1. Introduction

Regarding the fact that coal is still themain fuel used in electricity generation around the world and it contains impurities that significantly increase pollutant emissions, new combustion techniques are developed, e.g. air staging, reburning and flue gas circulation [1]. Fossil fuel depletion forces the use of renewable fuels such as biomass; in existing power stations, biomass is milled and burned simultaneously with coal. However, low-emission combustion techniques, including biomass co-combustion, have negative effects: directly influence on process control stability/efficiency and indirectly on combustion installations via increased corrosion or boiler slagging [2]. These effects can be minimised using additional information about the process that makes combustion monitoring (diagnosis) system necessary to apply [3].

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

The combustion efficiency of pulverised fuel depends on several parameters. The commonly applied, low-emission techniques use recirculation vortexes that lengthen the paths of the coal grains passing through the flame to minimise generation of thermal oxides of nitrogen (NOx). To make co-combustion of pulverised coal more efficient and environment-friendly, it is necessary to measure its key parameters.

inaccuracies of the model simplicity, the term of robust control is used in [4, 5] to describe control systems that explicitly consider the discrepancies between the model and the real processes.

Adaptive Robust Control of Biomass Fuel Co-Combustion Process

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Depending on the technique used to design the controllers, there are different approaches in modelling uncertainties. The most extended techniques are frequency response uncertainties and transfer function parametric uncertainties. Most of the cases assume that the plant can be exactly described by one of the models belonging to a family. That is, if the family of models is composed of linear models, the plant is also linear. In case of model predictive control (MPC) approach, the uncertainties can be defined about the prediction capability of the model.

Frequency uncertainties are usually described by a band around nominal frequency response. The plant frequency response is presumed to be included in the band. In case of parametric uncertainties, each coefficient of the transfer function is presumed to be bounded by uncertainties limit. The plant is then presumed to have a transfer function with parameters within the uncertainty set. There is an assumption that the plant is linear with a frequency response within the uncertainty band for the first case and the plant is linear and of the same order as

The control models in MPC are used to predict what is going to happen: future trajectories. The appropriate way to describe uncertainties in this context seems to be the model (or a set of models) that instead of generating a future trajectory may also generate the band of trajectories in which the process of trajectory will be included when the same input is applied, in spite of uncertainties. In case of availability of good process model, this band is narrow, and the

The most general way of posing problem in MPC considers a process whose behaviour is

where y(t)∈Y and u(t)∈ U are n and m vectors of outputs and inputs, ψ∈ Ψ is a vector of

where <sup>b</sup>y tð Þ <sup>þ</sup> <sup>1</sup> is the prediction of output vector for instant <sup>t</sup> + 1 generated by the model <sup>b</sup><sup>f</sup> is a vector function, usually simplification of f, nna and nnb are the number of past outputs and inputs considered by the model and θ∈ Θ is a vector of uncertainties about the plant. Variables that are although influencing the plant dynamics are not considered in the model due to the

The dynamics of the plant in (1) are completely described by the family of models (2) if for any y(t), ⋯, y(t � ny)∈Y, u(t), ⋯, u(t � nu) ∈ U, z(t), ⋯, z(t � nz)∈Z and ψ ∈ Ψ, there is a vector of

parameters, possibly unknown, and z(t) ∈Z is a vector of possibly random variables.

Consider the model or family of models, for the process described by:

necessary simplifications or for the other reasons are represented by the z(t).

� �; u tð Þ;…; u tð Þ � nu ; z tð Þ;…; z tð Þ � nz ;<sup>ψ</sup> � � (1)

<sup>b</sup>y tð Þ¼ <sup>þ</sup> <sup>1</sup> <sup>b</sup>f ytð Þ;…; y tð Þ � nna ð Þ ; u tð Þ;…; u tð Þ � nnb ; <sup>θ</sup> (2)

that of the family of models for the case of parametric uncertainties.

y tð Þ¼ þ 1 f ytð Þ;…; y t � ny

uncertainty level is low.

dictated by the equation:

parameters θi∈ Θ such that:

The information taken at the output is delayed and averaged. Although there are several combustion diagnostic direct techniques, the most of them are expensive or impossible to utilise under industrial conditions. The radiation emitted by the flame reflects the combustion process occurring in chemical reactions and physical processes. The fast and minimally invasive optical methods allow to use image processing-based information in process control system. Such approach gives non-delayed and spatially selective additional information about the ongoing combustion process. The still and apparent position of flame is the result of dynamic equilibrium between the local flame propagation speed and the speed of the incoming fuel mixture. It allows assuming that the shape of a flame can be an indicator of the combustion process, occurring under certain conditions.

As a result, the relationship between the parameters describes the variation of the flame and the temperature of the exhaust gas in the chamber or the amount of air flow in the secondary factor. Thus, if the temperature is slowly varying value, having an inert nature, the reasonable approach is including a single or a set of the image parameters that would provide fast information to the synthesis of the controller. Due to the incomplete knowledge about the control plant or various changes in its performance, the control system with fixed parameters is insufficient. Then, it is recommended to use the adaptive control approach. The required knowledge of the complex nonlinear object may be achieved using different methods but due to the process, they ought to be robust and secure. It seems to be a very interesting application for robust adaptive control algorithms.
