in special cases. However, we show that these designs are no longer optimal when typical input and/or output constraints are present. By utilizing the integral controllability condition, this approach to experimental design is applicable to ill- or well-conditioned nxn systems, for any combination of input and output constraints. Comparisons are made to previous results for experimental design and examples are included which demonstrate the effectiveness of the approach.