Category Adaptive Control of Solar Energy Collector Systems

What Was Left Out?

A number of topics, although important for the matters treated above, have been left out. Some brief comments on them are therefore useful in order to establish what might be called the “boundary conditions” of this book.

The first topic is a more thorough treatment of control design by taking advantage of the fact that DCSF are bilinear systems, a class of nonlinear systems for which there is a rich plethora of results, for analysis as well as for controller design (Elliot 2009). Exploring possibilities offered by this family of methods, for which some work already exists for DCSFs (Carotenuto 1985, 1986), might be of interest to the more mathematically oriented reader.

Optimal Control (Speyer 2010; Geering 2007) provides also valuable tools that can be coupled with adaptation mechani...

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Cyber-Physical Systems

More involved problems reinforce the view that adaptive controllers such as the ones addressed in this book are basic “building blocks” of more complicated systems, such as networked systems connecting renewable energy sources that face uncertainty. The “green island” paradigm provides an example of such type of problems: Consider an island for which a number of power production and storage utilities are available. These utilities include DCSFs but also wind turbine fields and fossil fuel power generator units. The problem consists of taking advantage of these units such as to produce the electric power consumed by the island. DCSFs’ production are subject to random variations due to incoming solar radiation. Wind turbines are also subject to random disturbances associated to wind speed...

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Market with Changing Prices

While classical energy markets are characterized by a strong regulation, with central­ized power control being adequate, recent trends point in directions with increased degrees of freedom. An example is provided by distributed power grids with some degree of authority among local producers and energy markets with varying prices. Figure 8.3 illustrates a typical problem posed by new coming scenarios in relation to renewable energy production plants, including DCSFs.

As depicted in Fig. 8.3, at the present time tp the plant dispatch manager accepts a contract that commits the plant to produce, between future times ts and tf a certain target value of power that should be inside a tolerance band...

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Efficiency and Operational Constraints

When considered in isolation, the objective of a DCSF is to convert as much solar power as possible to thermal energy that can be used, for instance, for energy produc­tion. As shown in Fig. 8.2, the fluid outlet temperature should be closed to the value Topt that yields the maximum efficiency. However, due to the stochastic disturbances discussed in Sect. 1.3, the fluid temperature is not kept at an exact value, but instead randomly varies around its mean value with some probability density function (pdf). Let us call A to this pdf and T* to the corresponding mean value (see Fig. 8.2).

For safety reasons, the percentage of samples of the temperature value that are allowed to be above a certain threshold is limited. This threshold corresponds to an operational constraint (shown in Fig. 8...

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The Context of Renewable Energy Production

The importance of control of DCSFs, and of adaptive control in particular, may perhaps be only fully understood by considering the wider context of renewable energy production. Of course, control is required to maintain energy production plants in a state that is adequate for their objectives, while ensuring equipment integrity

Подпись: Fig. 8.2 Managing the outlet fluid temperature of a DCSF to maximize efficiency

and an extended useful life, i. e., enlarging the period in which the plant is able to operate in adequate conditions. However, the trend in energy markets raise new challenges that increasingly motivate the use of advanced control and optimization algorithms (Giannakis et al...

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Finally, one should mention the way in which constraints are tackled. Given an estimate of the plant model parameters, the control algorithms considered in this book that optimize a cost compute the manipulated variable using an explicit formula. This is no longer possible if an hard constraint, that is to say a constraint on the exact value of the manipulated variable is imposed. Nevertheless, as discussed in Sect.3.6.3, it is possible for some algorithms to impose a probabilistic constraint on the manipulated variable by adjusting the weight on the term of the cost associated to the manipulated variable...

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Tackling the Adaptation Transient

Another example of a topic of central interest for applications is tackling the adap­tation transient. Every adaptation algorithm entails an initial phase in which the estimates of the model parameters upon which the control decision relies are much deviated from the actual parameter values. This estimation error entails a transient in the plant that is beneficial to improve the estimates (the varying transient data is more informative), but that causes a loss in performance, (because the output temperature deviates significantly from the reference to track).

One possibility to prevent strong initial adaptation start-ups is to address the so-called dual control problem. The dual control problem, discussed in Sect. 3...

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Exploiting DCSF Structure

In MMAC, at least implicitly, local linear controllers are patched together to form an approximation to a global nonlinear controller. It is thus possible to take advantage of this fact to compensate some plant nonlinearities. This compensation is only approximate because it relies on a finite number of local controllers being patched. Furthermore, it may not be clear how to design the local controllers in a systematic way to achieve this objective. The examples provided for both a pilot air heating turbofan in Sect. 4.3 and for a DCSF in Sect. 4.4 that rely on the variables that define the operational regimes of these plants, and qualitative physical insight, provide clues for designing this type of controllers.

A much better compensation of the nonlinearities requires the DCSF models dis...

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