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.

Bharath Bhikkaji

Department of Electrical Engineering

Polynomials

CONTINUOUS SYSTEM

INPUT/OUTPUT CONSTRAINTS

Limited spectrum

LINEAR CONTINUOUS-TIME

Linear relationships

NON-NEGATIVITY CONSTRAINTS

Power constraints

Simulation example

Continuous time systems

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

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

2015 European Control Conference, ECC 2015

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

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.

Industrial and Engineering Chemistry Research

Optimal plant friendly input design for system identification

Measurement Science and Technology

On the calculation of theD-optimal multisine excitation power spectrum for broadband impedance spectroscopy measurements

Automatica

Robust optimal experiment design for system identification

On input signal synthesis in parameter identification

Journal	Data powered by Typeset2015 European Control Conference, ECC 2015
Publisher	Data powered by TypesetInstitute of Electrical and Electronics Engineers Inc.
Open Access	No