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| Fuzzy logic is a form of logic whose underlying modes of reasoning are approximate instead of exact. Unlike crisp logic, it emulates the ability to reason and use approximate data to find solutions. Despite having a name that has the connotation of uncertainty, researches have shown that type-1 fuzzy logic systems have difficulties in modeling and minimising the effect of uncertainties. One reason limiting the ability of a type-1 fuzzy set to handle uncertainty is that the membership grade for a particular input is a crisp value. Recently, a new type of fuzzy set characterised by membership grades that are themselves fuzzy have been attracting interest. As illustrated in Figure 1, a type-2 fuzzy set may be obtained by starting with a type-1 membership function (MF) and then blurring it. The blurred area, referred to as the Footprint of Uncertainty (FOU), is bounded by upper and lower membership functions. Points within the "blurred area'' have membership grades given by type-1 membership functions. The FOU provides an extra mathematical dimension, thereby enabling the uncertainties in the shape and position of the type-1 fuzzy set to be represented.
This work focuses on examining whether a type-2 fuzzy logic system is better able to handle uncertainties in a controlled system than its type-1 counterpart. The study was conducted by utilising a type-2 fuzzy logic controller, evolved by a genetic algorithm (GA), to control a liquid-level process. The type-2 fuzzy logic controller is designed using a partially dependent approach. A best possible type-1 fuzzy logic system is first evolved, and is then used to initialise the parameters of the type-2 fuzzy logic system. Such an approach has the following advantages: (i) smart initialisation of the parameters of the type-2 fuzzy logic controller, and ii) a baseline design whose performance can be compared with that of the type-2 fuzzy logic controller, and iii) the GA can converge at a faster speed because the number of parameters that need to be tuned is usually fewer.
Figure 2 shows the coupled-tank apparatus used in the experimental study. A simulation model of the liquid level process was first implemented and used to evolve the type-1 and type-2 fuzzy logic controllers (FLC). As the non-linear characteristic of the pumps and the transport delay are not captured by the simulation model, the experimental results are an indication of the controller’s ability to handle modelling uncertainties. For the nominal system, the performances of both fuzzy logic controllers are similar. The flow rate between the two tanks was then reduced by lowering the baffle. This change gave rise to a system with slower dynamics than the simulation model. The experimental results are shown in Figure 3. Clearly, the type-2 FLC outperforms its type-1 counterpart. The main advantage of the type-2 FLC appears to be its ability to eliminate persistent oscillations. As the type-2 FLC can tolerate bigger modelling errors, it is more robust than type-1 fuzzy logic controllers. Furthermore, robustness is obtained with little performance trade-offs as the performances of both fuzzy logic controllers are similar for the nominal plant.
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Contact Person: Dr WW Tan |
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