Fuzzy Logic in Rule Based
Systems
With applications to reactor control
Frequently there are control problems that resist precise mathematical definition for one reason or another. Also traditional control technologies often rely on the availability of robust signals from field transmitters to provide necessary measurement values. However such robust signals are not always available or provide sufficient information about the controlled process. For these reasons there is a need for a methodology other than mathematical reasoning. One such methodology is a fuzzy logic rule based system.
Typically a control system needs to keep track of a variety of measured parameters. First of all there are absolute values of parameters such as temperature, volume, density, mass, etc. Often absolute values fall short of describing everything that is happening within the controlled environment. Derivatives (rates of change) of absolute values such as speed of temperature change can provide some improvement in the perception of the controlled processes by the system. Additionally possible equipment and other errors and their impact need to be considered. Operating conditions such as maintenance or production can have impact on the significance of all measures.
A control problem can require several conditions to be considered in logical combinations. Such combinations may be difficult or impossible to express using purely mathematical language. A traditional control system is essentially a collection of functions with interconnected inputs and outputs. Number of functions to consider can be very large. Possible number of ways to interconnect them is even larger. A set of precise logical rules can be extremely large for all possible combinations of input and output parameters.
Fuzzy logic rule based control system uses a combination of language and numerical values. A typical rule in a traditional control system can be as follows:
“If temperature is more than 5F below set point then open steam valve by 10%”
This rule is very simple and precise but it covers only a very limited range of situations that might happen. It does not explain what to do if the temperature is far below the set point while human intuition tells that the valve may need to be open by more than 10%. It also does not explain what to do if the temperature is below the set point but by a smaller amount.
Typical human thinking on the other hand might be something like this:
“If temperature is below the normal value by a small amount open the steam valve a little bit”
This rule is very easy to understand but it does not contain any definite values for a machine to work with. “Normal value” can be any range of values. “Small amount” can be anything depending on the situation. “Little bit” can also mean almost anything.
Humans implicitly assign exact values or ranges of values to these concepts based on their experience.
Typical fuzzy logic rule is in a way a combination of human thinking and precise logic. A fuzzy logic rule might look something like this:
“If temperature is below 51F to 49F range by more than 5F to 7F open the steam valve by (temperature – 49F) * 10% but no more than 100%”
This rule is very easy to understand and implement. Yet this rule works more like the human thinking even though it is precise enough to be implemented by a machine.
However the machine does not have the benefit of experience therefore the above values have to be precisely adjusted before the system is operational. As an alternative to human experience temporal difference learning can be applied to allow the system fine tune its understanding of fuzzy logic concepts such as “small”, “normal” and “large”.
The basic contribution of fuzzy logic techniques is to integrate fuzzy decision concepts with precise control measurements and control actions. This is achieved by the three components of a fuzzy control system:
1. Fuzzification interface - which transforms precise process measurements into fuzzy input variables.
2. Inference engine - which can execute logical condition tests using the fuzzy input variables to generate fuzzy output variables;
3. Defuzzification interface - which transforms fuzzy output variables into precise control actions.
In the physical world, process variables are measured as precise values with engineering units, such as °F. In the fuzzy world, variables are measured in relative terms, such as high, low, or normal. These terms cover a range of values, and their ranges can overlap. The linear or non-linear curves define the degree of membership value for each condition (low, normal, high) and are called membership functions. They can be expressed mathematically with constants that affect their shape. Changing these constants thereby affects results of the fuzzification function, and is one means of fine-tuning the performance of a fuzzy logic control system.
Another way is to introduce more subsets of data such as very low, low, normal, high and very high. However increasing the number of subsets also increases the number of rules needed to handle all possible situations. Fortunately not all variables need to be considered together, and the set of all logical combinations can usually be broken down into more appropriate subsets.
Defining more subsets provides more resolution for decision making, but the number of logical possibilities increases according to the rules of combinations and permutations.
One option to work around this problem is to design rules for all possible combinations of input variables. The alternative is to design rules for all possible output combinations. Which choice is easier depends on the relative number of controlled and manipulated variables.
Fuzzy logic rule based control systems bring the flexibility of human like thinking to the problem of process control which allows easier understanding and programming of the necessary conditions for the control actions involved. However sometimes the number or complexity of fuzzy logic rules can be too high for an effective fuzzy logic system implementation which may make traditional mathematical methods preferable. Therefore fuzzy logic rule based systems usefulness can vary depending on the specific control problem at hand.
References:
[1]. Lew Gordon, Rule-based Reactor Control. Control Engineering July 2005
[2]. Lew Gordon, Advanced Process Control: Fuzzy logic and Expert Systems. Control Engineering September 2005
[3]. A.C.F. Guimaraes, C.M.F. Lapa, Fuzzy inference to risk assessment on nuclear engineering systems. Applied Soft Computing June 2005