The primary objective in solving optimal input design problems is to obtain maximally informative inputs to be used as perturbation signals in system identification experiments. In plant-friendly identification, the designer has to respect constraints on experiment time, input and output amplitudes or input move sizes. This work focuses on plant friendly input design with constraints on input move size and output power. We present a convex relaxation to the problem of designing an informative input subject to input move size and output power constraints. The problem is finitely parametrized using ideas from Tchebycheff systems and reformulated as a SemiDefinite Programme. © 2011 American Chemical Society.

Raghunathan Rengaswamy

Department Of Chemical Engineering

Sridharakumar Narasimhan

S. Arun Srikanth

J. V. N. Sreeram

CONVEX RELAXATION

Input and outputs

INPUT DESIGN

OPTIMAL INPUT DESIGN

Output power

PERTURBATION SIGNALS

Primary objective

Experiments

Optimization

Relaxation processes

Design

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IIT Madras

Industrial and Engineering Chemistry Research

This paper presents a method for designing inputs to identify linear continuous-time multiple-input multiple-output (MIMO) systems. The goal here is to design a T-optimal band-limited spectrum satisfying certain input/output power constraints. The input power spectral density matrix is parametrized as the product ϕu(jω)=12H(jω)HH(jω), where H(jω) is a matrix polynomial. This parametrization transforms the T-optimal cost function and the constraints into a quadratically constrained quadratic program (QCQP). The QCQP turns out to be a non-convex semidefinite program with a rank one constraint. A convex relaxation of the problem is first solved. A rank one solution is constructed from the solution to the relaxed problem. This relaxation admits no gap between its solution and the original non-convex QCQP problem. The constructed rank one solution leads to a spectrum that is optimal. The proposed input design methodology is experimentally validated on a cantilever beam bonded with piezoelectric plates for sensing and actuation. Subspace identification algorithm is used to estimate the system from the input-output data. © 2019, South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature.

Control Theory and Technology

Optimal finite-dimensional spectral densities for the identification of continuous-time MIMO systems

Input design is the process of designing informative inputs which maximizes the information about system dynamics using minimal cost and resources in a system identification experiment. In this work, we focus on designing inputs based on the economic framework for identification of constrained processes. The process is nominally constrained and feasibility during identification is ensured by "backing off" (or moving away) from the active constraints. The economic cost or penalty due to the "back-off" is minimized while ensuring feasibility and satisfying constraints on the quality of the identified model. The proposed economic based formulation results in a nonconvex optimization problem. This problem can be solved using the bisection algorithm for single input-single output (SISO) systems. We present a two-stage iterative solution algorithm to solve for multi-input-multi-output (MIMO) systems where a convex optimization problem is solved at each stage. The optimal input is realized as a white noise passing through an M-tap filter. The filter coefficients are obtained by a noniterative spectral factorization technique. The efficacy of the proposed approach has been successfully demonstrated in a mass spring damper system as well as in a Van der Vusse reactor system. Copyright © 2018 American Chemical Society.

Economically Optimal Input Design Approach for Identification of Constrained Processes

This paper presents a paradigm for designing inputs to identify linear continuous-time SISO systems. The goal here is to design a band-limited spectrum that is D-optimal and satisfies certain input/output power constraints. The D-optimal criterion with input/output constraints lead to a set of optimal moments. In order to determine the spectrum from these moments, it is first approximated by a finite order sum of squares (s.o.s.) polynomial. It is shown that the coefficients of the s.o.s. polynomial and its moments are linearly related. These coefficients can be determined by minimizing the distance between the optimal moments and the moments of the finite order approximation under the constraint that the spectrum is non-negative. Alternatively, the linear relationship between the moments and coefficients of the spectrum can also be enforced as additional constraints along with the power constraints and non-negativity constraints in the D-optimal framework. A simulation example, with a 2nd order system, is presented to illustrate the proposed method of determining the power spectrum and the input. © 2015 EUCA.

2015 European Control Conference, ECC 2015

D-optimal input design for identification of a continuous system using sum of squares polynomial

In several industrial processes, measurements are limited due to time or cost constraints. Hence, scheduling of these measurements to obtain maximally informative and accurate estimates of the states becomes important. The focus of this contribution is to determine a schedule of measurements that maximizes the quality of the estimates at the end of a finite time horizon. This work finds applications in batch chemical processes. The estimate covariance matrix as obtained by applying standard Kalman filtering theory is approximated and the original problem is relaxed and reformulated as a cone program. For a certain class of systems, the approximated covariance matrix is parameterized in terms of a point belonging to a moment space induced by a Tchebycheff system. The theory of Tchebycheff systems is used to determine an improved upper bound on the guaranteed minimum number of measurements. A tractable solution methodology to obtain the optimal cost and a parsimonious discrete schedule using the theory of cone programming, generalized barrier functions and Tchebycheff systems is described. © 2014. IEEE.

IEEE Transactions on Automatic Control

Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory

Input design is the process of designing an informative input that extracts maximal information about system dynamics using minimal cost and resources. In this work, we design inputs in the economic framework, where the objective is to minimize the cost incurred during the experiment, subject to plant friendly constraints as well as feasibility constraints. The cost is quantified in terms of departure from the nominally optimal operational policy. Typically, the nominal policy is to operate the plant at or near constraints. The economics based optimization formulation is non-convex, so we have proposed a 2-step iterative method to solve this problem. The solution also yields the conditions at which the identification experiment has to be carried out. The input is realized as white noise filtered by an M-tap FIR filter. © 2014 EUCA.

2014 European Control Conference, ECC 2014

Economical and plant friendly input design for system identification

A common practice in a system identification exercise is to perturb the system of interest and use the resulting data to build a model. The problem of interest in this contribution is to synthesize an input signal that is maximally informative for generating good quality models while being "plant friendly", i.e., least hostile to plant operation. In this contribution, limits on input move sizes are the plant friendly specifications. The resulting optimization problem is nonlinear and nonconvex. Hence, the original plant friendly input design problem is relaxed which results in a convex optimization problem. We formulate a SemiDefinite Programme using the theory of generalized Tchebysheff inequalities to derive tight bounds on the quality of relaxation. Simulations show that the relaxation results in more plant friendly input signals. © 2006 IEEE.

Plant friendly input design: Convex relaxation and quality

Optimal plant friendly input design for system identification

Cambridge University Press

Convex Optimization

Journal of Process Control

Constrained multisine input signals for plant-friendly identification of chemical process systems

2008 American Control Conference

Multi-objective optimal input design for plant friendly identification

Journal	Industrial and Engineering Chemistry Research
ISSN	08885885
Open Access	No