Automatismos Automatic Systems

Transcription

1 Automatismos Automatic Systems 5º Ingeniero de Telecomunicación Transparencias de la asignatura Fabio Gómez- Estern. ES Ingenieros Lesson 1 Index Introduction Evaluation of modelling tools Tables and phase diagrams Reduced state graph Petri Networks Introduction Description Modelling examples Advantages and comparison with other tools Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 2 1

2 Introduction Systems description A system description consists of the development of a model of the system itself. Two types of models can be distinguished: Structural models: defining the parts of the system Functional models: defining how the system works Petri Networks (PN) are intended for studying logic sequential systems from a functional point of view Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 3 Introduction Separation between Operating and Control Parts Most Logic Sequential Systems can be represented and divided into two Subsystems Operating part (OP): makes the process run by transforming the input variables into output variables, and issuing reports. It comprises the elements inside process (Sensors, motors, actuators, valves, etc.) Control part (CP): From the established set points, and the reports, it provides adequate orders for commanding the behavior Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 4 2

3 Introduction Separation between Operating and Control Parts Inputs Set p oints, references Operative Part Reports Commands Control Part Outputs External outputs, if required Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 5 Introduction Finite Automata: mathematical definition Definition of Automaton : Device capable of emulating or following certain movements. Formally, a finite automaton is a Discrete System defined by the quintuplet <E,S,Q,d,l> Finite set of input symbols: E={E i } Finite set of output symbols: S={S j } Finite set of internal states: Q={Q k } Transition function between states in terms of inputs and previous states: d:q x E Q Output function, in terms of inputs and states l:q x E S Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 6 3

4 Introduction Table representation of finite Automata Consider a finite Automaton with E={a,b} and S={x,y}. The prescribed behavior is: the output at an instant k should be S(k)=x if and only if the last three inputs follow the sequence a-b-a and S(k)=y otherwise. Q={Qa,Qab,Qbb} are the significant states of the problem Qa: last input was a Qab: last 2 inputs were a-b Qbb: last 2 inputs were b-b Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 7 Evaluation of Tools Phase diagrams and tables The procedure is: Build a table associating the states with the inputs in order to indicate the corresponding outputs and the new states. Graphical representation in phase diagrams. Phase table Phase diagram Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 8 4

5 Evaluation of Tools Phase diagrams and tables Example: Cart System When button M is pressed, the cart moves right (d), until B is rechaed. Once there, it starts moving left (i) until A is reached, and then stops. E={M,A,B} S={i,d} Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 9 Evaluation of Tools Table and phase diagrams - criticism They are exhaustive descriptions, as they gather all data of all possible combinations of inputs and states. Industrial systems are characterized by Large number of inputs and outputs. Largely unspecified. Many I/O pairs (E x Q) have no physical meaning. These methods have little practical use. They are difficult to implement when the number of inputs increases. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 10 5

6 Evaluation of Tools Reduced state graph It introduces the concept of Receptivity. When the system is in a specific state, it is only receptive (or sensitive) to a small subset of external events capable of inducing a state transition. Hence, there is no need to analyze all possible combinations of inputs for every single state. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 11 Evaluation of Tools Reduced state graph - Examples The RG (Reduced State Graph) is a graph where the logical condition that triggers a transition between 2 states is described as any logical function of the inputs. Moving Cart Example The resulting description is simpler, direct, and more intuitive. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 12 6

7 Evaluation of Tools Reduced state graph Examples continued Two carts come and go. They are synchronized at the right ends. Both carts must have reached (B,D) in order to start moving backwards. A small specification change (e.g. add a new cart) may affect the description significantly. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 13 Evaluation of Tools Reduced state graph Examples continued Three carts come and go, synchronized at the right ends. The number of states grow at a rate of 2 N+1-1, where N is the number of carts. All combinations of events are evaluated taking into account the order of occurrence, though it might be irrelevant. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 14 7

8 Evaluation of Tools Reduced state graph Examples continued Two simultaneous actions A and B, followed by C, are composed of subtasks. end(a) end(b) end(b) end(a) DRAWBACK: All possible finishing order of subtasks Should be considered Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 15 Evaluation of Tools Reduced state graph Criticism Advantages When introducing the concept of receptivity, the system description is significantly simplified. The information used for modelling is minimum and necessary. Drawbacks When there are concurrent evolutions, this method requires the evaluation of all possible chronological orderings of external events. Local changes may result in total redefinitions of the description. It is not suitable for a descending description ( top- down ). Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 16 8

9 Introduction Created by German Prof. C.A. Petri in the 60 s. Structure A Petri Network or (Petri Net) is a mathematical tool (with it associated graphical representation) that allows to model the behavior of a large variety of systems, being of special interest in the logical sequential and concurrent systems. It consists of an oriented graph, with two types of nodes: Places and Transitions, joined together arternatively by Arcs. The Places are represented by circles, and the Arcs by segments. The Arcs are oriented and they connect Places with Transitions and vice- versa, but never 2 Places or 2 Transitions at a time. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 17 (PN) Introduction (continued) permit to model and analyze the Control Subsystem (CP) of discrete systems with concurrent evolutions. In order to use them in application modelling, they must be endowed with an interpretation, by assigning physical meaning to the evolution conditions of the network and to the actions triggered by that evolution. Petri Net Structure Interpretation Physical Significance The evolution of a PN without interpretation is said to be autonomous. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 18 9

10 Introduction (continued) Behavior: A Place may contain a nonnegative number of Marks. Each mark is represented by a dot in the Place. The set of Marks associated, at a given time, to the places, is denoted the Network Marking. For the functional description of a PN, the following associations are made, Places actions or outputs Transitions events (as functions of inputs and actions) Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 19 Introduction (continued) Behavior: The dynamics of the PN is represented by the evolution of its marking. The basic rules conducting the evolution of the marking are, A Place Li is an input Place of the Transition Tj, if there exists an Arc oriented from Li to Tj. A Place Li is an output Place of the Transition Tj, if there exists an Arc oriented from Tj to Li. A Transition is enabled if all its input places are marked. An enabled Transition is fired if the event associated with it is verified. A Firing of a transition consists of removing marks from each of its input Places, and adding marks to each of its output Places. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 20 10

11 Description model. Structure Autonomous PN: When analyzing autonomous PN we must observe its structure and behavior. Structural model of a PN Generalized PN: a quadruplet R=<P,T,a,b a,b> such that P: Finite nonempty set of Places. T: Finite nonempty set of Transitions. a: P x T N Pre-incidence function b: T x P N Post-incidence function Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 21 Description model. Graphical Representation Oriented Graph with 2 types of nodes: Places (circles), to which long-lasting actions are associated. Transitions (line segments), to which instantaneous actions are associated. The Arcs join places with transitions and vice-versa. The marks reside in places and they represent their active state. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 22 11

12 Description model. Graphical Representation Each Arc is labelled with a nonnegaive integer a(p,t) or b(p,t) called weight of the Arc. There exists and Arc oriented from Place Pi to Transition Tj a(p i,t j ) >0. There exists and Arc oriented from Transition Tk to Place Pl b(t k, p l ) >0 As a general rule, a non-labelled Arc has weight 1 and if weight>1, it must be labelled with the corresponding weight. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 23 Description. For a generalized Petri Net, R=<P,T,a,b a,b>, txt, pxp; the following sets are defined: Set of input places ot t: t={ pxp / a(p,t)>0 }; Set of output places of t: t ={ pxp / b(t,p)>0 }; Set of input transitions of p: p={ txt / a(p,t)>0 }; Set of output transitions of p: p ={ txt / b(t,p)>0 }; Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 24 12

13 Description. Example: t1={pa,pb}; t1 ={pc,pd}; ph={t4,t8}; ph ={t6,t7}; Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 25 Description. Behavior Marking: the Marking M is a mapping P N that links an integer number (of Marks) to each Place. Marked Petri Net: A pair <R,M 0 >, where M 0 is the initial Marking. Enabled Transition: Transition t is enabled for the Marking M each input Place has, at least, a(p,t) marks. p X t, M(p) a(p,t) Evolution of Markings: the firing of an enabled Transition implies the removal of a(p,t) Marks from each Place p X t and the addition of b(t,p) Marks to each place p Xt. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 26 13

14 Description. Markings evolution. Examples Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 27 Description. Properties (Deadlocks) Live Transition: (for a given initial Marking M 0 ). If, for all marking M reachable from M 0, there is a marking, successor of M, from which the Transition can be fired. Live Petri Net: (for a given initial Marking M 0 ), if all its transitions are live for that Marking. Bounded Petri Net: (for a given initial Marking M 0 ). There is a constant k>0 such that any marking reachable from M 0 is such that no place has more than k Marks. Binary Petri Net: (for a given initial Marking M 0 ). If any Marking reachable from M 0 is such that no place has more than 1 Mark. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 28 14

15 Description. Properties. Example Is this a Live Petri net? Is this a Binary Petri Net? Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 29 Description. Properties. Live is too hard a property. Liveness levels. L(M 0 )=set of possible firing sequences from M 0. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 30 15

16 Description. Properties. Marking Related Properties Conformed Petri Net: If it is Live and Binary Conflicting Transitions: some simultaneously enabled transitions are in conflict if they are descendants from the same Place and this does not have enough number of Marks to fire them simultaneously. A conflict is made effective if the events associated to the transitions are verified simultaneously. An effective conflict corresponds to ambivalences in the description. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 31 Description. Properties. Example. Conformed Not Binary Are there conflicting transitions? And in the previous PN? Where? Not Live Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 32 16

17 Description. Matrix representation. A PN may be represented by means of two matrices. Assuming P =n and T =m, then we define Pre-incidence matrix C - =[C ij - ] n*m with C ij - =a(p i,t j ) Post-incidence matrix C + =[C ij + ] n*m with C ij + =b(t j, p i ) Ordinary PN: The one whose incidence functions values are 0 or 1. a(p i,t j ) X{0,1}, b(t j, p i ) X{0,1}, txt, pxp Pure PN: the one where no place is simultaneoulsy input and output place of the same transition. a(p i,t j ) b(t j, p i )=0 for all (i,j) The matrix representation of a PN may be simplified by using a unique incidence matrix C=C + - C - Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 33 Description. Matrix representation. Matrix representation of an ordinary pure PN Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 34 17

18 Matrix representation. Marking & Evolution The marking vector of an ordinary and pure PN is a column vector of P =n elements in the form M(p i ), where each element represents the number of existing marks in each place. Therefore, in the last example M 0 T =( ) Marking evolution rule: if transition t is enabled by the Marking M i and t is fired, the new parking M j for each place, p is evaluated as M j (p)=m i (p)+b(t,p)-a(p,t) Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 35 Matrix representation. Firing sequences A firing sequence (s) from a marking M 0 is represented by the sequence of transitions such that the firing of each of them leads to a marking that guarantees the enablement of the next transition in the sequence M 0 t1 M 0 t2 M 0 t3 tr M q M 0 s M q In the last example, the sequence of firings s=t 8 t 6 t 1 t 3 t 2 t 4 t 6 is applicable M 0 T =( ) s 1 M 7 T =( ) Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 36 18

19 Matrix representation. Firing sequences Characteristic vector associated to a sequence of firings: the vector sxn m whose i-th element is the number of times that transition t has been fired in the sequence. For instance, the characteristic vector associated to the sequence s=t 8 t 6 t 1 t 3 t 2 t 4 t 6 would be s 8T =( ) A Marking M is reachable from an initial marking M 0 there exists a sequence of firings applicable from M 0 that transforms M 0 into M. ls/ M 0 -s- M Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 37 Matrix representation. State equation Let be C the pre-incidence matrix of a pure and marked Petri Net. From the definition of C and the marking evolution rule the following Petri net state equation is derived. M k = M k-1 +C*U k = M 0 +C*s, if M 0 -s- M Where M k marking after the k- th firing M k-1 marking after the (k- 1)- th firing U k = vector with all zero elements except the i- th, if t i fires at instant k Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 38 19

20 Interpretation We have previously seen a Petri Net (generalized) as a mathematical structure, a marking and some evolution rules (dynamical properties). Un order for a PN to represent a real-world system, it is necessary to associate it with an interpretation which is defined as Physical meaning of firing conditions Actions generated by the evolution of the marking The internal state of a PN will be always given by the marking. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 39 Interpretation Interpreted : In order to give interpretation to a Petri Net it is necessary to define the following elements Set of inputs: X={x1,x2, xe} Set of outputs: Y={y1,y2, ys} Set of impulse outputs: Z={z1,z2, zq} Some other useful definitions External Condition (Ci): a combinational logic function of the input (and output) variables of the system. Event (Ei): a change in the logic state of an external condition. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 40 20

21 Interpretation Interpreted : Two types of interpretation Actions generated associated to places. Actions generated associated to transitions. As a general rule Transitions: Events, external conditions, impulse outputs Places: Level outputs If the activation of an output is linked to external conditions, it is said to be a conditioned output. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 41 Interpretation An interpreted PN: A marked PN An application T->E (events) An application T->C (external conditions) An aplication T->Z (impulse outputs) An application P*C->Y (level outputs) Three rules of marking evolution in interpreted 1. Firing of enabled transition ti: iff Ci&Ei. 2. When a transition is fired, all its associated impulse outputs are generated. 3. If a place p is marked and the associated external conditions are satisfied, all level outputs are activated. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 42 21

22 Lesson 2 Functional modelling of concurrent systems Table of contents: Concurrency. Shared resources and mutual exclusion Task Synchronization Classical modelling examples Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 43 Typical configurations Places: A place with several input/output arcs is called OR-node. There are two particular cases of OR-nodes: Selection: 1 input arc and several output arcs Attribution: several input arcs and 1 output arcs Transitions: A transition with several input/output arcs is called AND-node. There are two particular cases of AND-nodes: Distribution: 1 input arc and several output arcs Junction: several input arcs and 1 output arcs General OR-node Selection Attribution General AND-node Distribution Junction Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 44 22

23 Typical configurations OR-node: when one of the 3 transitions is fired (either 1st, or 2st or 3rd) the corresponding output place is selected. OR-node: when one of the 3 transitions is fired (either 1st, or 2st or 3rd) the output place is granted (attributed) the right to execute. AND-node: when the transition is fired, the execution (mark) is distributed between one place AND another AND another AND-node: when the transition is fired, the execution threads join together in a unique output place. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 45 Typical scenarios: Timing in Assume the system must stay in a specific place for a fixed time interval. An external Timer will be used. The timer starts when the place is activated (when its input transition is fired) The same timer may be associated to several transitions (if they are not conflicting) Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 46 23

24 Typical scenarios: Counting in Assume that the system must stay in a specific state until a certain number of events of one type have occurred. Automatismos. 5º Ing. Telecom. Slide 47 Fabio Gómez-Estern Modelling examples: moving carts Three carts Two carts Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 48 24

25 Modelling examples: simultaneous actions 2 simultaneous actions 2 simultaneous actions with subactions Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 49 Advantages and comparison of tools Clear advantages in concurrent systems Descriptions are less complex. In the moving carts example, the number of places is 4N vs. 2 N+1-1 states for the reduced state graphs (for N=10, 40 places vs states). This is due to the fact that the state is determined by the marking. It is much simpler to introduce local variations. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 50 25

26 Modelling of complex systems - Concurrency Concurrency refers to the simultaneous execution of processes, making it harder to visualize the concept of state. In, concurrency is modelled by means of transitions with more output places than input places (distribution), thus increasing the total number of marked places. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 51 Modelling of complex systems Mutual exclusion Mutual exclusion refers to resources that can only be used by a single process or a limited number of them. In, mutual exclusion is modelled by means of places with more output transitions than input transitions (selection). Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 52 26

27 Modelling of complex systems Synchronization Synchronization refers to the need for coordinating the endings of a set of processes. In, synchronization is modelled by means of transitions with several input places (distribution). They may represent task endings (junction) or synchronization points (wait points before a start). Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 53 Modelling of complex systems Alternating tasks Two processes (each modelled as Petri subnet) could alternate without any need for a common resource, and it can occur between more than two processes. For example, an alternating behavior is desired between Process A, B and C. Sequence: A- >B- >C- >A- >B- >C Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 54 27

28 Modelling of complex systems Modularity A set of sequences represented by a Petri subnet may be reused at several points of a network, by simply considering that the return point of the sequence must be remembered. Moreover, the function call will not be executed while the module is running. With this tool, modularity is gained, and smaller size designs are achieved Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 55 Modelling of complex systems Modularity Repeated sequence Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 56 28

29 Modelling of complex systems Modularity Repeated sequence Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 57 Modelling of complex systems Examples Shared resource between two carts A: Must wait in Ea until common tregion is free. Wait time in D Ta: 100s Same as A but with priority and Tb=50s Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 58 29

30 Modelling of complex systems Examples Shared resource between two carts COMMENTS 1) Initial condition: two carts at rest in Ca and Cb. 2) The central place models the access to the shared resource and it represents its idle state. 3) The output transitions of the resource are in conflict if they request it simultaneously. In order to solve the ambiguity, priority is given to cart B. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 59 Modelling of complex systems Examples Producer-consumer problem Producer Automatismos. 5º Ing. Telecom. Consumer Fabio Gómez-Estern Slide 60 30

31 Modelling of complex systems Examples Alternating sequences Surface treatment via immersion 2 treatment tanks (double time) 2 subcicles with operator acknowledgement Load Ungrease Treatment Vashing Unload Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 61 Modelling of complex systems Examples Alternating sequences Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 62 31

32 Modelling of complex systems Examples Readers and writers Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 63 Modelling of complex systems Examples Philosophers dinner Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 64 32

33 AWL Programming in S7-300 TIMERS AND COUNTERS Timers: Elements capable of adopting a sequence of states in time. They are fired through the evaluation of a condition (raising edge) Each CPU model has a determined quantity of timers There exist hardware timer modules Timers programming: initial setup Fixed Setup: L S5T#4S200MS H:HOURS, M:MINUTES, S:SECONDS, MS:MILLISECONSDS Variable setup (e.g. 4.2s): L MW 120 At address 120: Base time: 00:0.01s; 01:0.1s; 11:10s BCD value Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 65 AWL Programming in S7-300 TIMERS AND COUNTERS Timer types: SI: Impulse U E0.1 L S5T#42S500MS SI T1 Usage: on raising edge of E0.1. T1 takes value 1 for 42,5 seconds as long as E0.1 remains at 1 SV: Extended Impulse U E3.0 L S5T#125S SV T3 Usage: on raising edge of E3.0. T3 takes value 1 for 125s, independent of E0.3. Moreover, it can be fired again (raising edge of E3.0 restarts countdown) Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 66 33

34 AWL Programming in S7-300 TIMERS AND COUNTERS Timer types: SE: Connection delay U E3.5 L S5T#700MS SE T2 Usage: on raising edge of E3.5, T2 takes value 1 AFTER 0.7 seconds, as long as E3.5 remains at 1, and it will remain there until E3.5 goes back to 0 SA: Disconnection delay U E3.4 L S5T#8S SA T3 Usage: on raising edge of E3.4, T2 takes value 1. When E3.4 returns to 0, T2 will be zero AFTER 8s. May be refired. Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 67 AWL Programming in S7-300 TIMERS AND COUNTERS Counters: Elements capable of storing, increasing a decreasing an integer value. Its initial setup, increase or decrease are fired through the evaluation of a logical condition (raising edge) Each CPU model has a determined quantity of counters There exist hardware counter modules Initialization: Fixed Setup: L C#37 Variable setup (e.g. 153) L MW 160 At address 160: BCD value Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 68 34

35 AWL Programming in S7-300 TIMERS AND COUNTERS Counter operations: S: Initialize ZR: Decrease ZV: increase =: Query Usage: On raising edge of 3.0, Z1 takes value 1,. A raising edge of E3.1 increases by 1 the value of Z1. On falling edge of E3.2, it is decreased by 1. A4.0 is 1 if Z1 is nonzero U E 3.0 L C#21 S Z 1 U E 3.1 ZV Z 1 UN E 3.2 ZR Z 1 U Z 1 = A 4.0 Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 69 AWL Programming in S7-300 TRANSFER OPERATIONS Accumulators ACU1 (32 bits). Stores results ACU2 (32 bits) Overflow bit: OV L: Loads the contents of a byte, word or double word into ACU1. Old contents of ACU1 move to ACU2. L EB 7 PAE byte 7 to lower byte of ACU1 L EW 7 PAE bytes 7-8 to lower w. ACU1 L -312 Bipolar constant 16bits L 2# bits binary constant L W#16#FFFF 16bits HEX constant L -1.3e+3 Floating point Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 70 35

36 AWL Programming in S7-300 TRANSFER & LOGICAL OPERATIONS T: Transfers the contents of ACU1 to a byte, word or double word of memory. ACU2 remains unchanged. T AB 8 T AW 8 T MW 5 T MD 10 Logical operations(the result is soterd in ACU1) UW logical AND between ACU1 and ACU2 (16 lower bits) OW logical OR between ACU1 and ACU2 (16 lower bits) XOW logical XOR between ACU1 and ACU2 (16 lower bits) Example L EW 90 ( ) L W#16#F0A9 UW Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 71 AWL Programming in S7-300 ARITHMETIC OPERATIONS +I -I *I /I ACU1=ACU1+ACU2 (16bits) ACU1=ACU2-ACU1 (16bits) ACU1=ACU1*ACU2 (16bits) ACU1=ACU1*ACU2 (16bits) (In case of overflow, OV is activated) ==I <>I >I >=I <=I ACU2>ACU1? ACU2>=ACU1? ACU2<=ACU1? L EW ACU2-L L Z ACU1-L <I =A 1.2 (A1.2=0) Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 72 36

37 AWL Programming in S7-300 FLANK EVALUATION POSITIVE (FP) OR NEGATIVE (FN) REQUIRES A MEMORY MARK Positive flank (Raising edge) U E1.0 U E1.3 FP M1.0 =A4.0 Negative flank (falling edge) U E2.1 O M2.0 FN M1.1 =A4.1 Automatismos. 5º Ing. Telecom. Fabio Gómez-Estern Slide 73 37