# Fuzzy

• What is fuzzy logic (FL)?

class of AI, Based on the nature of fuzzy human thinking, deals with problems that have fuzziness or vagueness, defined as multi-valued logic (0 to I), deals with imprecise information

• What's a fuzzy set?

fuzzy set (fuzzy value) theory based on FL, a particular object has a degree of membership in a given set that may be anywhere in the range of O (completely not in the set) to 1 (completely in the set)

• What's a Fuzzy problem ?

an input/output, static, nonlinear mapping problem through a "black box," as shown, all the input information is defined in the input space, it is processed in the black box, and the solution appears in the output space.

• mapping can be static or dynamic, and the mapping characteristics are determined by the black box's characteristics.
• The black box cannot only be a fuzzy system, but also an ES, neural network, general mathematical system, such as differential equations, algebraic equations, etc., or anything else.
• What's a Membership Function? give examples .

An MF is a curve that defines how the values of a fuzzy variable in a certain region are mapped to a membership valueμ ( or degree of membership) between 0 and I.

• What are the possible operations on fuzzy ? what are its properties ?

## Operatoins

OR : max ( A,B)

AND : min ( A,B)

NOT : NOT(A)= 1-(A)

Product : (same x axis ) multiply MFs

Power : raise MF to power of m( positive)

## Properties :

• What does a fuzzy inference problem consist of ?

• Step l: Fuzzification of input variables • Step 2: Application of fuzzy operator (AND, OR, NOT) in the IF (antecedent) part of the rule • Step 3: Implication from the antecedent to the consequent (THEN part of the rule) • Step 4: Aggregation of the consequents across the rules • Step 5: Defuzzification

• Mention some of the implication methods used in FL.

## Sugeno Type

### Singleton (zero-order)

rules states a K

### first-order

rules state operands

each rule as defining the location of a moving singleton. that is. the singleton output spikes can move around in a linear fashion in the output space depending on the input signal values

Fuzzy model on DC Machine

• What's defuzzifaction? mention its methods.

it's the conversion of the fuzzy output ( the aggregated union of the fired rules output) into a crisp output

its methods are :

1. Center of Area (COA) method [ centre of gravity]

discrete :

Ex:

2. Height Method

COA but consider only the height of each contributing MF at the mid-point of the base.

3. Mean of Maxima (MOM) Method

takes only the z of the highest MF (for above example Z0= 3 )

for m number of MFs that have the same height take the average

4. Sugeno Method

zero order

first order

• What's Fuzzy Control (FC)?

Fuzzy control is basically an adaptive and nonlinear control, which gives robust performance for a linear or nonlinear plant with parameter variation

• How to implement a P, PI and PID control in fuzzy?

only by using the E error and CE change of error signals we can use

## P control

as example rule: IF E = positive small (PS) THEN U = positive big (PB)

so, only kp = K and KE=U

## PI Control

Rule I: IF E = ZE AND CE= NS THEN DU= NS Rule 2: IFE= PS AND CE= NS THEN DU= ZE

and to get U we integrate or sum

so,

## PID Controller

example rule: IF E = PS AND CE= NS AND e' E = PS THEN DU= ZE,

• Draw a general fuzzy control block diagram, with the general structure of a fuzzy feedback control system.

in control of the speed in induction machine (VC based)

the general structure of a fuzzy feedback control system

• What are the available control implementation methods for fuzzy control ?
1. Using real time computation (C program, FL Toolbox or DSP ASIC chips)
1. Using a look up table where all computation are done a head in hierarchical tables (coarse, medium and fine)

• What is the fuzzy logic control design methodology?
1. Analyze if the problem requires FC ?
1. if plant model available simulate it and study its characteristics.
1. identify functional elements where to apply FL.
1. identify the inputs and outputs of each fuzzy sys.
1. define universe of discourse and convert to pu values.
1. formulate fuzzy sets, choose MF shapes
• sensitive : need more fuzzy sets
• more precision near S.S : crowding of MFs near the origin
1. formulate rule table.
1. if there is a plant model , test and iterate fuzzy sets and rules

if not available, design a conservative fuzzy control and test on plant operation.

1. implement in real time, and iterate to improve performance

• Mention some of fuzzy logic control applications in power electronic systems.

Applications include 1. speed control of dc and ac drives

2. feedback control of converter 3. off-line P-I and P-I-D tuning. 4. nonlinearity compensation 5. on-line and off-line diagnostics 6. modeling 7. parameter estimation. 8. performance optimization of drive systems based on on-line search 9. estimation for distorted waves

• Draw the fuzzy MFs for induction motor speed control.

• write down a rule matrix for fuzzy speed control

• draw the typical speed response with stepped load torque TL, and then show a similar response with four times the rotor inertia, comment.

The performances are superior to conventional PI control. The robustness in the response is evident from the results., with more inertia it took more time to get to ss but it did due to robustness of the controller and parameter variation (inertia) didn't affect its response not mentioning its stability.

• draw the block diagram of the wind generation system incorporating all the control elements.
• Discuss the fuzzy control loops in wind mppt

• FLC-1: On-line search of generator speed to maximize output power

• power is the product of torque and speed and turbine power equals line output power.
• the output Delta w added with some amount of the Last Delta w signal to avoid local minima due to wind vortex and torque ripple.

### Factors Calculation

The scale factors KPO and KWR, shown in Figure 11.28, are a function of generator speed so that the control becomes somewhat insensitive to speed variation. Although scale factors are normally generated by mathematical expression, in this case, they arc generated by fuzzy computation

• FLC-2: On-line search of machine excitation current to optimize machine efficiency at light load

• FLC-3: Robust control of generator speed

• Discuss efficiency improvement under FLC1 and FLC2

• The gain due to FLC- I by tuning the generator speed to optimal value can be very high at low wind velocity although P0 may be small
• It decreases to zero near 0.7(pu) wind velocity
• and then increases again
• the efficiency gain by FLC-2 decreases because of higher generator loading.

### Paper Microgrid PV MPPT (hill climbing)

• define Microgrids.

Microgrids are defined as systems that have at least one distributed energy source and associated loads and can form intentional islands in the electrical distribution systems

• What are PV systems main problems?
1. High fabrication cost
1. Low conversion efficiency especially under variable weather conditions
1. The nonlinearity between the PV array output power and current
• what's Ripple correlation control (RCC)

is an optimization technique that takes advantage of the converter signal ripple to track the MPP

• what are the drawback of old MPPT tracking methods (fuzzy or not)

like current-power change method is that the operating point is mover away from the maximum point when irradiance changes

• show the effect of increasing radiation and temperature on P-D curve.

1. Simplicity
1. Easy implementation
1. low cost

1. Slow converge to optimum point
1. at SS power oscillates around MPP, causing losses
1. during cloudy when irradiance varies, operating point may move away from MPP.
• what are the conventional method to overcome hill-climbing shortcomings

adaptive-based controller to enhance the steady state and converging-speed performance. At steady state, the incremental step is small and during a transient stage the incremental step size is large.

• What's the proposed hill climbing using FLC.

• How to ensure PV output doesn't diverge from mpp with varying weather (3rd drawback solution)

To ensure that the PV output power does not diverge from the optimum point during varying weather conditions, ΔP passes through a gain controller to reverse its direction.

• Write down rules of hill climbing, and MF function

• What advantages does the FLC hill-climbing MPP has?

The FLC computes variable step sizes to increment or decrement the duty cycle, therefore the tracking time is short and the system performance during steady-state conditions is much better than with conventional hill-climbing algorithm. Moreover, divergence problem no longer exist since the controller input, change of power (dP), reverses its direction in response to atmosphere condition variation

• Explain the power divergence due to weather variation

• what's the effect of partial shading on hill climbing technique?

# Artificial Neural Networks

• What are the general applications of Neural Networks? What are neural networks used for ?
• Classification
• Regression
• Combinatorial optimization
• Define 2-Class classification and multi class decision surface.

## 2-class classifier

a general equation for Linear 2-class classifier

## Mutli-class classifier

• How to form a non-linear classifier?

• Show the typical neuron structures.

• What are the common activation functions?

## Unipolar Sigmoidal function

• Neural Networks based on a layered perceptron, explain.
• Why do we need bias ?
• What's the objectives of neural network ?

compute the weights to obtain the desired decision for the given input patterns

• What are the NN learning or training techniques ?
• steepest descent (error backpropagation)
• Random search
• Genetic algorithm
• Particle swarms
• How do we calculate error and error function in NN ?
• Show the steps of backpropagation.
• What is the difference between supervised and unsupervised learning ?

supervised where we se the error function to modify the weights

unsupervised is where the nn alters its own weights

• Show a case of NN unsupervised learning.

# Genetic Algorithm

• What's Genetic Algorithm ?
• a search technique used in computing to find true or approximate solutions to optimization and search problem.
• global search heuristics
• class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover (recombination)
• probabilistic intelligent search algorithm, which searches a population of points in parallel.
• In what does GA differ from other optimization techniques ?

• It searches a population of points in parallel • It uses probabilistic rules rather than deterministic ones • It can process an encoding set of parameters

• Give an overview of the evolution process in GA.
1. starting from a population of randomly generated individuals
1. then evolution happens in generations
1. In each generation, the fitness of every individual in the population is evaluated
1. multiple individuals are selected from the current population (based on their fitness)
1. the selected individual are modified to form a new population.
1. new population is used in the next iteration of the algorithm
1. To terminate algorithm either 1) a max. number of generations 2) satisfactory fitness level acquired.

• Start with a large “population” of randomly generated “attempted solutions” to a problem • Repeatedly do the following:  Evaluate each of the attempted solutions  (probabilistically) keep a subset of the best solutions  Use these solutions to generate a new population • Quit when you have a satisfactory solution (or you run out of time)

• Define, individual, Population and Fitness.

Population : Group of all individuals Target (search space)

Individual : Any possible solution also called chromosome

Fitness : function that we optimize (each individual has a fitness)

• What's penalty cost ?

To initiate the population, a number of individuals are randomly formulated in the range of variables Each individual in the randomly-created population is tested for violating the constraints If the solution is infeasible, a suitable additional penalty cost is assigned to the individual The performance of each individual is evaluated by calculating the value of objective function and adding the corresponding penalty term if exists

• What's individuals fitness value ?
• The individuals are ranked depending on their corresponding costs and a suitable fitness value is assigned to each one
• The fitness values could be calculated depending on the position of the individuals within the population rather than their distinct performance
• Fitness values between maximum and minimum limits are calculated with fixed incremental steps and assigned to the ranked individuals
• Use a random population pool to represent the GA steps.
• What's the Constraints representation problem in GA ? and what are the approaches to solve this problem ?
• To employ GA with a tightly-constrained problem, it is possible to generate only feasible solutions by avoiding individuals which violate the given constraints
• but, the infeasible solutions mostly cover the search space at the initial generation, so the avoidance will cause missing the area of global minimum

Approaches,

1. Move the infeasible individuals to the nearest feasible area,
• but this would be too complex and a very time consuming
1. Penalty function convert to an unconstrained problem by augmenting additional cost terms with the main objective function
• nonlinear costs for solutions that violate the constraints depending on their relative locations with respect to the feasibility boundaries
• ensure adequate choice of the penalty functions and their parameters for rapid rejection
• differentiate in performance between the infeasible individuals themselves, which will help in the evolution process
• higher cost value has to be assigned to any infeasible solution than the feasible members, for fast rejection

• Draw a flowchart defining the GA search algorithm.
• What's crossover?

Crossover is a genetic process to exchange information between members of the population.

It's the generation of new individuals of the next generation by mating parents by choosing a crossover point

or can be a two point cross over to mate the middle part genes, avoiding genes at the beginning and end of chromosome

or can be by choosing random subset from one parent and replacing it from the another parent.

• What's Mutation?

it's small disruptive change in the new generation members

• Suppose we want to maximize the number of ones in a string of (L) binary digits An individual is encoded (naturally) as a string of l binary digits The fitness (f) of a candidate solution is the number of ones in its genetic code

We start with a population of “n” random strings. Suppose that L= 10 and n= 6

1. We toss a fair coin 60 times and get the following initial population:

2. We randomly select a subset of the individuals based on their fitness according to

3. Suppose that, after performing selection, we get the following population::

4. we choose 0.6 of the 6 chosen to perform crossover, choose random two point cross over

5. after crossover we get new 0.6*6 = 4 individuals (initial strings in the next photo)

6. these 4 new individuals we allow for 0.1 mutation (one bit)

And now, iterate … In one generation, the total population fitness changed from 34 to 37, thus improved by ~9% At this point, we go through the same process all over again, until a stopping criterion is met

• What are selection methods in GA?
1. Roulette wheel (one pointer)

you will need N rolls to get N solutions

2. N equally space pointers

one roll will give you N solution

• How to do recombination in non-binary chromosomes ?

### Crossover

Crossover is a genetic process to exchange information between members of the population.

For the real-valued encoding, the max-min arithmetical crossover operator can be used as follows

### Mutation

It is the second process in the recombination, which is used to escape from possible local minima. The mutation in the real-coded representations is accomplished by disturbing the gene values with low probability.

• What's Elitism?
• to ensure that the best solutions are not lost in moving from one generation to the next.
• some of the fittest members of each generation are saved and copied into the next generation.
• the average fitness of the new generation is improved.
• Give a numerical example of a GA problem parameters

### Number of individuals per subpopulation (20)

for migration purposes.

### Total population size (200)

the number of individuals

### Generation gap (0.8)

number of individuals recombination are made on

### Insertion rate (0.9)

that 0.9 of the new generation will replace the worst same number of individuals in the old generation

### Probability of mutation (0.01)

how much of the genes will be mutated

### Maximum generations (1000)

the number of generation at which the algorithm terminates

• We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost$6/ft2. If the box must have a volume of 50ft3 determine the dimensions that will minimize the cost to build the box