Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete-time systems

A neural network enhanced self-tuning controller is presented, which combines the attributes of neural network mapping with a generalised minimum variance self-tuning control (STC) strategy. In this way the controller can deal with nonlinear plants, which exhibit features such as uncertainties, nonminimum phase behaviour, coupling effects and may have unmodelled dynamics, and whose nonlinearities are assumed to be globally bounded. The unknown nonlinear plants to be controlled are approximated by an equivalent model composed of a simple linear submodel plus a nonlinear submodel. A generalised recursive least squares algorithm is used to identify the linear submodel and a layered neural network is used to detect the unknown nonlinear submodel in which the weights are updated based on the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model therefore the nonlinear submodel is naturally accommodated within the control law. Two simulation studies are provided to demonstrate the effectiveness of the control algorithm.

Relationship between deadbeat and pole-placement discrete-time PID controllers

This paper considers PID control in terms of its implementation by means of an ARMA plant model. Two controller actions are considered, namely pole placement and deadbeat, both being applied via a PID structure for the adaptive real-time control of an industrial level system. As well as looking at two controller types separately, a comparison is made between the forms and it is shown how, under certain circumstances, the two forms can be seen to be identical. It is shown how the pole-placement PID form does not in fact realise an action which is equivalent to the deadbeat controller, when all closed-loop poles are chosen to be at the origin of the z-plane.

A critique of neural networks for discrete-time linear control

This paper discusses the use of multi-layer perceptron networks for linear or linearizable, adaptive feedback.control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parametrization. A comparison is made with standard, non-perceptron algorithms, e.g. self-tuning control, and it is shown how gross over-parametrization can occur in the neural network case. Because of the resultant heavy computational burden and poor controller convergence, a strong case is made against the use of neural networks for discrete-time linear control.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Assessment of the consistency of H2O line intensities over the near-infrared using sun-pointing ground-based Fourier transform spectroscopy

We report on the consistency of water vapour line intensities in selected spectral regions between 800–12,000 cm−1 under atmospheric conditions using sun-pointing Fourier transform infrared spectroscopy. Measurements were made across a number of days at both a low and high altitude field site, sampling a relatively moist and relatively dry atmosphere. Our data suggests that across most of the 800–12,000 cm−1 spectral region water vapour line intensities in recent spectral line databases are generally consistent with what was observed. However, we find that HITRAN-2008 water vapour line intensities are systematically lower by up to 20% in the 8000–9200 cm−1 spectral interval relative to other spectral regions. This discrepancy is essentially removed when two new linelists (UCL08, a compilation of linelists and ab-initio calculations, and one based on recent laboratory measurements by Oudot et al. (2010) [10] in the 8000–9200 cm−1 spectral region) are used. This strongly suggests that the H2O line strengths in the HITRAN-2008 database are indeed underestimated in this spectral region and in need of revision. The calculated global-mean clear-sky absorption of solar radiation is increased by about 0.3 W m−2 when using either the UCL08 or Oudot line parameters in the 8000–9200 cm−1 region, instead of HITRAN-2008. We also found that the effect of isotopic fractionation of HDO is evident in the 2500–2900 cm−1 region in the observations.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

Mismatch effects on discrete-time poles

The presence of mismatch between controller and system is considered. A novel discrete-time approach is used to investigate the migration of closed-loop poles when this mismatch occurs. Two forms of state estimator are employed giving rise to several interesting features regarding stability and performance.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Discrete demand side control performance under dynamic building simulation: a heat pump application

This study presents the findings of applying a Discrete Demand Side Control (DDSC) approach to the space heating of two case study buildings. High and low tolerance scenarios are implemented on the space heating controller to assess the impact of DDSC upon buildings with different thermal capacitances, light-weight and heavy-weight construction. Space heating is provided by an electric heat pump powered from a wind turbine, with a back-up electrical network connection in the event of insufficient wind being available when a demand occurs. Findings highlight that thermal comfort is maintained within an acceptable range while the DDSC controller maintains the demand/supply balance. Whilst it is noted that energy demand increases slightly, as this is mostly supplied from the wind turbine, this is of little significance and hence a reduction in operating costs and carbon emissions is still attained.

Smooth Regrading of Discretized Data

Methods for producing nonuniform transformations, or regradings, of discrete data are discussed. The transformations are useful in image processing, principally for enhancement and normalization of scenes. Regradings which “equidistribute” the histogram of the data, that is, which transform it into a constant function, are determined. Techniques for smoothing the regrading, dependent upon a continuously variable parameter, are presented. Generalized methods for constructing regradings such that the histogram of the data is transformed into any prescribed function are also discussed. Numerical algorithms for implementing the procedures and applications to specific examples are described.

A global view of the extratropical tropopause transition layer from Atmospheric Chemistry Experiment Fourier Transform Spectrometer O3, H2O, and CO

The global behavior of the extratropical tropopause transition layer (ExTL) is investigated using O3, H2O, and CO measurements from the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on Canada’s SCISAT-1 satellite obtained between February 2004 and May 2007. The ExTL depth is derived using H2O-O3 and CO-O3 correlations. The ExTL top derived from H2O-O3 shows an increase from roughly 1–1.5 km above the thermal tropopause in the subtropics to 3–4 km (2.5–3.5 km) in the north (south) polar region, implying somewhat weaker tropospherestratosphere- transport in the Southern Hemisphere. The ExTL bottom extends ~1 km below the thermal tropopause, indicating a persistent stratospheric influence on the troposphere at all latitudes. The ExTL top derived from the CO-O3 correlation is lower, at 2 km or ~345 K (1.5 km or ~335 K) in the Northern (Southern) Hemisphere. Its annual mean coincides with the relative temperature maximum just above the thermal tropopause. The vertical CO gradient maximizes at the thermal tropopause, indicating a local minimum in mixing within the tropopause region. The seasonal changes in and the scales of the vertical H2O gradients show a similar pattern as the static stability structure of the tropopause inversion layer (TIL), which provides observational support for the hypothesis that H2O plays a radiative role in forcing and maintaining the structure of the TIL.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

A high-resolution near-infrared extraterrestrial solar spectrum derived from ground-based Fourier transform spectrometer measurements

A detailed spectrally-resolved extraterrestrial solar spectrum (ESS) is important for line-by-line radiative transfer modeling in the near-infrared (near-IR). Very few observationally-based high-resolution ESS are available in this spectral region. Consequently the theoretically-calculated ESS by Kurucz has been widely adopted. We present the CAVIAR (Continuum Absorption at Visible and Infrared Wavelengths and its Atmospheric Relevance) ESS which is derived using the Langley technique applied to calibrated observations using a ground-based high-resolution Fourier transform spectrometer (FTS) in atmospheric windows from 2000–10000 cm-1 (1–5 μm). There is good agreement between the strengths and positions of solar lines between the CAVIAR and the satellite-based ACE-FTS (Atmospheric Chemistry Experiment-FTS) ESS, in the spectral region where they overlap, and good agreement with other ground-based FTS measurements in two near-IR windows. However there are significant differences in the structure between the CAVIAR ESS and spectra from semi-empirical models. In addition, we found a difference of up to 8 % in the absolute (and hence the wavelength-integrated) irradiance between the CAVIAR ESS and that of Thuillier et al., which was based on measurements from the Atmospheric Laboratory for Applications and Science satellite and other sources. In many spectral regions, this difference is significant, as the coverage factor k = 2 (or 95 % confidence limit) uncertainties in the two sets of observations do not overlap. Since the total solar irradiance is relatively well constrained, if the CAVIAR ESS is correct, then this would indicate an integrated “loss” of solar irradiance of about 30 W m-2 in the near-IR that would have to be compensated by an increase at other wavelengths.