(61d) Experiment Design for Identification of Integral-Controllable Dynamic Multivariable Models

Integral controllability is a fundamental property of multivariable models to be used in decoupling model-based control that maintains closed-loop stability when detuned.  It has been shown that experiments for identification of integral-controllable models cannot rely on standard PRBS (pseudo-random binary sequence) inputs, particularly when the process to be identified is ill-conditioned.  A number of investigators (MacGregor et al., Braatz et al., Darby and Nikolaou) have shown that experiment design based on rotated inputs can produce better results, namely the integral controllability condition can be satisfied by models resulting from experiments of shorter duration.  All prior results rely on direct identification of the steady-state gain matrix of the process to be controlled, because the integral controllability condition involves the steady-state gain matrix of the controlled process.  However, a full dynamic model must be identified for use in model-based control.  Consequently, experiment design methods are needed for efficient identification of dynamic models that satisfy the integral controllability condition.  In this work, we present an approach to designing such experiments.  Specifically, we extend prior results that transform the integral controllability condition into a manageable inequality that can be used directly in numerical optimization.  Optimal inputs result from this optimization.  The approach proposed in this work assumes that a reasonable frequency range for all inputs is approximately the same, whereas the correlation between input amplitudes is determined through numerical optimization.  A numerical simulation on an ill-conditioned distillation column is used to illustrate the proposed approach.