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.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

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.

Measurements and modelling of airflows in houses using passive sampling and HAM software

Passive samplers have been predominantly used to monitor environmental conditions in single volumes. However, measurements using a calibrated passive sampler- Solid Phase Microextraction (SPME) fibre, in three houses with cold pitched roof, successfully demonstrated the potential of the SPME fibre as a device for monitoring air movement in two volumes. The roofs monitored were pitched at 15° - 30° with insulation thickness varying between 200-300 mm on the ceiling. For effective analysis, two constant sources of volatile organic compounds were diffused steadily in the house. Emission rates and air movement from the house to the roof was predicted using developed algorithms. The airflow rates which were calibrated against conventional tracer gas techniques were introduced into a HAM software package to predict the effects of air movement on other varying parameters. On average it was shown from the in situ measurements that about 20-30% of air entering the three houses left through gaps and cracks in the ceiling into the roof. Although these field measurements focus on the airflows, it is associated with energy benefits such that; if these flows are reduced then significantly energy losses would also be reduced (as modelled) consequently improving the energy efficiency of the house. Other results illustrated that condensation formation risks were dependent on the airtightness of the building envelopes including configurations of their roof constructions.

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.

Assessing bee species richness in two Mediterranean communities: importance of habitat type and sampling techniques

The decline of bees has raised concerns regarding their conservation and the maintenance of ecosystem services they provide to bee-pollinated wild flowers and crops. Although the Mediterranean region is a hotspot for bee species richness, their status remains poorly studied. There is an urgent need for cost-effective, reliable, and unbiased sampling methods that give good bee species richness estimates. This study aims: (a) to assess bee species richness in two common Mediterranean habitat types: semi-natural scrub (phrygana) and managed olive groves; (b) to compare species richness in those systems to that of other biogeographic regions, and (c) to assess whether six different sampling methods (pan traps, variable and standardized transect walks, observation plots and trap nests), previously tested in other European biogeographic regions, are suitable in Mediterranean communities. Eight study sites, four per habitat type, were selected on the island of Lesvos, Greece. The species richness observed was high compared to other habitat types worldwide for which comparable data exist. Pan traps collected the highest proportion of the total bee species richness across all methods at the scale of a study site. Variable and standardized transect walks detected the highest total richness over all eight study sites. Trap nests and observation plots detected only a limited fraction of the bee species richness. To assess the total bee species richness in bee diversity hotspots, such as the studied habitats, we suggest a combination of transect walks conducted by trained bee collectors and pan trap sampling

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Sampling series for determination of probability density of CDMA multiple access interference

Consideration is given to a standard CDMA system and determination of the density function of the interference with and without Gaussian noise using sampling theory concepts. The formula derived provides fast and accurate results and is a simple, useful alternative to other methods