Comparison between control-based continuation and phase-locked loop methods for the identification of backbone curves and nonlinear frequency responses

Control-based continuation (CBC) and phase-locked loops (PLL) are two experimental testing methods that have demonstrated great potential for the non-parametric identification of key nonlinear dynamic features such as nonlinear frequency responses and backbone curves. Both CBC and PLL exploit stabilizing feedback control to steer the dynamics of the tested system towards the responses of interest and overcome important difficulties experienced when applying conventional testing methods such as sine sweeps to nonlinear systems. For instance, if properly designed, the feedback controller can prevent the system from exhibiting untimely transitions between coexisting responses or even losing stability due to bifurcations. This contribution aims to highlight the similarities that exist between CBC and PLL and present the first thorough comparison of their capabilities. Comparisons are supported by numerical simulations as well as experimental data collected on a conceptually simple nonlinear structure primarily composed of a thin curved beam. The beam is doubly clamped and exhibits nonlinear geometric effects for moderate excitation amplitudes

Comparison between control-based continuation and phase-locked loop methods for the identification of backbone curves and nonlinear frequency responses

Control-based continuation (CBC) and phase-locked loops (PLL) are two experimental testing methods that have demonstrated great potential for the non-parametric identification of key nonlinear dynamic features such as nonlinear frequency responses and backbone curves. Both CBC and PLL exploit stabilizing feedback control to steer the dynamics of the tested system towards the responses of interest and overcome important difficulties experienced when applying conventional testing methods such as sine sweeps to nonlinear systems. For instance, if properly designed, the feedback controller can prevent the system from exhibiting untimely transitions between coexisting responses or even losing stability due to bifurcations. This contribution aims to highlight the similarities that exist between CBC and PLL and present the first thorough comparison of their capabilities. Comparisons are supported by numerical simulations as well as experimental data collected on a conceptually simple nonlinear structure primarily composed of a thin curved beam. The beam is doubly clamped and exhibits nonlinear geometric effects for moderate excitation amplitudes

Third-order nonlinear optical study on sublimated/Langmuir-Blodgett thin films of lanthanide porphyrin phthalocyanine dimer/heterodimer and symmetric trimer systems by time-resolved non-degenerate four-wave mixing

Time-resolved four-wave mixing (TRFWM) studies have been carried out on sublimated films of the neodymium phthalocyanine dimer Pc[superscript 2-Nd[superscript III]Pc[superscript point], the cerium porphyrin phthalocyanine sandwich mixed heterodimer Pc[superscript 2-]Ce[superscript IV]TPP[superscript 2-], the cerium porphyrin phthalocyanine symmetric trimer TPP[superscript 2-]Ce[superscript III]Pc[superscript 2-]Ce[superscript III]TPP[superscript 2-], the neodymium porphyrin phthalocyanine trimer Pc[superscript 2-]Nd[superscript III]TPP[superscript 2-]Nd[superscript III]Pc[2-], and Langmuir-Blodgett films of the cobalt porphyrin phthalocyanine mixed dimer CoPC [subscript 22][superscript 4+] / H[subscript 2]PcTS [subscript 4-]. In this work, we have presented a number of novel results: the first non-degenerate time-resolved four-wave mixing (NDTRFWM) experiment on a sublimated film, the first observation and identification of the diffusion contribution to the degrating process, the first observation and identification of photorefractive effect in an organic multimer thin film, and the first observation and identification of a correlated phonon mode shifting phenomenon. The absolute values of the third-order nonlinear optical susceptibility [chi superscript (3)] of the samples have been determined by comparing the third-order nonlinear optical responses of the samples with those of a slide of reference fused quartz under the same experimental conditions. It is shown that TRFWM is a very useful, very sensitive and very powerful tool to investigate the dynamics of the third-order nonlinear optical processes in a medium, especially those that can not be detected by transient absorption and other means of probing nonlinear optical properties. Through this work, it can be seen that lanthanide porphyrin phthalocyanine dimer/heterodimer trimer/heterotrimer systems could be a new family of organic materials most promising for the investigation and the applications of photorefractive effect. They are very versatile and have a great potential as nonlinear optical materials

Adaptive tracking control of Euler-Lagrange systems with bounded controls

"We solve the simultaneous closed?loop identification and tracking?control problems for fully actuated Euler-Lagrange systems under input constraints. We use a nonlinear adaptive controller reminiscent of computed?torque?type controllers in which linear correction terms are saturated in order to comply with the imposed bounds on the control inputs. Adaptation, reminiscent of gradient methods, is used also with saturation. With respect to related literature, our contribution consists in establishing uniform global asymptotic stability. Therefore, our control scheme ensures robustness with respect to bounded perturbations and uniform convergence of the estimation errors for any initial conditions.

A unified parameter identification method for nonlinear time-delay systems

This paper deals with the problem of identifying unknown time-delays and model parameters in a general nonlinear time-delay system. We propose a unified computational approach that involves solving a dynamic optimization problem, whose cost function measures the discrepancy between predicted and observed system output, to determine optimal values for the unknown quantities. Our main contribution is to show that the partial derivatives of this cost function can be computed by solving a set of auxiliary time-delay systems. On this basis, the parameter identification problem can be solved using existing gradient-based optimization techniques. We conclude the paper with two numerical simulations

Optimal Control for a Pitcher's Motion Modeled as Constrained Mechanical System

In this contribution, a recently developed optimal control method for constrained mechanical systems is applied to determine optimal motions and muscle force evolutions for a pitcher's arm. The method is based on a discrete constrained version of the Lagrange-d'Alembert principle leading to structure preserving time-stepping equations. A reduction technique is used to derive the nonlinear equality constraints for the minimization of a given objective function. Different multi-body models for the pitcher's arm are investigated and compared with respect to the motion itself, the control effort, the pitch velocity, and the pitch duration time. In particular, the use of a muscle model allows for an identification of limits on the maximal forces that ensure more realistic optimal pitch motions

Optimal Input Design for Active Parameter Identification of Dynamic Nonlinear Systems

There are many important aspects to be considered while designing optimal excitation signal for system identification experiment in control applications. Active parameter identification is an important issue in system and control theory. In this dissertation, the problem of optimal input design for active parameter identification of dynamic nonlinear system is addressed. Real life physical systems are identified by excitation with a suitable input signal and observing the resulting output behavior of the system. It is important to choose the input signal intelligently in the sense that it is responsible to determine the accuracy and nature of the unknown system characteristics. This leads to a spurred interest in designing such an optimal excitation signals that can yield maximal information from the identification experiment. The information obtained from parameter identification is usually not accurate due to incomplete knowledge of the system, disturbance as exogenous inputs and noisy measurements. Hence, the input spectrum is designed in such a way that it can improve the system performance and shape the quality of obtained information. A welldesigned input signal can maximize the amount of information and reduce the experimental cost and time. The input signal is usually given some a-priori characteristics (knowledge on the pdf) so that \u201cexcitation\u201d of the system is guaranteed. In this thesis, a closed-loop method is investigated which is able to improve the parameter identification on the basis of the actual system\u2019s behavior. The effectiveness of the proposed algorithm is presented by the experimental results which corresponds to the perfect identification of the unknown parameter vector. The major technical contribution of this work is to propose an optimal feedback input design method for active parameter identification of dynamic nonlinear systems. The proposed framework can design such optimal excitation signals, considering the information from the identified parameters, that can maximize the amount of information from the identified parameters, guarantee to meet the specified control performance and minimize some cost function of the error covariance matrix of the identified parameters. The problem is formulated in a receding horizon framework where extended Kalman filter is used for system identification and the optimal input is designed in a nonlinear model predictive control framework. In order to carry out a comparison study, also Unscented Kalman Filter and Gaussian Sum Filter are used for the active parameter identification of dynamic nonlinear system. Towards this end, a suitable optimality criterion related to the unknown parameters is proposed and motivated as an information measure. The aim of the optimal input design is to yield maximal information from the unknown system by minimizing the cost related to the unknown parameters while maintaining some process performance and satisfying the possible constraints. Simulations are performed to show the effectiveness of the proposed algorithm

A method to study ageing of polydomain ferroelectrics using measurements of nonlinear permittivity

It is known that the permittivity of the ferroelectric films is affected by several phenomena, which deteriorate the material quality (e.g. the redistribution of the crystal lattice defects, appearance of the electrode-adjacent non-ferroelectric layers or the spontaneous polarization screening due to a free charge injection across the electrode-adjacent layer, etc.). It is also known that the permittivity of ferroelectric polydomain films is controlled by the sum of two contributions: the crystal lattice (intrinsic) contribution and the domain wall movement (extrinsic) contribution. It is the latter one, which is very sensitive to the aforementioned phenomena and which plays a key role in the deterioration of the dielectric response of the ferroelectric polydomain films. In this Article, there is presented a method for the identification of the process, which is responsible for the ferroelectric ageing. The method is based on the analysis of the evolution of both the linear and nonlinear permittivity during ageing. Applicability of the method is theoretically demonstrated on four ageing scenarios in two qualitatively different systems where the evolution of the nonlinear permittivity is controlled, first, by a redistribution of the pinning centers on the domain wall and, second, by microstructural changes at the interface between the ferroelectric layer and the electrode. It is shown that each ageing scenario is characterized by unique trend in the evolution between the linear and nonlinear part of the permittivity, which can be verified experimentally.Comment: Submitted to Ferroelectric