Microcontrollers in Practice (Mitescu M., 2005)

The module DISPLAY.ASM contains the software routines needed to control the four-digit seven-segments display unit described in Appendix A14.

error (the error dot) is positive, then the output is high.” This translates to: “If the temperature of the controlled system is lower than the set-point temperature, and the difference between the two values tends to become bigger, then the output must be high.” Which is pretty close to the natural human language.

The general structure of these rules is: “If (A and B), then C”, where A, B, and C are logic sentences referring to the inputs e(t), d(t) and the output Vout(t), respectively.

(A and B) is called the antecedent of the proposition, and C is the consequent.

Note that in fuzzy logic the truth value of a proposition is not 0 or 1, but a number in the interval [0, 1]. A, B, C and the proposition “If (A and B) then C” are all fuzzy logic propositions.

The total number of rules that describe the behavior of the system is K = N M, where N is the number of fuzzy subsets associated with the input e(t), and M is the number of subsets associated with d(t). In the example presented in this chapter, N = 3 and M = 3, which leads to a total of K = 9 rules.

For maximum clarity, the nine rules can be presented in two tables (Tables 15.1 and 15.2): one containing the values for the antecedent, the other for consequent.

The antecedent table and the consequent table define the rule matrix. The whole system of rules defines the rule base.

Knowing the membership functions for x = e(t) and y = d(t), it is possible to determine at any moment the truth value of the sentences Ai and Bi corresponding to the antecedent of each rule. In fuzzy logic, if ( Ai ), (Bi ) are the truth values of the sentences Ai , Bi , then the truth value of the sentence Ai and Bi is zi = ( Ai and Bi ) = min(( Ai ), (Bi )).

One possible way to obtain the crisp output Vout is by combining all the rules in the rule matrix, according to the following formula:

K

It is now possible to compute the crisp value of Vout, according to the formula (15.1), which is a weighted average of the values in the consequent table, with the weights extracted from the corresponding cells of the antecedent table.

15.3 A Microcontroller Implementation of a Fuzzy Controller

From a hardware perspective, nothing distinguishes a fuzzy controller from a micro- controller-based PID controller. It’s the software that makes the difference. The project described in this chapter uses exactly the same hardware as that used for the PI temperature controller described in the previous chapter.

The key element in designing the software for this application is the way of representing the membership functions, The simplest solution to do this is to use the values of e(t) and d(t) as the offset in ROM tables associated with every function. In this case, obtaining the degree of membership for any value of the variable ERR = e(t) is as simple as this:

190 15 Fuzzy Logic Temperature Controller

This fragment of code assumes that ERR is an 8-bit unsigned integer. In practice, things are a bit more complicated because e(t) and d(t) can take values in the range [−255, 255]. To cover this range, the variables associated with e(t) and d(t), called ERR and DERIV, must be 16-bit signed integers.

To avoid working with negative offsets in a table, a simple solution is to split the table associated with a membership function in two distinct tables: one for the positive values of the variable, the other for the negative values. Here is an example of code that uses this artifice:

Besides the obvious simplicity of the program, defining membership functions as tables has another important advantage: it allows the use of any shape for the membership functions without the need to change anything in the code, only the tables.

The general structure of the software application, defined in MAIN.ASM, is very similar to the implementation of the PI temperature controller, described in the previous chapter.

INCLUDE 68HC11F1.DEF

INCLUDE AS11.MAC

INCLUDE MAP.ASM

CODE

VECTOR_RESET

INPUT.ASM contains the code to read the status of the digital input lines (the START and STOP buttons, and the rotary encoder used to select the variable to display) and the values of the analog inputs AN0, AN1, AN2, assigned to the variables TS – set-point temperature, TM – measured temperature, and TD – the time interval used to compute the error dot. The variable ERR is updated here with the values of the difference TS – TM by the subroutine CERR, listed below:

The rest of the preprocessing task is performed in the module DERIV.ASM, which calculates the derivative of the error, by comparing the current value of ERR with the previous value, stored in the variable PREVERR. The time interval between two successive samples is obtained using a software timer, and it is made adjustable by multiplying the timer quantum with the value of the variable TD, which stores the analog value of the potential on the cursor of the potentiometer R13. The effect is that the variable DERIV = ERR − PREVERR is updated at time intervals of 100 ms*TD.

The six membership functions associated with the subdomains N, Z, and P of e(t) and d(t) are defined as tables in module MFTAB.ASM. This also contains the nine-byte consequent table SGTAB.

The actual fuzzy inference is performed in FUZZY.ASM, by the subroutine CAT (Create Antecedent Table), which updates the contents of the 9-byte RAM table ATAB, according to the rule matrix described above. Finally, the subroutine CRISP computes the crisp output of the controller, and updates the variable VOUT, as the weighted average of the values in SGTAB, with the weights extracted from the antecedent table ATAB.

The value of VOUT is used in OUTPUT.ASM to determine the moments when the triac that drives the heater must be open, as described in the previous chapter.

192 15 Fuzzy Logic Temperature Controller

Exercises

SX 15.1

What is the influence of the parameter TD on the overall behavior of the fuzzy controller described above?

Solution

TD determines the time between the moments when the variables ERR and PREVERR are updated. The values of the error dot d(t) = e(t2) − e(t1) = e(t1 + TD × k) − e(t1) are directly related to the parameter TD and to the response time of the controlled system. When TD is too small, t2 is very close to t1, d(t) tends to zero, and the process is misinterpreted as being at equilibrium. Therefore, the control system exerts low-to-moderate action on the process, even if the error is positive and high.

On the contrary, when TD is too large, the controller tends to react drastically even at small variations of the temperature, and the system tends to become unstable. In practice, TD should be set to high values only for slow response processes.

SX 15.2

What is the effect of changing the shape of the membership functions associated with the subdomains N, Z, P of e(t) to the shape presented in Fig. 15.6?

Fig. 15.6. Membership functions for exercise SX15.2

Solution

The slope of a function f(x) contains information about the speed of variation of the function. For high values of the slope, even small variations of the argument x produce important variations in f(x). In this particular example, the controller senses the variations of e(t) as being more significant when the slope of the membership functions is higher, and therefore Vout will change more drastically when Tm is far from Ts , than in the vicinity of the equilibrium point.

Note the similarity between the slope of the membership functions associated with e(t) and the proportional gain K p of a PID controller. Using membership functions with the shape presented in Fig. 15.2 is equivalent to dynamically adjusting the parameter K p of a PID controller. The risk of overshoot is reduced in this case, compared to the case of triangular membership functions.

16

Remote Relay Controller over Telephone Lines

16.1 In this Chapter

This chapter contains the description of a device that interfaces a microcontroller to a telephone line, and is capable of receiving and decoding a series of DTMF signals, and to execute commands received this way.

16.2 Description of the Hardware Solution

Since telephone lines are available almost anywhere, it is interesting to design a device that, when connected to a phone line, is able to answer a call, and to recognize and execute a series of commands generated directly from the keypad of the telephone set that initiated the call.

This device operates according to the following set of rules:

•The human operator initiates a call, using a regular telephone set.

•The relay controller senses and counts the ring tones generated by the central office.

•After a specified number of rings, the relay controller answers the call and transmits a specific audible tone over the telephone line to acknowledge its presence.

•Using the telephone keypad, the operator generates a series of DTMF (Dual Tone Multi Frequency) tones, having a determined structure, which are received and decoded by the controller. The DTMF tones are audio signals, consisting of a combination of two sine waves, having precise frequencies in the range 697–1633 Hz. Each key of the telephone set keypad is associated with a distinct combination of frequencies, so that the receiving device can easily identify the key pressed.

•The relay controller sends back to the operator distinct audible tones after the reception of correct, or erroneous DTMF series.

•After 30 seconds of inactivity, i.e. if no DTMF tone is received for 30 seconds, the controller closes the line, and terminates the session.