FUENTES DE LA COMUNICACIÓN INSTITUCIONAL

Since the introduction of the Fuzzy sets theory by L. Zadeh back in the sixties of the last century, fuzzy logic received a good deal of attention in the field of control due to its ease of use, simplicity, robustness, and especially because it does not need the dynamics of the controlled plant since it look at the input output behaviour of the system, in another word, FLC looks at the system as a black box. Thus, it became a good choice in the controller design area (Leonid, 1997; Murphy, 1992).

For the purpose of controlling the Vdd value, the Mamdani type of FLC is used (Leonid,

1997), with two inputs, namely Frequency and the power, and one output, which is Vdd. Five

linguistic sets were used to describe the fuzzy inputs, as is seen in table (4.1), which gives the sets and the range of the fuzzy inputs and output.

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Fuzzy Set

Name Type Fuzzy Sets Range

Frequency Input Zero (Z) Low (L) Medium (M) High (H) Very High (VH) [5 10]

Power Input Zero (Z) Low (L) Medium (M) High (H) Very High (VH) [-8 -2]

Vdd Output Zero (Z) Low (L) Medium (M) High (H) Very High (VH) [0.2 4] In addition, the used membership function is the Gaussian distribution function given by

𝜇(𝑥) = 𝑒−(𝑚−𝑥)22.𝜎2 _(4.1)

Where m is the centre of the membership function (mean),  is the width of the membership function (standard deviation) and x is the input variable.

The membership functions where distributed equally on the universe of discourse with the ranges shown in table (4.1). The distribution of the membership functions for the inputs and the output are shown in Figure (4.2)

Figure (4.2): Fuzzy Membership Distribution along the Universe of Discourse, a) Frequency Memberships (input), b) Power Memberships (input), c) Vdd Memberships (output).

(a)

(b)

Chapter Four Smart Power Manager Unit Design

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The reason behind using the Gaussian membership function is to produce a smother control surface, as it is shown in Figure (4.3). A smoother control surface will ensure a lower study state error in the system output (Leonid, 1997; Murphy, 1992).

The linguistic rules used in the FLC are shown in Table (4.2) and can be read as: If Frequency is S and Power is VL THEN Vdd is Z.

Form the fuzzy rule table and by using the AND fuzzy operation, the output universe of discourse is concluded. The output of the FLC is calculated using the center of gravity algorithm.

Table (4.2): Fuzzy Rule Table.

Frequency/Power Z S M H VH Z Z VL M H VH VL Z Z M H VH M Z Z VL H H H Z Z VL M H VH Z Z Z M M

The rule table and the input/ output ranges produced the control surface shown in Figure (4.3).

Figure (4.3): Control Surface of the proposed FLC.

In the previouse figure, it is noted that the FLC trise to reduce the voltage to its minimum value to ensure that the power consumption is at its lowest posible rate, and that is seen in the blou area of the figure. The problem arises when the frequency is high which mean

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that FLC must increase the voltage so that it will overcome the missed pulse condition. This is seen in the light blue and green areas. The worst case happened when the frequency is very high, in this case FLC must produce a very high voltage to ensure a proper logic circuit operation. Since FLC does not have a knoledge about how much is the circuit Tmax, then it has

to preduct the value of Vdd according to the input frequency and the calculated power

consumption. That explaines the ripples in the control service. 4.4.1. Choosing the Right Fuzzy Universe of Discourse.

It can be seen from table (4.1) that the ranges of the input do not represent the actual values of the expected power or frequency because the actual range of frequency will range from 1 MHz up to 10 GHz. On the other hand, the actual power may range from 10s of mW to W, which is difficult to be fed and recognized by the fuzzy controller. Hence, a pre-scaling step was implemented to the input so that the higher and the lower ranges of both frequency and power can be recognized by the fuzzy system. The scaling of the frequency is done by taking the log of the input values, given in equations (4.2) and (4.3). This kind of scaling explains the negative values of the power range.

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 𝑙𝑜𝑔10(𝐹) (4.2)

𝑃𝑜𝑤𝑒𝑟 = 𝑙𝑜𝑔₁₀(𝑃_𝑑) (4.3)

Throughout the literature, the input to FLC was always linear because its input was measured in a limited range. In this thesis, the range was very wide so the log scale was the choice of scaling. As far as the author knowledge this is the first time that such scaling technique is used with FLC. This scaling technique will enable FLC to contribute more in the fields where the input values has a wide range specially in high frequency communication systems.

FLC can be implemented as a ROM that contain the values of the control surface shown in Figure (4.3). The address of the bytes inside the ROM will be presented by the values of the power and frequency while the byte vale will be the Vdd values (Tapou & Al-raweshidy,

2012; Tapou et al., 2011). It was shown in the literature that implementing FLC in this way will add an extra 18% to the system power consumption (H. R. Pourshaghaghi & de Gyvez, 2010; Tapou et al., 2011).