The Learning Curve

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** 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]