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Introduction This document explains how to build a control simulation under GAF. A brief description of basic concept and steps to build a simulation is presented. Then, a simple example of water heater control is used to explore the basics of GAF. What is a segment A segment is a text file contains: · configuration information · variable declarations (IN, OUT, INOUT, and LOCAL) · symbol (fuzzy membership set) declarations · condition to enable the segment · initialization · reset · pre-processing · post-processing · fuzzy rules Just like dividing the system into several manageable portions, GAF allows a control system to be divided into segments. For example, a simulated control environment under GAF may have these different segments: · control segment(s) · reference calculation and supporting segment(s) · simulation (or feedback) segment(s) · evaluation segment The feedback and evaluation segments are used for simulation and adaptation. Segment Construction To construct a segment is quite similar to construct a simple program. Please refer to FCL.DOC for detail syntax and *.gaf, *.fbk, *.sim, and *.evl files for examples. Note that these steps can be in any order to your convience. These steps are: 1. Define variables All variables must be declared before they can be used either by fuzzy rules or any statements in a segment. There are four types of variables: IN, OUT, INOUT, and LOCAL. IN Variables IN variables are used as "references" in this segment. IN variables must be in one of the categories: · calculated by other segment (as OUT or INOUT) · an input from real world, i.e. a sensor, in the simulation this input may be an OUT from a feedback segment. · application constants, can be modified through interactive interface during simulation OUT variables OUT variables are calculated outputs by this segment. OUT variables are either: · an output signal to a real world device · be used by other segment as IN variables · for diagnostic purpose · evaluation result Note that for each output variable, there must be only one segment declares it as an OUT or INOUT variable. If more than one segment declares an output variable as OUT or INOUT, the result is undefined. INOUT variables INOUT variables are both referenced and modified by this segment, i.e., it is the combination of both IN and OUT variables. Normally INOUT variables are referenced by this segment and other segments. All of the IN, OUT, and INOUT variables are visible to other segments, i.e. other segments can use this segment's OUT as its IN. LOCAL variables LOCAL variables are local to this segment. Normally, local variables are used to store temporary values so it can be used by fuzzy rules or other statements within the segment. 2. Define fuzzy membership The second step would be define the fuzzy membership set. GAF uses four points for each set. In general, fuzzy sets should be defined for each variable, either in out or local, that is used in the fuzzy rules. For example, as described in the following figure. A simple way to define membership sets for a variable is to equaly divide the range of the variable into six to obtain five sets - very low (VL), low (LO), medium (M), high (HI), and very high (VH). ----- - - - ----- \ / \ / \ / \ / \ / \ / \ / \ / X X X X / \ / \ / \ / \ / \ / \ / \ / \ +-----+-----+-----+-----+-----+-----+ -1 -0.67 -0.33 0 0.33 0.67 1 | very low | medium | very high | | low | high | As the above diagram shows these five membership sets are symmatrically divided. Then, use these membership sets for the starting point. SYMBOL very_low (-1.00, -1.00, -0.67, -0.33, 1.0) SYMBOL low (-0.67, -0.33, -0.33 0, 1.0) SYMBOL medium (-0.33, 0, 0, 0.33, 1.0) SYMBOL high ( 0, 0.33, 0.33, 0.67, 1.0) SYMBOL very_high ( 0.33, 0.67, 1, 1, 1.0) 3. Translate ideas into fuzzy rules Defining fuzzy rules is quite straight forward. Basically, this step is simply converting an imprecise idea of how things should work into fuzzy rules. For example, based on common sense to control a water heater, a simple rule may be like: "if water usage is heavy and water is cold, then the gas fuel valve to heat the tank must be full open" This idea can turn into a rule like: IF water_usage IS heavy AND water IS cold THEN fuel_valve IS full_open Where water_usage and water are IN variables, fuel_valve is an OUT variable; heavy, cold, and full_open are membership sets defined for corresponding variables. Note that all variables that are part of "THEN" statement must be declared as OUT or INOUT. Please refer to step 6 for more information. 4. Initializes the segment Next step is to define what do you want the segment to be initialized. In general, the initialization of a segment is to initialize all outputs (OUT and INOUT variables) and its local variables. The initialization will be executed when the system "comes up" (i.e., the first time it runs the segment) or requested from user interactive interface. The initialization formulas and other processing formulas are arranged like this: what's in the text remarks ------------------- ---------------------------------------- INITIALIZATION must have this key word ... ; statements for initialization each statement must end with ';' RESET optional key word for reset processing ... ; optional statements for reset processing PRE_PROCESSING optional key word for pre-processing ... ; optional statements for pre-processing POST_PROCESSING optional key word for post-processing ... ; optional statements for post-processing END; must have this key word (with ';') Note that INITIALIZATION must be the first statemant and END must be the last statement. For example, for the above water heat control, the segment should initialize the fuel_valve to close. INITIALIZATION fuel_valve = 0; PRE_PROCESSING ... END; 5. Reset processing Similar to initialization, the reset processing is to reset the segment when the segment is disabled. The reset processing is only necessary when it is different from the initialization. 6. Pre-processing and post-processing The pre-processing is a set of statements to be calculated before the fuzzy rules are inferenced. The post-processing is a set of statements to be calculated after the fuzzy rules are inferenced. The formulas can be used for calculating references or other simple mathematical models. Pre-processing is calculated before any fuzzy rule been evaluated, so the results of these formulas may be used by fuzyy rules to inference the result. 7. Segment enable condition Now, it's time to decide how and when should this segment be enabled. The enable condition determines whether the segment shoud run or not. If enable condition is not specified GAF treats the segment as enabled all the time. Example: Water Heater Temperature Control Let's use a simple water heater control to illustrate these steps in constructing a control segment. First, let's explain the simple device that we are going to control. The water heater The following diagram shows the physical layout of the water heater. temperature sensor ! ! /-------!-------\ valve high | ! <=======x======= water in sensor----x ! | | ! | | ! | | ! | | ! | | ! | | ! | | ! | | ! | low | ! x----sensor water valve | | out <=====x====== | \---------------/ ^^^^^^^^^ burner ! !<======x=======fuel valve As shown in the diagram, these are the major devices for the water heater and can be used by the controller to control the water temperature. 2 water valves: in & out 2 water sensors: high & low 1 water temperature sensor 1 fuel valve Let's also assume that the heater can heat a full tank of water up one degree per second with max gas fuel. The water tank can be drained in 100 seconds with full-open water out valve. To simplify the problem, let's split the controller into two part: a water temperature control and a water volume control. The reason, besides cover this example in few pages, is to isolate the temperature controller from the water controller. So, inside the temperature controller we can assume that the water volume is a constant. Step 1: Define variables Since we are only controling the water temperature, it is quite easy to identify the output of the controller, i.e., the fuel valve. The inputs to this controller are: the water consumption (from the valve of water out), the water temperature from the sensor. Also, there should be a target temperature as an input to this controller. After identify these variables, now we can find out their range and declare these variables. IN Target_Temp (32, 212) ! target temperature IN Temperature (32, 212) ! measured temperature IN Water_out (0, 1) ! 0 - 1 input from the water out valve OUT Gas_valve (0, 10) ! 0 - 10 volts output to the fuel valve Step 2: Define Pre-processing and Initialization Because we only care about the temperature error, which is the difference between the reference and the measured water temperature. So, we can use the pre-processing to calculate the temperature error before inference the fuzzy rules. In order to do this, a new local variable has to be put in: LOCAL Temp_error (-180, 180) Then the pre-processing and initialization is: INITIALIZATION Gas_valve = 0; ! turn off the valve Temp_error = 0; ! PRE_PROCESSING Temp_error = Temperature - Target_Temp ; END; Step 3: Define Fuzzy Membership Let's start defining membership set by using the simple method discussed. Note that for the water consumption, and gas valve only the right half (> 0) is used. The Water_out variable divided into 5 bands, i.e., very heavy, heavy, medium, light, and zero comsumption. The result would be: - - - - ------- \ / \ / \ / \ / \ / \ / \ / \ / X X X X / \ / \ / \ / \ / \ / \ / \ / \ +-----+-----+-----+-----+-----+ 0 0.2 0.4 0.6 0.8 1.0 ! below low high above truth SYMBOL Zero OF Water_out ( 0.0, 0.0, 0.0, 0.2, 1.0) SYMBOL Light OF Water_out ( 0.0, 0.2, 0.2, 0.4, 1.0) SYMBOL Medium OF Water_out ( 0.2, 0.4, 0.4, 0.6, 1.0) SYMBOL Heavy OF Water_out ( 0.4, 0.6, 0.6, 0.8, 1.0) SYMBOL VeryHeavy OF Water_out ( 0.6, 0.8, 1.0, 1.0, 1.0) The Temp_error variable is divided into these five membership sets (with extended VeryHot and VeryCold): ------- - - - ----- \ / \ / \ / \ / \ / \ / \ / \ / X X X X / \ / \ / \ / \ / \ / \ / \ / \ +-..--+-----+-----+-----+-----+--..-+ -180 -40 -20 0 20 40 180 ! below low high above truth SYMBOL VeryCold OF Temp_error (-180.0, -180.0, -40.0, -20.0, 1.0) SYMBOL Cold OF Temp_error ( -40.0, -20.0, -20.0, 0.0, 1.0) SYMBOL OnTarget OF Temp_error ( -20.0, 0.0, 0.0, 20.0, 1.0) SYMBOL Hot OF Temp_error ( 0.0, 20.0, 20.0, 40.0, 1.0) SYMBOL VeryHot OF Temp_error ( 20.0, 40.0, 180.0, 180.0, 1.0) The Gas_valve variable: - - - - ------- \ / \ / \ / \ / \ / \ / \ / \ / X X X X / \ / \ / \ / \ / \ / \ / \ / \ +-----+-----+-----+-----+-----+ 0 2 4 6 8 10 ! below low high above truth SYMBOL Off OF Gas_valve ( 0.0, 0.0, 0.0, 2.0, 1.0) SYMBOL VeryLow OF Gas_valve ( 0.0, 2.0, 2.0, 4.0, 1.0) SYMBOL Low OF Gas_valve ( 2.0, 4.0, 4.0, 6.0, 1.0) SYMBOL High OF Gas_valve ( 4.0, 6.0, 6.0, 8.0, 1.0) SYMBOL VeryHigh OF Gas_valve ( 6.0, 8.0, 10.0, 10.0, 1.0) Step 4: Translate Ideas Into Fuzzy Rules Using common sense to implement rules, such as turn this idea if the water consumption is very heavy and the water is very cold then full open the gas fuel valve into a rule IF Water_out IS VeryHeavy AND Temp_error IS VeryCold THEN Gas_valve IS VeryHigh There is an easy approach for this simple controller - by filling a table. As shown in the following table, this rule's output VeryHigh is in the top left cell. The rest of the table can be filled in based on this kind of common ideas. VeryHeav Heavy Medium Light Zero -------- -------- -------- -------- -------- VeryCold VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh Cold VeryHigh VeryHigh VeryHigh High High OnTarget VeryHigh High Low VeryLow Off Hot High Low VeryLow Off Off VeryHot Low VeryLow Off Off Off Note that some may argue that the "table filling" approach can be applied not just simple controls but also complex controls by pairing two inputs and one output. But a system built with this approach (without optimization) may require intense CPU power and contain extremely complicated rule set. Step 5: Segment Enable Condition In order to avoid unnecessary sensitive reaction from the controller, a hysteresis null band can be put in to enable or disable the control segment. As in the example file heattank.sim, the output variable Heating is calculated based on a hysteresis null band. So, we can add an ENABLE condition to achieve this: ENABLE = Heating; This will disable the segment within the hysteresis null band. When the segment is disabled we want shut off the output Gas_valve, because this is identical to the initialization, so it's not necessary to define the RESET processing. Results Please refer to the accompany files heattank.x01 and heattank.x02 for the result of this excercise. Note: 1. The Temp_error is calculated outside this control segment. 2. The symbol Off and VeryHigh defined for Gas_valve have special "center" values, which define the output center value for these fuzzy sets. 3. The .x02 has incorporated some simplifications of the rules (from the above rule table). The heattank.fbk emulates the reaction of the water tank with simple calculation based on the input/output energy. A few rules are added to introduce some heat loss and non-linear portion of the system.