CHAPTER 4 FUZZY LOGIC CONTROLLER

Transcription

1 62 CHAPTER 4 FUZZY LOGIC CONTROLLER 4.1 INTRODUCTION Unlike digital logic, the Fuzzy Logic is a multivalued logic. It deals with approximate perceptive rather than precise. The effective and efficient control using fuzzy logic has emerged as a tool to deal with uncertain, imprecise or qualitative decision making problems. Fuzzy Logic derived from fuzzy set theory. Fuzzy logic was first proposed by Lotfi Zadeh in Recently the Fuzzy Logic is utilized in many applications, such as adjustable speed drive, aircraft engines, helicopter control, missile guidance, automatic transmission, wheel slip control, auto focus cameras, washing machines, railway engines for smoother drive and fuel consumption and many industrial processes. Many literatures say that the Fuzzy Logic Control provides better results than the conventional PID controllers. The Fuzzy set theory represents the human reasoning with knowledge that is almost impossible to represent in quantitative measures or for that control plants that are hard to control or ill defined. Fuzzy inference system models the system using if-then rules. Fuzzy set theory proposed the membership function at range of numbers (0, 1) or False or True membership function. This theory provides the mathematical strength to check the uncertainty connected with human thinking or reasoning. Fuzzy logic is suitable for model that is hard to control or non-linear models. This system also provides over MIMO systems and also allows decision making with

2 63 incomplete information. Human reasoning can also be known as multi valued 4.2 DESIGN OF FUZZY LOGIC CONTROLLER In Fuzzy Logic controller design, the first step is to understand and characterize the system behavior by using knowledge and experience. The second step is to directly design the control algorithm using fuzzy rules, which describe the principles of the controller's regulation in terms of the relationship between its inputs and outputs. The last step is to simulate and debug the design. The fuzzy logic controller (FLC) can be designed without the exact model of the system. For FLC, it is sufficient to understand the general behavior of the system. Such a FLC is designed and implemented for DC-DC converter fed DC motor. The FLC involves three stages namely Fuzzification, Rule-Base and Defuzzification. The Sugeno type controller is performed for present control because it has singleton membership in the output variable. Moreover it can be easily implemented and number of calculations can be reduced. The general structure of Fuzzy Logic controller is given in Figure 4.1. Rule Base Preprocessing Fuzzification Inference Engine Defuzzification Post processing Figure 4.1 Structure of Fuzzy Logic Controller

3 Fuzzification In Fuzzy logic system the linguistic variables are used instead of numerical variables. The process of converting a numerical variable (real number or crisp variables) in to a linguistic variable (fuzzy number or fuzzy variable) is called fuzzification. In this work, the motor variables are speed and current (ia). The speed is controlled by FLC. The error e(k) and change in error e(k) is given as input to the FLC. The error is found by comparing the actual speed (k) with reference speed r(k). From the error e(k) and pervious error eprevious(k) the change in error is calculated and then it is normalized, in order to use the same FLC for different reference speed. This process stage is called as preprocessing which is shown in Figure 4.1. Then the error and change in error are fuzzified. Seven linguistic variables are used for the input variable e(k) and e(k). That are negative big (NB), negative medium (NM), negative small (NS), zero (Z), positive small (PS), positive medium (PM) and positive big (PB). There are many types of membership functions, such as triangularshaped, Gaussian, sigmoidal, pi-shaped trapezoidal-shaped, bell-shaped etc. the triangular membership function is used for simplicity and also to reduce the calculations. (4.1) (4.2) Defuzzification The reverse process of fuzzification is called defuzzification. The linguistic variables are converted in to a numerical variable. As the weighted sum method is considered to be the best well-known defuzzification method,

4 65 it is utilized in the present model. The defuzzified output is the duty cycle dc(k). The change in duty cycle dc (k) can be obtained by adding the pervious duty cycle pdc(k) with the duty cycle dc(k) which is given in equation 8. This process stage is called as post processing which is also shown in Figure 4.1. (4.3) Figure 4.2. The input and output fuzzy membership functions are shown in Figure 4.2 Fuzzy memberships used for simulation

5 Rule Table and Inference Engine The control rules that relate the fuzzy output to the fuzzy inputs are derived from general knowledge of the system behavior, also the perception l e (k) is Y, then e(k) and dc(k) respectively. The rule table for the designed fuzzy controller is given in the Tab Table 4.1 Fuzzy rule table for seven membership functions Change in Error Error NB NM NS Z PS PM PB NB NB NB NB NB NM NS Z NM NB NB NB NM NS Z PS NS NB NB NM NS Z PS PM Z NB NM NS Z PS PM PB PS NM NS Z PS PM PB PB PM NS Z PS PM PB PB PB PB Z PS PM PB PB PB PB

6 SIMULATION OF FLC IN MATLAB The detailed design procedure for the development of Fuzzy Logic Controller using MATLAB is given here. As mentioned in the previous section there are three variables chosen, two for input variables Error and Change in Error the third one is for output variable duty cycle. The general procedures to develop the FLC are Step I : Identify the inputs and their ranges and name them Step II : Identify the outputs and their ranges and name them Step III: Create the degree of fuzzy membership function for each input and output Step IV: Construct the rule base that the system will operate under Step V : Decide how the action will be executed by assigning strengths to the rules Step VI: Combine the rules and defuzzify the output Table 4.2 shows the membership function names and ranges of input variable Error. Here Seven triangular membership function were used and ranges between -1 to +1. The triangular membership function is simple and easy to implement. Figurs 4.2 represents the input membership function for Error. The range of membership function shows that the maximum possible normalised speed error is +1 and minimum is -1. This range is possible for controlling the speed of the motor. From many litrerature the seven membership function is the suitable choice of selection and the shape of the membership function is selected.

7 68 Linguistic variable for Error Linguistic Value Notation Numerical Value Negative Big NB [ ] Negative Medium NM [ ] Negative Small NS [ ] Zero Z [ ] Positive Small PS [ ] Positive Medium PM [ ] Positive Big PB [ ] Figure 4.3 Input membership function for Error

8 69 Linguistic variable for Change in Error Linguistic Value Notation Numerical Value Negative Big NB [ ] Negative Medium NM [ ] Negative Small NS [ ] Zero Z [ ] Positive Small PS [ ] Positive Medium PM [ ] Positive Big PB [ ] Figure 4.4 Input membership function for Change in Error

9 70 Similarly the membership function is chosen for the change in error. The membership function range for change in error is maximum +2 and minimum is -2. Change in error is the difference between present error and previous error. Table 4.3 shows the membership function names and ranges of input variable Cahnge in Error. Figure 4.4 represents the input membership function for Change in Error. Likewise the membership function is chosen for the output variable Table 4.4 shows the membership function names and ranges of output variable Duty Cycle. Figure 4.5 represents the output membership function for Duty Cycle. Figure 4.6 and 4.7 shows the rule viewer and surface viewer of the designed Fuzzy Logic Controller respectively. Linguistic variable for Duty Cycle Linguistic Value Notation Numerical Value Negative Big NB Negative Medium NM Negative Small NS Zero Z 0.00 Positive Small PS 0.33 Positive Medium PM 0.66 Positive Big PB 1.00

10 71 Figure 4.5. Output membership function for Duty Cycle Figure 4.6 Rule viewer of FLC

11 72 Figure 4.7 Surface viewer of FLC 4.4 SIMULINK MODEL OF THE SYSTEM WITH FUZZY LOGIC CONTROLLER The complete simulation model of the DC series motor drive system with Fuzzy Logic Controller is given in Figure 4.8. The fuzzy controller block from fuzzy logic toolbox is used to test and evaluate the FLC. As mentioned in the PID controller here also the actual speed and the set speed is given to the FLC preprocessing to generate the error and change in error signals. The error and change in error are given as the input to the FLC, the controller produce the duty cycle, during post processing the change in duty cycle is obtained and it is given to the PWM generator unit. The PWM generator unit generates the PWM with the switching frequency of 1KHz by comparing the repeating sequence signal with the FLC output. Then the PWM is given to the current controller, the current controller allows the PWM if the actual motor current is within the limits of the set current value. Further the PWM is given to the DC chopper unit to give the variable DC voltage to the DC series motor. There by the motor speed is controlled.

12 73 Figure 4.8 Simulink Model of DC series motor with FLC The Structure of the fuzzy controller including preprocessing and postprocessing using MATLAB/Simulink is shown in Figure 4.9. In preprocessing stage error is calculated by subtracting the actual speed from the reference speed ref. The error is normalized by dividing with reference speed. The range of normalized speed is from 0 to 1. Then the change in error is calculated from the present error with the previous error using the memory block. The error and change in error is given as input to the FLC through a mux block. The output of the FLC is duty cycle. In postprocessing stage the change in duty cycle is obtained by adding the present duty cycle with previous duty cycle. Figure 4.9 Simulink model of FLC

13 RESULTS AND DISCUSSION FOR THE FLC WITH SEVEN MEMBERSHIP FUNCTION The DC series motor model through the DC-DC converter including FLC was simulated using MATLAB simulation. The fuzzy controller was designed and DC-DC converter fed DC series motor was tested. The simulated waves of gate pulse, output voltage, motor current and speed with respect to time for r=1800 rpm are shown in Figure The expanded view is shown in Figure Figure 4.10 Pulse, Output Voltage, Motor Current and Speed Variation with respect to Time Response for r=1800 rpm

14 75 Figure 4.11 Expanded view of Pulse, Output Voltage, Motor Current and Speed Variation with respect to Time at r=1800 rpm From the Figure 4.11 it is clearly seen that the time duration between each pulse is sec means that the switching frequency is 1 KHz. When the pulse is ON the motor current is increasing and decreasing when the pulse is OFF due to the chopping action of the DC-DC converter. The FLC regulate the speed at 1800 rpm. The performance comparison of developed FLC for DC-DC converter fed 220V DC series motor with PID controller and reported result in Yousef et al (1995) is given in Table 4.5. From the table 4.5 it is seen that all the performance parameter has been reduced considerable amount, which shows that the FLC is superior out of other controllers shown.

15 76 Table 4.5 Performance comparison of developed FLC for 220V DC series motor with rated speed Controller Rise Time (sec) Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm) Classical PI Yousef et al (1995) Fuzzy Yousef et al (1995) Developed PID During rated speed and 10% load Not mentioned Not mentioned Developed FLC Not mentioned Not mentioned Load Change from 25% to 50% +10 ± Not mentioned Not mentioned +20 ±9

16 77 Figure 4.12 Speed variation for the step change in reference speed at different interval with 10% load torque The Figure 4.12 shows the speed variation and current variation for the step change in reference speed from 500rpm to 1000rpm at 4 sec and 1000rpm to 1800rpm at 7 sec with 10% load torque. The current is always chopping between maximum to minimum. It is seen from figure that when the speed is increased from 500rpm to 1000rpm the motor takes 0.32 sec whereas in the initial stage it took almost 0.35 sec to reach 500rpm. This may be due to the inertia in the beginning. The FLC provides proper speed regulation for all the speed changes. The comparative time domain parameters of Speed variation for various set speed changes are depicted in Table 4.6.

17 78 Table 4.6 Time domain parameter of FLC for different set speed change with 10% load Set Speed Changes 0 to 500rpm 500 to 1000rpm 1000 to 1800rpm Max. Over Shoot (%) Settling Time (sec) The simulated result of speed regulation for a step change in the load torque from 10% to 25%, 25% to 50% and 50% to 100% applied at t=2.5 sec is shown in Figure 4.13, 4.14 and 4.15 respectively. The FLC gives proper response to the system for the load changes from 10% to 100%. At 100% load there is a small dip in the speed response and it is recover the speed with in 1.1 sec. The expanded part of different load changes is given in Figure 4.16 for comparison. The comparative time domain parameters of Speed variation for various load changes are depicted in Table 4.7. Figure 4.13 Speed variation for the step change in load torque from 10% to 25% applied at t=2.5 secs with the speed of 1800 rpm.

18 79 Figure 4.14 Speed variation for the step change in load torque 25% to 50% applied at t=2.5secs with the speed of 1800 rpm. Figure 4.15 Speed variation for the step change in load torque 50% to 100%applied at t=2.5 sec with the speed of 1800 rpm.

19 80 Figure 4.16 Comparison of Speed variation for the step change in load torque applied at t=2.5 sec with rated speed Figure 4.16 provides the comparative analysis for the FLC with various load torque changes. When the load changes from 50% to 100%, the speed variations completely abolished and the speed drop is more than the lesser load conditions. Table 4.7 Time domain parameter of FLC for the load changes for 220V DC Series Motor with rated speed Load Variations 10% to 25% 25% to 50% 50% to 100% Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm) ±10 ±9 +3.3

20 81 The Overall time domain parameters of developed PID controller and FLC for 220V DC series motor for rated speed with 10% load, set speed changes and the load torque changes are illustrated in the Table 4.8. From the Table 4.8 it is seen that comparatively the FLC is good in all the aspects. Table 4.8 Overall time domain parameter of developed FLC for 220V DC series motor Controller Developed PID During rated speed and 10% load Developed FLC Rise Time (sec) Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) +10 ±2 Set Speed Change from 500 to 1000rpm Max. Over Shoot (%) Settling Time (sec) Load Change from 25% to 50% Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm) +20 ±9 4.6 DESIGN OF MODIFIED FUZZY LOGIC CONTROLLER Initially the FLC is designed with seven triangular membership function of equal width and then it was reduced to five of variable width membership function. The width of the membership function is varied in order to reduce the number of membership function from seven to five. In this five membership function, the width of the center membership function is considered to be narrow and it has been wide towards outer.

21 82 Five linguistic variables are used for the input variable e(k) and e(k). That are negative big (NB), negative small (NS), zero (Z), positive small (PS) and positive big (PB). There are many types of membership functions, such as triangular-shaped, Gaussian, sigmoidal, pi-shaped trapezoidal-shaped, bell-shaped etc. the triangular membership function is used for simplicity and also to reduce the calculations. Figure Modified Fuzzy memberships used for simulation In most of the work seven membership functions were preferred for accurate result. In this work only five membership functions were used for the input, error and change in error. To reduce the number of membership

22 83 function the width of the membership functions were kept different. The membership function width for the center membership functions is considered narrow and wide towards outer. The input and output fuzzy membership functions are shown in Figure The rule table for the designed fuzzy controller is given in the Table 4.9. The element in the first row and first column means that If error is NB, and change in error is NB then output is NB. Table 4.9 Fuzzy rule table for five membership functions Change in Error Error NB NS Z PS PB NB NB NB NB NS Z NS NB NB NS Z PS Z NB NS Z PS PB PS NS Z PS PB PB PB Z PS PB PB PB 4.7 RESULTS AND DISCUSSIONS FOR MODIFIED FLC WITH 110V DC SERIES MOTOR The FLC performance was also analyzed in different aspects as in the PID controller analysis in the previous section. In this section the motor parameter for 110V DC series motor is considered for analysis. The same MATLAB/Simulink model shown in Figure 4.8 was utilized to test the performance by replacing the 220V motor model parameter with 110V motor parameter given in Table 3.8. The simulated waves of gate pulse, output voltage, motor current and speed with respect to time for r=1500rpm are shown in Figure The expanded view is shown in Figure 4.19.

23 84 Figure 4.18 Pulse, Output Voltage, Motor Current and Speed Variation with respect to Time Response for r=1500 rpm Figure 4.19 Expanded view of Pulse, Output Voltage, Motor Current and Speed Variation with respect to Time Response for r=1500rpm

24 85 The switching frequency of PWM is 1 KHz. The FLC regulate the speed at 1500rpm. The performance comparison of developed FLC for DC-DC converter fed 110V DC series motor with PID controller is given in Table From the Table 4.10 it is seen that all the value of performance parameters are less for FLC than the PID controller, which shows that the superiority of FLC. Table 4.10 Performance comparison of developed Fuzzy Logic Controller for 110V DC Series Motor with PID controller Controller Developed PID Developed FLC Rise Time (sec) Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) Figure 4.20 Speed variation for the step change in reference speed at different interval with 10% load torque

25 86 The Figure 4.20 shows the speed variation for the step change in reference speed from 500rpm to 1000rpm at 3 sec and 1000rpm to 1500 rpm at 7 sec with 10% load torque. It is seen from the Figure 4.20 due to the inertia in the beginning the motor takes 0.36 sec to reach the speed from 0 to 500rpm whereas in the second step it took 0.34 sec only to reach from 500 to 1000rpm. The FLC provides proper speed regulation for all the step speed changes. The comparative time domain parameters of speed variation for various set speed changes are depicted in Table Table 4.11 Time domain parameter of FLC for different set speed change with 10% load Set Speed Changes 0 to 500rpm 500 to 1000rpm 1000 to 1800rpm Max. Over Shoot (%) Settling Time (sec) The simulated result of speed regulation for a step change in the load torque from 10% to 25%, 25% to 50% and 50% to 100% applied at 3 sec, 5.5 sec and 8 sec are shown in Figure The FLC provides proper regulation to the system for the load changes from 10% to 100%. At 100% load the oscillations in speed is eliminated due to high load torque. The comparative time domain parameters of Speed variation for various load changes are represented in Table 4.12.

26 87 Figure 4.21 Performance of DC series motor with FLC for load variation at 3sec, 5.5sec and 8sec with rated speed Table 4.12 Time domain parameter of FLC for the load changes for 110V DC Series Motor with rated speed Load Variations 10% to 25% 25% to 50% 50% to 100% Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm) The Overall time domain parameters of developed PID controller and FLC for 110V DC series motor for rated speed with 10% load, set speed changes and the load torque changes are illustrated in the Table From

27 88 the Table 4.13 it is seen that comparatively the FLC is superior in all the aspects. Table 4.13 Overall time domain parameter of developed FLC for 110V DC series motor Controller Developed PID During rated speed and 10% load Developed FLC Rise Time (sec) Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) Set Speed Change from 500 to 1000rpm Max. Over Shoot (%) Settling Time (sec) Load Change from 25% to 50% Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm) RESULTS AND DISCUSSIONS FOR MODIFIED FLC WITH DC SEPARATELY EXCITED MOTOR In this section the DC separately excited motor is considered for analysis. Then the same MATLAB/Simulink model shown in Figure 4.8 was utilized to test the performance by replacing the 220V DC series motor model with DC separately excited motor shown in Figure 2.8. The simulated

28 89 waves of speed response with respect to time for Figure r=1800rpm is shown in Figure 4.22 Speed response with respect to time of DC Separately Excited Motor with Fuzzy controller for rated speed and 10% load torque The switching frequency of PWM selected for this case is also the same 1 KHz. The FLC regulate the speed at rated value of 1800rpm. The performance comparison of developed FLC for DC-DC converter fed DC separately excited motor with PID controller for rated condition is given in Table 4.14.

29 90 Table 4.14 Performance comparison of developed FLC for DC Separately Excited Motor Controller Developed PID During rated speed and 10% load Developed FLC Rise Time (sec) Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) +23 ±12 Figure 4.23 Speed variation for the step change in reference speed at different interval with 10% load torque

30 91 The Figure 4.23 shows the speed variation for the step change in reference speed from 500rpm to 1000rpm at 4 sec and 1000rpm to 1500rpm at 7 sec with 10% load torque for 220V DC series motor and DC separately excited motor. The modified FLC provides proper speed regulation for all the step speed changes for both the motor. The comparative time domain parameters of speed variation for various set speed changes are depicted in Table Table 4.15 Time domain parameter of FLC for different set speed change with 10% load Set Speed Changes 0 to 500rpm 500 to 1000rpm 1000 to 1800rpm Max. Over Shoot (%) Settling Time (sec) Figure 4.24 Speed variation for the step change in load torque 10% to 25% applied at t=3 sec when the speed is 1800rpm.

31 92 The simulated result of speed regulation for a step change in the load torque from 10% to 25%, 25% to 50% and 50% to 100% applied at 3sec for 220V DC series motor and DC separately excited motor are shown in Figure 4.24, 4.25 and 4.26 respectively. The FLC provides appropriate speed regulation to both DC series and DC separately excited motor for the load changes from 10% to 100%. At 100% load the speed drop of DC series motor is 0.72% and it takes 1.1 sec to recover the original speed where as in DC separately excited motor the speed drop is 0.5%, it is almost equal to speed drop in series motor but it takes 0.18 sec only to recover the speed. While seeing this case the modified FLC is more suited for DC separately excited motor than DC series motor. The comparative time domain parameters of Speed variation for various load changes are represented in Table Figure 4.25 Speed variation for the step change in load torque ( TL=50%) applied at t=3 sec when the speed is 1800rpm.

32 93 Figure 4.26 Speed variation for the step change in load torque 50% to 100% applied at t=3 sec when the speed is 1800rpm Table 4.16 Time domain parameter of FLC for the load changes for DC separately excited motor with rated speed Load Variations 10% to 25% 25% to 50% 50% to 100% Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm)

33 94 The Overall time domain parameters of developed PID controller and FLC for DC separately excited motor for rated speed with 10% load, set speed changes and the load torque changes are illustrated in the Table From the Table 4.17 it is seen that comparatively the FLC is superior in all the aspects than the PID controller. Table 4.17 Overall time domain parameter of developed FLC for DC Separately Excited Motor Controller Developed PID During rated speed and 10% load Developed FLC Rise Time (sec) Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) +23 ±12 Set Speed Change from 500 to 1000rpm Max. Over Shoot (%) Settling Time (sec) Load Change from 25% to 50% Max. Speed Drop (%) Recovery Time (sec) Steady State Error (rpm) HARDWARE IMPLEMENTATION WITH FLC The developed modified Fuzzy Logic Controller was implemented by using a NXP 80C51 based microcontroller (P89V51RD2BN). A DC-DC buck converter was built with the MOSFET using IRFP450, and the controllers were tested with DC series motor and DC separately excited

34 95 motor. The speed of the motor was sensed by a pulse type digital speed sensor and to feed back the signal to the controller. The Figure 4.29 shows the experimental setup of the proposed system with DC series motor. The microcontroller (P89V51RD2BN) has an 80C51 compatible core with the following features: 80C51 Central Processing Unit, 5 V Operating voltage from 0 to 40 MHz, 64 kb of on-chip Flash program memory. It also has an PCA (Programmable Counter Array) with PWM and Capture/Compare functions. The PWM is generated at a frequency of 10 khz. A LEM make current sensor LTS25NP is used to sense the motor current and it is compared with the reference current using the comparator LM 399. The AND gate is used to allow the PWM waveform when the actual current is less than the reference current. The PWM from the microcontroller was then amplified for a level through the open collector optocoupler CYN 17-1 and fed to the DC DC power converter through an isolator and driver chip IR2110. The DC-DC buck converter output was given to the DC series motor whose speed is to be controlled. The speed sensor connected to the motor shaft gives the pulse output which again converted in to voltage using f/v converter and this DC voltage is fed to the ADC available in the microcontroller. The implementation of FLC in a microcontroller was done using to develop and compile the C programming for FLC. The C program is compiled and converted into hex file. Finally the hex code was embedded in to the microcontroller used. The hex code is downloaded by using the magic is given in Figure 4.27 and 4.28 respectively.

35 96 Figure 4.27 Screen shot for Keil uvision compiler software Figure 4.28 Screen shot for Flash Magic software to download the hex code

36 97 The Figure 4.29 shows the experimental setup of the system with FLC. The experimental response of the DC series motor and DC separately excited motor for the step change in reference speed are given in Figure 4.30 and 4.31 respectively. Figure 4.29 Hardware setup of the system with FLC Figure 4.30 Experimental graph of speed variation for the step change in reference speed r=1800rpm using fuzzy controller for DC Series Motor

37 98 Figure 4.31 Experimental graph of speed variation for the step change in reference speed r=1800rpm using fuzzy controller for DC Separately Excited Motor Figure 4.30 shows the speed response with the set speed of 1800rpm for Modified FLC controller for DC series motor and Figure 4.31 shows the speed response with the set speed of 1800rpm for Modified FLC controller for DC separately excited motor. From the Figurers it is noted that the DC series motor is taking the settling time of 6 sec and for separately excited motor is 3.2 sec. The modified FLC has produced more oscillations in the response, but it is due to the nature of the FLC. The Table 4.18 exposes the performance comparison of hardware of proposed system with Fuzzy controller.

38 99 Table 4.18 Hardware Performance Comparison of developed FLC with PID controller Controller Settling Time (sec) Max. Over Shoot (%) Steady State Error (rpm) Developed PID controller Series Motor Sep. Ext. Motor Developed FLC Series Motor Sep. Ext. Motor ±17 ± CONCLUSION In this chapter the performance of Fuzzy Logic controller and modified Fuzzy Logic Controller for DC series motor with 220V and 110V motor parameter and DC separately excited motor were analyzed. The performances were analyzed with different load torque and different set speed changes for both DC series and separately excited motor and found that the speed can be controlled effectively with the modified FLC for all the motors. Also in modified FLC the number of membership function is less. Hence the memory required is less during the implementation. The modified FLC reduces the peak overshoot, settling time and steady state error of the system for all the cases. All the response of the system with modified FLC is found to be satisfactory but still it is needed to be reduced the settling time and the speed variations.