Comparison between the Conventional Controller and the Advanced Fuzzy

Stabilisation

Conventional Controller

It was demonstrated previously in Chapter 4 that there were two resonant modes which threaten the stability of the closed loop magnetic bearing system. The conventional lead compensator cannot handle the two dominant resonant modes of the magnetic bearing system. This necessitates the design of two notch filters to filter out the unwanted characteristics at the resonant frequencies. From the analytical and experimental models of the MBC500 magnetic bearing system, it was found that the two resonant modes are located at approximately 749 Hz and 2069 Hz. After two notch filters were designed to handle the two resonant modes, a lead compensator was designed to stabilise the magnetic bearing system. The lead compensator added a positive phase to the system in a given frequency range. The compensator design was based on the analytical rigid body model where the shaft was a point mass with no angle variable ө.

The performances of the conventional lead compensator and the two notch filters designed have been evaluated via simulation using both the analytical model and the model obtained via system identification. The designed lead compensator and notch filters were also implemented in real time for the MBC 500 magnetic bearing system. The controller designed worked for all four channels of the MBC 500 magnetic bearing system. Tests were performed to test the dynamic response and robustness of the conventional controller and the notch filter designed and each test was successful.

Advanced Fuzzy Logic Controller (FLC)

A PD-like FLC was designed for stabilising the magnetic bearing system. Two different numbers of rule sets (25-rule and 49-rule) were formulated for the PD-like FLC. Two different fuzzy inference methods, the Mamdani and Sugeno methods, have been used. The performance of the designed FLC has been evaluated via simulation. Comparison studies of the FLC performances with two different sets of rules, two different inference methods, different membership functions, different t-norm and s-norm operations, and different defuzzification methods have been investigated. Simulation results show that the FLC designed leads to a good system performance. To further improve system performance, scaling factors have been tuned. Simulation has also been carried out based on the analytical model derived that represented both the rigid body and bending modes. Again, simulations have shown highly promising results.

The simulation performance showed that the FLC designed can handle the resonant modes very well without the presence of the two notch filters.

Based on all the simulation results reported above, it was concluded that the designed 49-rule FLC uses triangular membership functions for the inputs and output, MIN for t-

norm operation, MAX for s-norm operation, MAX for aggregation, MIN for

implication, and CENTROID for defuzzification provides the best result.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Time in seconds M a gn et ic b e a ri n g d is p la c e m e nt o u tp ut

Conventional controller with two notch filters FLC without notch filters

Figure 5.18 Comparison results of the step response of the magnetic bearing system with the designed conventional controller and the designed FLC

Figure 5.18 shows the step response of the magnetic bearing system with the designed conventional controller and the designed FLC based on the identified model of the MBC 500 magnetic bearing system. Comparing the simulation results of the conventional controller and the advanced PD-like FLC, it can be seen that the response with the designed conventional controller has less settling time. The step response with the designed advanced PD-like FLC has longer setting time but less steady-state error. Moreover, the advanced PD-FLC can handle the two resonant modes without the need of using the two notch filters.

5.6

Summary

This chapter started with the structure of a basic FLC. Two different fuzzy inference methods, the Mamdani and Sugeno methods, have been reviewed. The process of developing and designing the FLC for the stabilisation of the magnetic bearing system has been described. The performance of the designed FLC has been evaluated via simulation. The simulation result shows that the FLC designed leads to a good system performance. Comparison studies of the FLC performances with two different sets of rules, two different inference methods, different membership functions, different t-norm and s-norm operations, and different defuzzification methods have been investigated. To further improve system performance, scaling factors have been tuned. Again, simulations have shown highly promising results.

Finally, this chapter has compared the controller simulation for both the conventional controller and advanced PD-like fuzzy logic controller via evaluating controller performance. The advantage of using the conventional controller lies in its simplicity for real-time implementation. The disadvantage of using the conventional controller is that it cannot handle the resonant modes and as a result additional notch filters are needed in this method. If the notch filters are not designed properly, they can lead to the instability of the system. In addition, four separate conventional controllers were designed, based on the four models of the four channels of the magnetic bearing system. The first advantage of the PD-like FLC is that it can handle the resonant modes well without using notch filters. As a result, this will not threaten the stability of the system. The second advantage of the PD-like FLC is that as the FLC is nonlinear, the PD-like FLC designed for one channel should work for all other three channels. However, the PD-like FLCs are more computationally intensive than the conventional controller. Due

to the speed limit of the DS1102 DSP card, the PD-like FLC cannot be implemented at this stage. The overall conclusion and direction for future development will be discussed in the next chapter.