

                   **  APPENDIX A ** (Preliminary Docs.)
 
                        ACES MODULES Version 1.1

Type of Module  Code         Description & Diagram
---- -- ------  ----         ---------------------

Arc Sine          A          Computes the angle (in radians) for the
                             sine of e1 ( maximum +- Pi/2.) If a value
                             equivalent to the sign of the cosine is
                             input to e2 the output range is extended 
                             to +- Pi radians.
                                        __________
                              e1  -----|          |\
                                       |          | \
                                       |     #    | A>----- eo
                                       |          | /
                              e2  -----|__________|/


-------------------------------------------------------------------------

Bang-Bang         B          The output, eo, of this module is TRUE (+1)  (Comparator)                if  e1 > e2 and FALSE (-1) if e1 <= e2.


                                        __________
                              e1  -----|          |\
                                       |          | \
                                       |     #    | B>----- eo
                                       |          | /
                              e2  -----|__________|/


-------------------------------------------------------------------------


Cosine            C          The output, eo, is the cosine of e1 
                             (e1 is in radians.)
                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | C>----- eo
                                       |          | /
                                       |__________|/


-------------------------------------------------------------------------

Dead Space        D          The output, eo, contains a "dead-zone",
                             positioned about 0.0, equal to value of 
                             P1 - P2 .

               /
          P1  /    ^                    __________
          |__/     |                   |          |\
         / | |    eo                   |          | \
        /   P2                 e1 -----|     #    | D>----- eo
       /                               |          | /
                                       |__________|/
        --> e1                           O      O
      (Slope eo/e1 = 1.0)               P1      P2      
 
-------------------------------------------------------------------------

Log function      E          The output, eo, is the natural logarithm
(Base e )                    of input e1 + P1.


                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | E>----- eo
                                       |          | /
                                       |__________|/
                                         O
                                        P1
-------------------------------------------------------------------------

Flag              F          The output, eo, is normally FALSE (-1) as 
(latch)                      long as e1 <= P1. Once e1 > P1, eo becomes
                             TRUE (+1). (Can not be reset during run.) 
                             There is an indicator on the Control 
                             Panel which lights if any flag is set.

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | F>----- eo
                                       |          | /
                                       |__________|/
                                         O
                                        P1
-------------------------------------------------------------------------

Gain              G          The output, eo, is computed by multiplying
(Potentiometer)              e1 by P1.

                                        ________
                                       /        \
                                      /          \
                             e1 -----|     #    G |----- eo
                                      \          /
                                       \ _______/
 
                                                    (a circle really)
------------------------------------------------------------------------ 

     
Half Power        H          The output, eo, is calculated as the 
 (Square Root)               square root of the ABSOLUTE value of e1. 

                             The square  root of 0.0 gives an output 
                             of 0.0 (Special case).

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | H>----- eo
                                       |          | /
                                       |__________|/
                                      
                                   
-------------------------------------------------------------------------


Integrator        I           The output, eo, is equal to P1/IC (t=0) 
                              plus the integral of the sum of e1 plus 
                              (P2 * e2) plus (P3 * e3). 

                              A maximum of 25 modules can be used.

                                            P1/IC
                                        __O________
                               e1 -----|          |\
                                       |          | \
                               e2 ----O|     #    | I>----- eo
                                    P2 |          | /
                               e3 ----O|__________|/
                                    P3

-------------------------------------------------------------------------

Jitter            J           The output, eo, is a random number between
                              -1.0 and +1.0 . The seed can be controlled
                              by setting P1. If P1 = 0.0 the same seed 
                              is used for each run. P1 set > 0.0 results
                              in a new seed for each run.

                                        __________
                                       |          |\
                                       |          | \
                                       |     #    | J>----- eo
                                       |          | /
                                       |__________|/
                                         O
                                        P1
-------------------------------------------------------------------------

Konstant          K           The output, eo, is a constant value
(Reference                    numerically equal to P1.
 Source)
                                        ________
                                       /        \
                                      /          \
                                     |     #    K |----- eo
                                      \          /
                                       \ _______/
 
                                                    (a circle really)

------------------------------------------------------------------------   

Limiter           L           The output, eo, is limited on the high
                              end to the value of P1 and on the low end
                              to the value of p2.
                                                                                                                 __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | L>----- eo
                                       |          | /
                                       |__________|/
                                         O      O
                                        P1      P2
                                   
-------------------------------------------------------------------------

Magnitude         M           The output, eo, is simply the absolute
                              value of input e1.

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|    #     | M>----- eo
                                       |          | /
                                       |__________|/


-------------------------------------------------------------------------

Negative clipper   N          The output, eo, is limited to positive
                              values.
                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|    #     | N>----- eo
                                       |          | /
                                       |__________|/


-------------------------------------------------------------------------

Offset             O          The output, eo, is the sum of e1 and P1.

                                  
                                              |\
                                      e1 -----|#\
                                              | O>----- eo
                                             O| /
                                           P1 |/


-------------------------------------------------------------------------

Positive Clipper    P         The output, eo, is limited to negative 
                              values.

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|    #     | P>----- eo
                                       |          | /
                                       |__________|/

-------------------------------------------------------------------------

Quit Element         Q        The output, eo, is unused. The occurrence
                              of e1 > e2 causes the operate period to be
                              interrupted and the run terminated.

                                        __________
                              e1  -----|          |\
                                       |          | \
                                       |     #    | Q>
                                       |          | /
                              e2  -----|__________|/

-------------------------------------------------------------------------

Relay                R        The output, eo, is equal to e1 if e3
                              is TRUE (Greater than 0.0) and equal to e2
                              if e3 is FALSE ( Less than 0.0).


                                        __________
                              e1  -----|          |\
                                       |          | \
                                       |     #    | R>----- eo
                                       |          | /
                              e2  -----|__________|/
                                             |
                                         e3--|

-------------------------------------------------------------------------

Sine Function        S        The output, eo, is the sine of angle e1.
                              (e1 is in radians).

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|    #     | S>----- eo
                                       |          | /
                                       |__________|/


-------------------------------------------------------------------------

Time Pulse           T       The output, eo, is a pulsed logic signal.
Generator                    The pulse width is a single time step. The
                             repetition rate is set by P1. The
                             starting state is set by e1 as follows:
      
                             If e1 initially minus, eo starts FALSE
                             and starts pulsing when e1 becomes TRUE.

                             If e1 initially zero, eo starts FALSE 
                             and a pulse ends each period.

                             If e1 initially plus, eo starts with a
                             pulse and a pulse starts each period.

                                                       
                                        __________      _
                                       |          |\  _| |_
                                       |          | \
                               e1 -----|     #    | T>----- eo
                                       |          | /
                                       |__________|/
                                         O
                                        P1
-------------------------------------------------------------------------



Unit Delay           U       The unit delay module delays the input
(Transport                   e1 for a specific period determined by
 Delay)                      the setting of P2. The initial output of
                             eo being set by P1. The delay will be an 
                             even multiple of time step (maximum 50). 
                             A maximum of three modules can be used.

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | U>----- eo
                                       |          | /
                                       |__________|/
                                         O      O
                                        P1      P2
                                  
-------------------------------------------------------------------------

Vacuous              V       An element used in conjunction with the
                             wye (Y) element. eo is used to provide
                             an input to modules directly in the
                             implicit range of the wye element. The
                             input of the V element is always con-
                             nected to the corresponding output of the
                             wye element.  (Use highest block numbers
                             for vacuous modules.) 


                                   |\
                                   |#\
                            e1 ----|-->---- e0
                                   |V/
                                   |/
  
-----------------------------------------------------------------------

Weighted Summer       W      The output, eo, is the sum of e1 * P1 plus
                             e2 * P2 plus e3 * P3.


                            e1 ----O|\
                                 P1 |#\
                            e2 ----O| W>---- e0
                                 P2 | /
                            e3 ----O|/
                                P3

-----------------------------------------------------------------------

Multiplier            X      The output, eo, is the product of e1 and e2.

                                        __________
                              e1  -----|          |\
                                       |          | \
                                       |          | X>----- eo
                                       |          | /
                              e2  -----|__________|/


-------------------------------------------------------------------------

Wye                  Y       This module is used in conjunction with
                             the vacuous (V) module to solve for
                             situations where a high-gain operational
                             amplifier would be utilized. With this 
                             module, inverses and algebraic loops can be 
                             solved.

                             P1 sets max. allowable error and P2 sets the
                             convergence rate (0.1 - 0.9).

                                        ___________
                              e1  -----|          /\
                                       |    #    /  \
                                       |--------|   Y>----- eo
                                       |         \  /
                              e2  -----|__________\/
                                          O     O
                                          P1    P2
-------------------------------------------------------------------------

 Zero-order-hold     Z       A hybrid device. The output, eo, tracks the
 (Sample-hold)               input e1 as long as e2 is TRUE. when e2 
                             becomes FALSE the output, eo, maintains the
                             last value of e1. Initial output, eo, = p1.
 
                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | Z>----- eo
                                       |          | /
                                       |__________|/
                                         |      O
                                    e2 __|      P1
                                   
-------------------------------------------------------------------------
  
Plus Summer          +       The output, eo, is the sum of e1, e2, and 
                             e3. (Less overhead the weighted summer).

                            e1 ----|\
                                   |#\
                            e2 ----| +>---- e0
                                   | /
                            e3 ----|/
                                
-----------------------------------------------------------------------

Divider             /        The output, eo, is the result of division
                             of e1 by e2. Division by zero results in an
                             error terminating the run.

                                        __________
                                       |          |\
                                       |          | \
                               e1 -----|     #    | />----- eo
                                       |          | /
                                       |__________|/
                                         |      
                                    e2 __|  
                                   
-------------------------------------------------------------------------

Arbitrary            1       The output, eo, is the function of e1 
function type        2       between the limits of  P2 to P1. There
                     3       are 20 equally-spaced segments utilizing
                             continuous linear interpolation within each
                             segment. P2 is the higher limit of X and 
                             P1 the lower. The 21 points of the abscissa
                             can be any reasonable value. There can be 3
            .                function types and any number of each type.
    .   .  /|\
 _ /|\./|\/|||\    (Y)                  __________
  |||||||||||||\_   ^                  |          |\
  ||||||||||||||    |                  |          | \
                               e1 -----|     #    | *>----- eo
  P2 ..........P1                      |          | /
                                       |__________|/
        (X) ->                            O    O      * 1,2,or 3
                                         P1    P2
                                   
-------------------------------------------------------------------------
  
                            
Logical AND gate      &      The output, eo, is the logical AND of inputs
                             e1, e2, and e3. That is: If e1, e2, and e3
                             are TRUE eo will be TRUE.

      
                                       _________
                              e1 -----|         \
                                      |          \
                              e2 -----|    #    &|----- eo
                                      |          /    __
                              e3 -----|_________/\___ eo


-------------------------------------------------------------------------
Single Shot           ^      The output, eo, of this module is a logic
                             signal. Normally the output is FALSE. When
                             e1 becomes TRUE and e2 is enabled a TRUE
                             pulse, equal in time to to the value of p1,
                             is output. Pulse time is a multiple of time
                             step. 
                                        ___________
                          (S) e1  -----|           |\   
                                       |           | \         (Q)
                                       |     #     | ^|---- eo  _
                                       |           | / \___    (Q)
                          (E) e2  -----|___________|/       -e0 
                                          O   
                                          P1 
-------------------------------------------------------------------------


Rectalinear to        >      The output, eo, is the resultant vector
Polar conversion             quantity ( sqrt. ( X sqd. + Y sqd.)) and
                             output -eo is the angle (in radians). The
                             range of angle is from -Pi to +Pi radians.


                                        __________
                         (X)  e1  -----|          |\
                                       |          | \
                                       |     #    | >>----- eo (R)
                                       |          | /
                         (Y)  e2  -----|__________|/\___ -eo  (theta)


-------------------------------------------------------------------------


Polar to              <      The output, eo, is equal to the cosine
Rectalinear                  of angle e2 times e1. The output -eo 
conversion                   is equal to the sine of e2 times e1. 
                             (angle e2 is in radians). If input e1 is
                             equal to 1.0 then eo and -eo are the
                             cosine and sine of angle e2.


                                        __________
                       (R)    e1  -----|          |\
                                       |          | \
                                       |     #    | <>----- eo  (X)
                                       |          | /
                     (theta)  e2  -----|__________|/\___ -eo  (Y)


-------------------------------------------------------------------------


Iteration             ?      The output, eo, is proportional to an
control module               error term formed by the difference
                             e1 - e2 . This module only works in
                             conjunction with the REP-OP mode. The
                             parameter usage varies with the mode of
                             operation as follows.

                             P3 = 1: (increment/decrement mode).
                                      eo = P1 (t=0) period 1.
                                      eo = eo + P2 after each
                                           operate period.

                             P3 = 2: (inc./dec. error mode).
                                       eo = P1 (t=0) period 1.
                                       eo = eo + sign(e1-e2) * abs(P2)
                                            after each operate period.

                             P3 = 3 (inc./dec. prop. error mode).
                                        eo = P1 (t=0) period 1.
                                        eo = eo + ((e1 - e2) * p2).

                             P3 = 4.0 (inc./dec. prop. sqd. error mode).
                                        eo = P1 (t=0) period 1.
                                        eo = eo + (e1 - e2) ** 2 
                                             * sign(e1-e2) * P2.
                                              
                                        __________
                              e1  -----|          |\
                                       |          | \
                                       |     #    | ?>----- eo
                                       |          | /
                              e2  -----|__________|/
                                         O   O   O
                                         P1  P2  P3
-------------------------------------------------------------------------

Analog PID           %      The output, eo, is used to control a sim-
controller                  ulated process. e1 is the measured
                            variable. e2 the setpoint, and e3 the
                            the initial (manual) setting of the con-
                            trolled output eo.
                            P1 controls the proportional gain (+ =
                            direct acting.) (- = inverse acting.) P2 is
                            the integral (reset) gain and P3 is the
                            derivative (rate) gain. Up to 3 modules
                            can be used. The controllers can be used
                            in "cascade" fashion.
                           
                                        __________
                               e1 -----|          |\
                                       |          | \
  * Note Settings P2 &         e2 -----|     #    | %>----- eo
    P3 are gains in respect            |          | /
    to the proportional gain   e3 -----|__________|/
    and the independent vari-            O   O   O
    able per/sec.,per/min.               P1  P2  P3
    or per/hour...

-------------------------------------------------------------------------
                                 [end]

