#### LESSONS OF EASTER ISLAND

March 17th, 2016

The type of adaptive controller used may vary a lot. In this book, a major trade-off is concerned with the amount of plant knowledge embedded on the algorithm. At one extreme there are algorithms, addressed in Chap. 3, which assume that the plant is linear. Their main drawback consists in not taking into account plant nonlinearities when performing maneuvres that consist of large and relatively fast excursions of the output, or when rejecting fast disturbances, which is more common on DCSF operation. In DCSFs, these algorithms are mainly useful for temperature regulation around piecewise constant operating points. They can also be useful parts of the multiple model-based algorithms described in Chap.4.

The most powerful algorithms in this class are obtained by combining a linear model pred...

Read MoreDue to their large dimensions and specificity of operation, where a fluid circulates through a pipe located at the focus of solar energy collector mirrors, the dynamics of DCSFs depends on space as well as on time. Together with uncertainty sources in plant model, this dependency raises interesting challenges for controlling the temperature on DCSFs and motivates the consideration of the adaptive control methods addressed in this book.

The first step in designing a control system is to identify what are the plant outputs that relates to the control objectives, the manipulated variable (the variable that can be directly changed and that allows to exert an influence on the output variable), and to characterize the disturbances...

Read MoreAs discussed in Chap. 1, solar energy systems are quite wide in scope and they are currently the subject of a renewed interest associated to the search for renewable sources of energy that may form an alternative, or a complement, to other types

J. M. Lemos et al., Adaptive Control of Solar Energy Collector Systems, 207

Advances in Industrial Control, DOI: 10.1007/978-3-319-06853-4_8,

© Springer International Publishing Switzerland 2014

of energy sources, such as fossil fuels or nuclear, or even other renewable energy sources.

Motivated by this interest, this book addresses the control of distributed collector solar fields (DCSFs)...

Read MoreThe trajectory specified that links the initial value of the output with the final value is to be smooth...

Read MoreThis chapter shows how to develop an adaptive servo controller for a DCSF, using a motion planner based on orbital flatness. The structure of the controller considered in this chapter is shown in Fig.7.1 and comprises three main blocks:

• A motion planner;

• A feedback controller;

• An adaptation law.

Read MoreConsider now the boundary condition for z = 0. By Making z = 0 in (7.79) and taking the logarithm, we get

ln w(0, т) = —W(t + L) — ви(t). (7.80)

Combining (7.80) and (7.79) yields

(i)

where w (т) is the derivative of order i of the flat output. The formulas (7.83) and (7.84) express the process output and input as a function of the flat output derivative and of its derivatives, provided that the series converge.

Motion planning is made by making moves between successive stationary states defined by

dwss(z, t) dwss(z, т)

—= 0, (7.85)

d t дт

and a constant value u-s for the manipulated input. This condition implies that

= —в и– w(z), dz

w–(z) = w–(0) e eu–z

where w-s (0) is the boundary condition at z = 0, and u-s = f-, are constant values (u-sis the cons...

Read MoreFor the moisture control process, define the flat output y by the following boundary condition, imposed for z = L in the transformed time coordinate:

u z=L

There is not an algorithm to obtain a flat output. Instead, one has to be lead by intuition, in a trial-and-error procedure, and verify a posteriori wether a given function is actually a flat output. In this case, we get inspiration from a comparison with the flat output obtained for the DCSF that, as shown before, is the spacial gradient of the temperature at the pipe outlet (i. e., for z = L. Therefore, we seek as a flat output a gradient of a function of the moisture for z = L and, given the exponential decay in the expression of the general solution (7.73), we take this function as a logarithm...

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