RULES TABLE OF FUZZY Locic CONTROLLER 3) Defuzzification: For the Difuzzification, the centroid method 13 is applied to return a proper value for the duty cycle variation (AD). The difuzzified output value of the FLC must be added to a reference value of duty cycle which is considered equal to 0.5 for the current study. The result is the optimum value of D that has to be sent to the buck-boost converter as a control signal. To have a fair comparison between the controllers, the control model used is the same for all of them. An unit negative feedback loop system is used which is shown in Fig. 1. For simulation and analysis purpose, MATLAB/Simulink software is used to model the PID and Fuzzy Logic controllers in serial with a DC motor’s transfer function. Also, Embedded Matlab Function is used to implement PSO in finding an optimized FLC. In all the simulations, the step response is used as an indicator of the controller performance. Figure 1. Control model used for motor speed control system PSO PARAMETERS INITIALIZATION Based on the ptimization process, the scaling gains for inputs e, Ae and output are obtained as 1.5, 0.015 and 2000 respectively. The modified membership functions of inputs and outpt and also the surface diagram of inputs vs output are shown in Fig. 4. Figure 2. simple diagram for movement of a sample particle in PSO. PARAMERTERS OF THE PID CONTROLLER 7 The step response of three different controllers are graphed in Fig. 6. It shows that both FLC desiged have faster response than PID controller which was expected. However, PID con- troller works better than the normal FLC in terms of steady state error (SSE) and having lower overshoot (OS). The optimized FLC, so called FLCO, shows better profile in terms of fastness and accuracy compared to both other controllers. The exact values of the response parameters are tabulated in Table 4. There, The best value among all the three controllers are in bold for each parameters. the FLCO obviously shows betters performance for all the parameters. desiged with the same transfer function of DC motor and its parameters are set based on Table 3. Figure 4. The modified membership functions for inputs and output signals. Figure 5. Designed model in MATLAB/Simulink environment. to sudden load decrement and increment. The specifications of the hardware used are available in Appendix A. Two controllers are applied under the same circumstances to have a fair comparison, PID controller and the optimized FLC (FLCO). Wave forms of Fig. 7 are the results obtained from the experiment performed. The top waveform represents the speed response of the controllers to a sudden load increment Figure 6. Step response results for different controllers. Figure 7. Experimental results for the speed response to the load increment and decrement. while the bottom waveform is the speed response of the same controllers to a sudden load decrement. There is no overshoot or undershoot in the response of both controllers which is considered a good factor in the stability of the controllers. Both controllers also show low values of SSF in the response. In terms of fastness of the controller, the FLCO can settle the waveform in almost 2 seconds while it takes between 7 to 9 seconds for the PID contro to the desired value. Also, Fig. response to the load increment (le ler to settle the waveform 8 shows the waveforms of ft) and decrement (right) for the FLCO on the digital oscilloscope. So, the results obtained from the simulation and experiment clarify that the designed and optimized FLC is capable of responding the DC motor speed changes fast and accurate. Figure 8. The FLCO response waveforms on the digital oscilloscope, load increment (left) and load decrement (right).
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