CHAPTER 1

INTRODUCTION

Intelligent control is a control theory tehnique that uses artificial intelligence in process of controlling dynamical systems. Some types of intelligent control are neural networks, fuzzy logic, machine learning, ant colony and genetic algorithm. In this research, it will be discuss about use of genetic algorithm for tuning cascade PID controller.

Since PID controllers perform in real-time, external disturbances are always present. Cascade connection of PID controllers will be used to avoid those disturbances and to keep controlling process optimal.

Genetic algorithm is a simulation of a process of genetic inheritance in nature. It is effective way for transferring the best properties from generation to the next one. The best fitting genes from both parents are selected and incorporated into new generation.

Control theory is an interdisciplinary branch of engineering. and its essential part. There is a controlling process as a part of every dynamical system. Effective control makes the difference between feasible system and unfeasible one. PID control has been used in many applications and its tuning process can be a major challenge. The best fitting PID coefficients are needed for a system to have an optimal performance. This analogy can be used for development of genetic algorithm, which as a result, will have coefficients of PID controller. For these purposes, MATLAB tools will be used.After PID coefficient calculation, results will be analyzed and statistically processed, pattern in result changes according to system requirement changes will be found, so process of control will be kept optimal in situation of different input values.

At the end, practical implementation of cascade PID controlling process will be performed using FPGA integrated circuit. FPGA will be programmed using Verilog Hardware Description Language. System will be ready for practical application in industrial control processes (motor drive cascade PID controller).

CHAPTER 2

CASCADE PID CONTROL

2.1 PID Controller

PID controller is feedback loop controller used in industrial control systems. It was first introduced in 1939 and has remained the most widely used controller in process control until today. An investigation performed in 1989 in Japan indicated that more than 90 % of the controllers used in industries are PID controllers and its advanced versions (Araki, 2005).

A PID controller calculates an error value as the difference between a measured process variable and a set point. The controller minimizes the error by adjusting the process variable.

Figure 2.1 Block Diagram of a PID Controlled ProcessPID controller consists of three constant parameters: P - proportional to error function, represents present error; I - integral of error function, represents past errors; D derivative of error function, represents future errors. Manipulation of these parameters shapes the response of the controller to an error; the degree controller overshoots the set point, and the degree of system oscillation.

Two basic requirements are regulation (reaching given set point, disturbance rejection) and command tracking (implementing set point changes). Specific criteria for command tracking include settling time and rise time. An overshoot of the process variable beyond the set point must not be allowed if it would be unsafe. Otherwise, it must have an optimal value. Other processes must reduce the energy consumption in reaching a new set point.

PID controller tuning is the adjustment of its parameters, P, I and D, to the optimum values for the desired control response. Stability is a basic requirement, but various systems have different behavior, so different requirements need to be met and requirements may conflict with one another. If PID parameters are chosen incorrectly, the controlled process output can be unstable. Stabilization of response is required and the process must not oscillate for any combination of process set points and conditions.

PID tuning is a major engineering challenge, even though there are up to three parameters, because it must fulfill complex criteria of PID control. Various methods exist and more sophisticated techniques are the subject of patents. PID controller designing and tuning can be hard in practice, if conflicting targets such as high stability and short transient are to be achieved. PID controller performance can be improved by careful tuning. Initial designs need to be adjusted repeatedly until the system performs as requiredSome applications require only one or two actions to provide the appropriate system control. This is achieved by setting unnecessary parameters to zero. PI controllers are common, since derivative gain is sensitive to disturbances and noise and absence of an integral gain may prevent the system from reaching its target value.

2.2 Cascade Control

Major advantage of PID controllers is usage of two PID controllers together to improve better dynamic performance. This is called cascade PID control. In cascade control there is a connection of two controllers with one controlling the set point of another. First acts as outer loop controller, which controls the primary physical parameters. Second acts as inner loop controller, which reads the output of outer loop controller as set point, usually controlling a more rapid changing parameter. Cascade control is used to achieve fast rejection of disturbances. The main purpose of using cascade control as a strategy is to allow the secondary loop to control disturbances before they can affect the primary loop.

Figure 2.2 Cascade PID Control Block Diagram

As shown in figure 2.2, controller C1 in the outer loop is the primary controller that regulates the primary controlled variable y1 by setting the set-point of the inner loop. Controller C2 in the inner loop is the secondary controller that rejects disturbance d2 locally before it propagates to P1. (Mathworks, 2014)

2.3 Motor as an Object of Control

Induction motors are the most important parts of every industry branch and they are produced in large number. About half of the electrical energy generated in a developed country is ultimately consumed by electric motors, of which over 90 % are induction motors (Tze_Fun Chan, 2011). Induction motors have mainly been deployed in constant-speed motor drives. The development of power electronics devices and converter technologies has made possible efficient speed control by varying the supply frequency, giving rise to various forms of adjustable-speed induction motor drives (Tze_Fun Chan, 2011). There are advances in artificial intelligence techniques and control methods, including genetic algorithm, neural networks and fuzzy logics. Performance of induction motor can be improved with these techniques. Since the 1990s, AI-based induction motor drives have received greater attention and numerous technical papers have been published (Tze_Fun Chan, 2011). Speed-sensorless induction motors have become as an important branch of induction motor research. Some electric drive producers began to incorporate AI-control in commercial products.

CHAPTER 3

GENETIC ALGORITHM

Genetic algorithm is part of the class of evolutionary algorithms used in field of artificial intelligence. Evolutionary algorithms are search and optimization methods, based on the principle of natural selection in genetics. In general, any iterative, population based approach that uses selection and random variation to generate new solutions can be regarded as an EA. Genetic algorithms became known through the work of John Holland in the early 1970s and was popularized by Goldberg in 1989 and, as a result, the majority of control applications in the literature adopt this approach (Muhammet nal, 2013). Their applications include several types of problems such as designing the communication networks, optimizing the database query and controlling the physical systems. Thus, GA has become a robust optimization tool for solving the problems related to different field of the technical and social sciences (Muhammet nal, 2013).

3.1 Theoretical Foundations

GA scans the most suitable of the chromosomes that built the population in the potential solutions space. It tries to balance two opposite objectives: searching the best solutions and expanding the search space. During execution of GA, evolution of a population of solutions (phenotype) leads toward set of better solutions of an optimization problem. Each solution candidate has properties (genotype) which can be mutated and altered. Solutions are usually represented as strings of bits in binary code, but other encodings are possible. Coding method has a decisive effect on the performance of the GA. (Whitley, 1994).The selection usually starts from a population of randomly generated individuals which represents first generation, and is an iterative process, with the population in each iteration representing a new generation. In each generation, fitness of every individual has been evaluated. The fitness is usually the value of the objective function in the optimization problem being solved. Fit individuals are stochastically selected from the current population and each individual's genome is modified, recombined and possibly randomly mutated to form a new generation. The new generation of candidate solutions is then used in the next iteration of the algorithm. Usually, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population (Michalewicz, 1996).

A typical genetic algorithm requires a genetic representation of a solution domain and fitness function to evaluate the solution domain. When genetic representation and fitness function are defined, GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.

Initially, many individual solutions are randomly generated to form a population. The population size depends on the nature of the problem, containing several hundreds or thousands of possible solutions. The population is generated randomly, allowing the entire range of possible solutions. During each successive generation, a proportion of the existing population is selected to breed a new generation. Individual solutions are selected through a fitness-based process, where fitter solutions, according to a fitness function, are typically more likely to be selected. The fitness function is defined over the genetic representation and measures the quality of the represented solution and it is problem dependent.

Next step is to generate a second generation population of solutions from those selected through a combination of genetic operators, crossover and mutation. The crossover operator can be described as exchanging two chromosomes chosen as the parents. Crossover point number is one. The other important crossover method is uniform crossover. In this method, each parents genes crossed over with different probabilities (Syswerda, 1989). Mutation operator changes one or more genes in the chromosome. Traditionally, mutation operator is used rarely. Usually, the crossover probability (Pc) is chosen between 0.25 and 1, and mutation probability (Pm) is chosen between 0.01 and 0.001 (Bck, 1993).

GA process is repeated until a termination condition has been reached. Terminating conditions are:- solution is found that satisfies minimum criteria- fixed number of generations reached- computation time reached- the highest ranking solution's fitness is reached or has reached a point that successive iterations no longer produce better results- manual inspection

3.2 MATLAB Implementation

Genetic algorithm can be simulated and implemented with MATLAB tool. In the toolbox, the ga function may be used as GAs fitness function to optimize a MATLAB function (Mathworks, 2014). The basic steps of genetic algorithm are as follows. generate a random population of n chromosomes which have a proper form for the problem run fitness function; evaluate the fitness function using each chromosome in the population. evaluate results, if conditions are satisfied, then GA stops and outputs the best chromosome of current population. select two or more parent chromosomes from a population according to their fitness (the better the fitness of a chromosome, the greater is its chance of being selected). with a crossover probability cross over the parents to form a new offspring, if no crossover was performed, the offspring is an exact copy of the parents. with a mutation probability mutate new offspring at each locus (position in chromosome). place new offspring in the old population to create a new population and use a new generated population for a further run of the algorithm (Tze_Fun Chan, 2011).

CHAPTER 4

FPGA

4.1 General Notions

A field-programmable gate array is an integrated circuit designed to be field-programmable by a designer. The FPGA configuration is generally specified using a hardware description language. FPGA has large resources of logic gates and RAM blocks to implement complex digital computations. FPGA contains programmable logic components called logic blocks and a hierarchy of reconfigurable interconnections that allow the blocks to be wired together. Logic blocks can be configured to perform complex combinational, or simple logic functions like AND and XOR.

Some FPGAs have analog features in addition to digital functions. A few FPGA have integrated peripheral analog-to-digital converter and digital-to-analog converter.Application of FPGA includes digital signal processing, software-defined radio, medical imaging, computer vision, speech recognition, cryptography, bioinformatics, computer hardware emulation, radio astronomy, metal detection and other areas.

4.2 DE2-115 Development and Education Board

The Altera DE2-115 Development and Education board was designed by professors. It is an ideal vehicle for learning about digital logic, computer organization, and FPGA. Featuring an Altera Cyclone IV 4CE115 FPGA, the DE2-115 board is designed for university laboratory use. It is suitable for a wide range of exercises in courses on digital logic and computer organization, from simple tasks that illustrate fundamental concepts to advanced designs (Altera, 2014).

Figure 4.1 Altera Cyclone IV 4CE115 FPGA, the DE2-115

4.3 Verilog Hardware Description Language

Verilog is a hardware description language used to model electronic systems. It is most commonly used in the design and verification of digital, analog and mixed-signal circuits.

Hardware description languages are different from software programming languages because they include ways of describing signal propagation time and sensitivity.Verilog's concept of wire consists of both signal values and strengths. This system allows abstract modeling of shared signal lines, where multiple sources drive a common net. When a wire has multiple drivers, the wire's value is resolved by a function of the source drivers and their strengths.A subset of statements in the Verilog language is synthesizable. Verilog modules that conform to a synthesizable coding style can be physically realized by synthesis software. Synthesis software algorithmically transforms the abstract Verilog source into a net list, a logically equivalent description consisting only of elementary logic primitives (AND, OR, NOT, flip-flops, etc.) that are available in a specific FPGA or technology. Further manipulations to the net list ultimately lead to a circuit fabrication blueprint (such as a bit stream file for an FPGA).

CHAPTER 5

EXPERIMENTAL RESULTS (GA FOR CASCADE PID)

5.1 The Model

Next demonstration shows a PID controller optimized by MATLAB GA function ga when the control system is a Simulink model. To call Simulink model from MATLAB, the model must be built, and then a MATLAB programming function is used to call the Simulink model.

A Simulink model of a cascade PID control system is built, as shown in Figure 5.1. Cascade PID control system will be optimized by GA. It has been simulated by a Transfer function blocks. A Step block has been used to create a control reference. An Out1 block has been used to export calculation results of the Simulink model. The model has been saved with the filename PID_controller.mdl.

Parameters of cascade PID controller consist of three variables, P1, I1, D1=0 for inner PID and P2, I2; D2=0 for outer PID. Parameters D1 and D2 are set to 0 to avoid noise disturbances.

Figure 5.1 Cascade PID Simulink Model (modified) (Tze_Fun Chan, 2011)

5.2. Methodology

In order to call the Simulink model from MATLAB platform, a MATLAB function Call_PID.m has been programmed (Appendix 1.). In MATLAB/Simulink, there are two workspaces, one is named caller which stores variable values of MATLAB function and other workspace is named as base which stores variable values of Simulink model input and output. Because the ga function is a MATLAB function, an assignin function is employed to transfer data between two workspaces. In this way, the variable values may be exchanged between function Call_PID.m and model PID_controller.mdl.

Overshoot variable is changeable, in range from 1 to 1.5 of an output signal amplitude with 0.05 difference.

For loop calculates mean square error of the plant output and command reference R, then error function has been evaluated.

The GA simulation has been performed in PID.m file (Appendix 2.). After GA options and PID parameters boundaries have been set, value of fitness function has been calculated and the plot has been drawn, as shown in Figure 5.2.

Figure 5.2 Genetic Algorithm Simulation Plot

5.3. Results for Various Overshoot Values

GA has been simulated for different overshoot values of PID controller output. It is performed for each value (1.0 to 1.5 of a PID output signal amplitude, with 0.05 difference) ten times and the best fitting five fitness function values and corresponding PID parameters have been used, as shown in Table 5.1. For every overshoot value, one group of data has been chosen for statistical processing. For these purposes, MATLAB function cftool has been used.

Table 5.1 Cascade PID GA simulation results

5.4. Curve Fitting Tool and Conclusions

After GA simulation has been performed, curve fitting function has been used to find the pattern of cascade PID coefficients dependence on different overshoot values and its mathematical formulation. MATLAB cftool function executes this task. Graphical and mathematical form will help in better projection of system cascade PID control process.

Figure 5.3 P1 curve fitting

Coefficients:

a1 =0.6402 b1 =1.204 c1 =0.3399 a2 =0.128 b2 =1.474 c2 =0.08749

Figure 5.4 I1 curve fitting

Coefficients:

a1 =3.494 b1 =1.204 c1 =0.5045 a2 =0.5261 b2 =1.497 c2 =0.1026

Figure 5.5 P2 curve fitting

Coefficients:

a1 =3.514 b1 =2.531 c1 =4.549 a2 =0.5879 b2 =23.36 c2 =-11.1 a3 =0.3774 b3 =36.43 c3 =3.348

Figure 5.6 I2 curve fitting

Coefficients:

a1 =0.1462 b1 =3.622 c1 =3.015 a2 =0.01066 b2 =15.48 c2 =-3.88 a3 =0.02843 b3 =36.9 c3 =1.825

Cascade PID controller coefficients P1 and I1 can be represented with Gaussian normal distribution function. On the other hand, cascade PID controller coefficient P2 and I2 can be represented with sinusoidal function. Their variation caused by overshoot variation can be predicted and system can be controlled. GA results can successfully be used for cascade PID controller tuning.

CHAPTER 6

PRACTICAL IMPLEMENTATION (FPGA & PID)

6.1. The Model

Digital computers are necessary part of a control system. It is essential to convert real-world analog signals and its numerical representation to digital ones, so they could be properly processed.

FPGA integrated circuit uses 16-bit digital representation of an analog signal received after process of cascade PID tuning GA was performed. Digital display shows 4-digit number, with each digit representing 4-bits. The number symbolizes amplitude of an analog signal received from system response after PID controlling process.

After starting value, representing overshoot amplitude of the signal, each switching will change that value and it will represent oscillation process and decreasing will represent settling process(Appendix 3).

Figure 6.1 FPGA board performing PID control

6.2. The Final System

Final system for cascade PID controlling process is ready. Results of GA simulation used for cascade PID controller tuning will lead to required response of a system being controlled. On the other hand, FPGA will perform digital conversion and computer systems will be applicable in controlling process. The final system is ready for practical implementation of an induction motor cascade PID control.

CONCLUSION

Intelligent control advance in last few decades has improved industrial process and products in various branches. Many techniques have been used. As shown in this research, GA can be used in process of cascade PID controller tuning with satisfactory results in accordance with system requirements After GA simulation has been performed, cascade PID controller coefficients have been calculate and the controller have been tuned. Statistical processing of results has showed that pattern exists and controlling process can be predicted for different input values and requirements. Since system is feasible, it can be practically implemented using FPGA controlled by a computer system. Cascade PID controller can be used in process of induction motor drive control.

The research has shown that GA is advanced intelligent control technique that improves process of design and development of cascade PID controller and its tuning. As a consequence, process being controlled will be more accurate and reliable.

REFERENCES

Altera. (2014). http://www.altera.com/.Araki. (2005). Control System, Robotics and Automation - vol II - PID Control. Kyoto: Kyoto University.Bck, T. (1993). Optimal Mutation Rates in Genetic Search, Proceeding of the Fifth International Conference on Genetic Algorithms. CL, USA.Control Solutions, I. M. (n.d.). http://www.csimn.com/.Mathworks, I. (2014). http://www.mathworks.com/.Michalewicz. ( 1996). Genetic algorithms and data structures. Springer, USA.Mitchell, M. (1996). An Introduction to Genetic Algorithms. Cambridge, MA: MIT Press.Muhammet nal, A. A. (2013). Optimization of PID Controllers Using Ant Colony and Genetic Algorithms. Springer-Verlag Berlin Heidelberg.Syswerda, G. (1989). Uniform Crossover in Genetic Algorithms. In: Proceeding of theThird International Conference on Genetic Algorithms . NJ, USA.Tze_Fun Chan, K. S. (2011). Applied Intelligent Control of Induction Motor Drives. John Wiley & Sons (Asia) Pte Ltd.Whitley, D. (1994). A genetic algorithm tutorial, Statistics and Computing 4 (2).

APPENDIX 1

Call_PID.m MATLAB CODE

function s= Call_PID(x)assignin('base','P1',x(1));assignin('base','P2',x(2));assignin('base','I1',x(3));assignin('base','I2',x(4));[tout,xout,yout]=sim('PID_controller',200);z=yout;overshoot=0.1;%Overshoot is expressed as a percentage of amplitudes=0;[m,n]=size(z);%Evaluating the error functionif max(z)>1+overshoot s=1/eps;elseV=0;R=1;for i=1:m V=V+(R-z(i))^2;ends=V/m;endend

APPENDIX 2

PID.m MATLAB CODE

clc;%clear;options=gaoptimset(@ga);%Setting Genetic Algorithm optionsoptions=gaoptimset(options,'PlotFcns',{@gaplotbestf},'Display','iter');options=gaoptimset(options,'PopulationSize',40);options=gaoptimset(options,'EliteCount',10);options=gaoptimset(options,'CrossoverFraction',0.6);options=gaoptimset(options,'Generations',140);options=gaoptimset(options,'MutationFcn',@mutationadaptfeasible);%Setting bounds for P and I componentslb=[0 0 0 0];ub=[60 10 60 10];%calling the function[x,fval]=ga(@Call_PID,4,[],[],[],[],lb,ub,[],options);

APPENDIX 3

QUARTUS CODE FOR FPGA

module Edvin(SW, HEX0, HEX1, HEX2, HEX3);input [2:0] SW;output [6:0] HEX0, HEX1, HEX2, HEX3;wire [15:0] x, e1, e2, y1, y2, r1, r2;SI pravimoUlaz(SW[0], x);//Write PIPI vanjskiRegulator(r2, e2, SW[1],SW[2]);defparam vanjskiRegulator.k1=6;defparam vanjskiRegulator.k2=5;PI unutrasnjiRegulator(r1, e1, SW[1],SW[2]);defparam unutrasnjiRegulator.k1=6;defparam unutrasnjiRegulator.k2=5;PI prvaPolovina(y1, r1, SW[1],SW[2]);defparam prvaPolovina.k1=1;defparam prvaPolovina.k2=0;PI drugaPolovina(y2, y1, SW[1],SW[2]);defparam drugaPolovina.k1=1;defparam drugaPolovina.k2=0;assign e2=x-y2;assign e1=r2-y1;Disp7 Ispis(e2, HEX0, HEX1, HEX2, HEX3);endmodule

module SI(prekidac, kabl);input prekidac;output [15:0] kabl;assign kabl=150*prekidac;endmodule

module PI(output reg [15:0] u_out,input signed [15:0] e_in, input clk, input reset);parameter k1;parameter k2;reg signed [15:0] u_prev;reg signed [15:0] e_prev[1:2];//assign u_out = u_prev + k1*e_in-k2*e_prev[1];always @ (posedge clk)if (reset == 1) beginu_prev