System identification is the process of generating a dynamic model of a system using data and process knowledge. It is common practice to perturb the system of interest and use the resulting data to build the model. The problem of input design is to synthesize an input signal that is maximally informative for generating good quality models.

Identification is carried out on operating plants and hence it is important to ensure that the experiment is least hostile to operating conditions or equivalently, the input signal should be “plant friendly”. Plant friendliness requirements can be imposed in the form of input rate constraints, input and output magnitudes and experiment time [1]. We focus on input rate requirements in this contribution.

Some measures of plant friendliness with respect to input rate have been proposed in literature and surveyed in [1]. However, they are difficult to use in practice due to lack of closed form expressions or extensive computational requirements. In this work, we define input friendliness (Pf) using an intuitive metric that captures the input rate requirements. We show how a constraint of the form: Pf < c can be imposed as a convex constraint. The feasible set of the optimization problem is shown to be convex. It is well known that classical cost functions that minimize a scalar norm of the covariance matrix of the parameter estimates are convex [2]. Hence, the optimization problem is convex and can be solved to global optimality using powerful algorithms [3].

It has been reported that plant friendliness demands are often in conflict with requirements for good identification [1]. Hence, plant friendly input design is inherently a multi-objective problem and this was demonstrated in [4]. We quantify this trade-off between the input friendliness (Pf) and the variability of the parameter estimates.

References:

1. “PLANT-FRIENDLY” SYSTEM IDENTIFICATION: A CHALLENGE FOR THE PROCESS INDUSTRIES Daniel E. Rivera, Hyunjin Lee, Martin W. Braun and Hans D. Mittelmann, 13th International Symposium on System Identification (SYSID), Rotterdam, The Netherlands, pg 917-922, 2003.

2. Dynamic System Identification: Experiment Design and Data Analysis Graham C. Goodwin and Robert L. Payne Academic Press 1977

3. Convex Optimization, S Boyd and L Vandenberghe, Cambridge University Press, 2004.

4. Narasimhan, S., S. Rengaswamy and R. Rengasamy (2003). Multiobjective input signal design for plant-friendly identification. In: SYSID 2003. Rotterdam, The Netherlands.