Control Error Change
Change nb nms zr pms pb nb nb nb nb nms zr nms nb nb nms zr pms Error zr nb nms zr pms pb pms nms zr pms pb pb pb zr pms pb pb pb
Table 5.3: Five Term Fuzzy Logic Controller
Following on from the investigation into the seven term Fuzzy Logic Controllers the emphasis was on discovering if the number of membership function terms could be re- duced. Intuitively it is expected that the more rules and terms that can be utilised to describe the problem the better the system can be modelled. In the limit the system would be fully described. However the amount of work required to achieve this would be pro- hibitive, and maybe impossible. Conversely then the question becomes what is the mini- mum number of rules and membership function terms that would be able to successfully control the micro robot’s DC motors without a significant loss of control.
5.3
Selection of Type-1 and Type-2 controllers
This investigation was to compare the differences between a seven, a five and two three term controllers of type-1 and interval type-2. From the results of the previous investiga- tion the two Gaussian Fuzzy Logic Controllers had the highest RMSE values of the eight controllers. For this reason it was decided to remove the Gaussian membership function shapes completely from the investigation. In order to provide a reference controller an independent term PID controller was included in the investigation. This is described in Chapter 3. The rule base for the seven term controllers was that used in the first investi- gation given in Table 5.1.
The five term rule base was generated from the seven term rule base, by combining the NegMed and NegSmall terms give a NegMS term and combining the PosMed and
PosSmallterms to give a PosMS term. The rule base for the five term controllers is given
in Table 5.3 where nb - NegBig, nms - NegMS, zr - Zero, pms - PosMS and pb - PosBig. Finally the three term base was generated from the five term rule base, by combining
Control Error Change
Change nb cen pb
nb nb nb cen
Error cen nb cen pb
pb cen pb pb
Table 5.4: Three Term Fuzzy Logic Controller
the NegMS, Zero and PosMS terms into the Cen term. The rule base for the three term controllers is given in Table 5.4, where nb - NegBig, cen - Cen and pb - PosBig.
The type-1 seven term controller was a Trapezoidal Triangular Fuzzy Logic Con- troller, where the two outer membership function terms were trapezoids and the five inter- nal membership function terms were triangles, as shown in Figure C.2. The parameters for the type-1 seven term trapezoidal triangular controller are given Table C.4. This was decided upon due to the performance of the controller in the previous investigation being the best in the noise run. The NegBig and PosBig MFs were the trapezoids and the re- mainder triangles. This was due to the controller only infrequently operating at the top and bottom of the input and output ranges. The inputs and output linguistic variables used the same types and values for the membership functions in the controller. The mem- bership function shapes for the type-1 five term trapezoidal triangular controller were generated so that the new triangular membership functions had an apex at the average of the original triangular apexes with a base of 1.5V and the Zero term having a base of 1V about the zero. The shapes of the type-1 five term trapezoidal triangular membership functions and the surface are given in Figure C.9. The parameters used in the type-1 five term trapezoidal triangular controller are given in Table C.8.
There were two type-1 three term controllers generated. One was a Trapezoidal Tri- angular Fuzzy Logic Controller, where the single internal membership function term was a triangle. The other type-1 three term controller was a Trapezoidal Fuzzy Logic Con- troller, where all the membership function terms were trapezoids. The membership func- tion shapes for the three term type-1 triangular controller were generated from the type-1 five term controller using the seven to five generation method described previously. The membership function shapes for the three term trapezoidal type-1 controller had the Cen
5.3. Selection of Type-1 and Type-2 controllers 121 trapezoidal triangular membership functions and the surface are given in Figure C.10. The parameters used in the type-1 three term trapezoidal triangular controller are given in Table C.9. For the type-1 three term trapezoidal triangular membership functions, the shapes and the surface are given in Figure C.11. The parameters used in the type-1 three term trapezoidal controller are given in Table C.10.
5.3.1
Five and Three Term Type-2 Membership Functions
For the five and three type-2 controllers, the uncertainty interval method used to generate the seven term type-2 controllers was used. The uncertainty intervals were generated at approximately +/-14% about the type-1 membership function base end points. The choice of the FOU interval values was arbitrarily made since any value was uncertain. In the following membership function figures, the uniformly shaded regions are the FOUs for the interval type-2 fuzzy sets.
1. Five term type-2 trapezoidal triangular Fuzzy Logic Controller, where the two outer membership function terms were trapezoids and the three internal membership function terms were triangles. The shapes of the type-2 five term trapezoidal tri- angular membership functions and the surface are given in Figure C.12. The para- meters for the membership functions are given in Table C.11.
2. Three term type-2 trapezoidal triangular Fuzzy Logic Controller, where the two outer membership function terms were trapezoids and the single internal member- ship function term was a triangle. The shapes of the type-2 five term trapezoidal triangular membership functions and the surface are given in Figure C.13. The parameters for the membership functions are given in Table C.12.
3. Three term type-2 trapezoidal Fuzzy Logic Controller, where all the membership function terms were trapezoids. The shapes of the type-2 three term trapezoidal membership functions and the surface are given in Figure C.14. The parameters for the membership functions are given in Table C.13.