Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

Identification and control for heart rate regulation during treadmill exercise

This paper proposes a novel integrated approach for the identification and control of Hammerstein systems to achieve desired heart rate profile tracking performance for an automated treadmill system. For the identification of Hammerstein systems, the pseudorandom binary sequence input is employed to decouple the identification of dynamic linear part from input nonlinearity. The powerful ε-insensitivity support vector regression method is adopted to obtain sparse representations of the inverse of static nonlinearity in order to obtain an approximate linear model of the Hammerstein system. An H ∞ controller is designed for the approximated linear model to achieve robust tracking performance. This new approach is successfully applied to the design of a computer-controlled treadmill system for the regulation of heart rate during treadmill exercise. Minimizing deviations of heart rate from a preset profile is achieved by controlling the speed of the treadmill. Both conventional proportional-integral-derivative (PID) control and the proposed approaches have been employed for the controller design. The proposed algorithm achieves much better heart rate tracking performance. © 2007 IEEE

Nonparametric Hammerstein model based model predictive control for heart rate regulation.

This paper proposed a novel nonparametric model based model predictive control approach for the regulation of heart rate during treadmill exercise. As the model structure of human cardiovascular system is often hard to determine, nonparametric modelling is a more realistic manner to describe complex behaviours of cardiovascular system. This paper presents a new nonparametric Hammerstein model identification approach for heart rate response modelling. Based on the pseudo-random binary sequence experiment data, we decouple the identification of linear dynamic part and input nonlinearity of the Hammerstein system. Correlation analysis is applied to acquire step response of linear dynamic component. Support Vector Regression is adopted to obtain a nonparametric description of the inverse of input static nonlinearity that is utilized to form an approximate linear model of the Hammerstein system. Based on the established model, a model predictive controller under predefined speed and acceleration constraints is designed to achieve safer treadmill exercise. Simulation results show that the proposed control algorithm can achieve optimal heart rate tracking performance under predefined constraints

A unified framework for solving a general class of conditional and robust set-membership estimation problems

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic Control (2014

Exploiting structure in piecewise affine identification of LFT systems

Identification of interconnected systems is a challenging problem in which it is crucial to exploit the available knowledge about the interconnection structure. In this paper, identification of discrete-time nonlinear systems composed by interconnected linear and nonlinear systems, is addressed. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear components. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine (PWA) identification techniques are employed for modelling the nonlinearity. A numerical example analyzes the benefits of the proposed structure-exploiting identification algorithm compared to applying black-box PWA identification techniques to the overall system

SAW Correlator Temperature Compensation Using a Pulse Width Modulated Temperature Controller

A Surface Acoustic Wave (SAW) correlator built on a Lithium Niobate substrate is temperature compensated in order to maintain a constant center frequency. Frequency shifts as a result of temperature variations limit device performance. An Arduino®-based PWM temperature controller is developed to read the device temperature from a resistance temperature detector located on the SAW wafer and to regulate its temperature to a specified setpoint by providing current to a heater which is co-located with the temperature sensor on the SAW correlator substrate. The final temperature controller achieves frequency shifts of 0.013 MHz from room temperature with a worst-case PPM experienced over 30°C of temperature variation of 0.48 PPM°C. Linear and non-linear plant models are developed successfully to predict the device\u27s temperature based on any input setpoint. Although there are alternatives to limit temperature drift at different temperatures, this thesis presents a simple method that works on a standard Lithium Niobate substrate

Linear and nonlinear parametric hydrodynamic models for wave energy converters identified from recorded data

Ocean waves represent an important resource of renewable energy, which can provide a significant support to the development of more sustainable energy solutions and to the reduction ofCO2 emissions. The amount of extracted energy from the ocean waves can be increased by optimizing the geometry and the control strategy of the wave energy converter (WEC), which both require mathematical hydrodynamic models, able to correctly describe the WEC-fluid interaction. In general, the construction of a model is based on physical laws describing the system under investigation. The hydrodynamic laws are the foundation for a complete description of the WEC-fluid interaction, but their solution represents a very complex and challenging problem. Different approaches to hydrodynamic WEC-fluid interaction modelling, such as computational fluid dynamics (CFD) and linear potential theory (LPT), lead to different mathematical models, each one characterised by different accuracy and computational speed. Fully nonlinear CFD models are able to describe the full range of hydrodynamic effects, but are very computationally expensive. On the other hand, LPT is based on the strong assumptions of inviscid fluid, irrotational flow, small waves and small body motion, which completely remove the hydrodynamic nonlinearity of the WEC-fluid interaction. Linear models have good computational speed, but are not able to properly describe nonlinear hydrodynamic effects, which are relevant in some WEC power production conditions, since WECs are designed to operate over a wide range of wave amplitudes, experience large motions, and generate viscous drag and vortex shedding. The main objective of this thesis is to propose and investigate an alternative pragmatic framework, for hydrodynamic model construction, based on system identification methodologies. The goal is to obtain models which are between the CFD and LPT extremes, a good compromise able to describe the most important nonlinearities of the physical system, without requiring excessively computational time. The identified models remain sufficiently fast and simple to run in real-time. System identification techniques can ‘inject’ into the model only the information contained in the identification data; therefore, the models obtained from LPT data are not able to describe nonlinear hydrodynamic effects. In this thesis, instead of traditional LPT data, experimental wave tank data (both numerical wave tank (NWT), implemented with a CFD software package, and real wave tank (RWT)) are proposed for hydrodynamic model identification, since CFD-NWT and RWT data can contain the full range of nonlinear hydrodynamic effects. In this thesis, different typologies of wave tank experiments and excitation signals are investigated in order to generate informative data and reduce the experiment duration. Indeed, the reduction of the experiment duration represents an important advantage since, in the case of a CFD-NWT, the amount of computation time can become unsustainable whereas, in the case of a RWT, a set of long tank experiments corresponds to an increase of the facility renting costs