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Lecture note 7 discrete event control 1
Discrete Event Control
CONTENTS
1. Introduction
2. State Diagram
3. Boolean Logical Equation
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Discrete Event Control
1. Introduction
DEC: both input and output control variable are discrete
variables that change values as a result of the occurrence
of events
Multiple-input/multiple-output (MIMO) discrete logical
controller, see Figure 1, where Ii is discrete value-based
input variable, and Yi discrete value-based output.
Ii and Yi only take value 0 (off) or 1 (on).
Input and output devices are usually located at a distance
from the controller.
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Introduction
Figure 1
Discrete
Logic
Controller
Y1
I2
Ip
I1
Y2
Ym
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Figure 2
Figure 3
Level Limit LLS VSwitch Controller Valve
Introduction
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We need a method to represent system
dynamics. Control system: including bothplant and controller. However, in discrete
event driven system, plant dynamics is
ignored. Therefore, the control system fordiscrete event driven system reduces to
the controller only.
State and state diagram is the method.
Next, we discuss state and state diagram.
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State Diagram
States: indicators that system changes
State Variables: assign a name to each independent class of states
EX 1: Switch: on and off. (1,0).
State change has a cause. State diagram (Fig.4, Fig.5) representsthe cause-state change. In particular, node: state; edge: cause.
In this example, we define:
LLS=0 for the level of liquid is below L
LLS=1 for the level of liquid is above L
Is LLS state variable?
NO
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State Diagram
1. State -> System state.
2. System: components: valve, pump.
3. Fluid: is not a part of the system, though the fluid has
its state as well. Level of fluid in the tank can beconsidered as a kind of state, but not in the sense of
system state.
4. Since we concern system state, the level of fluid is not
considered as a state variable. Level of fluid is inputvariable in this case; see the next slide.
5. In future, state refers to system state, but we omit
word system here.
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State Diagram
Control system
(X: state variable)
Level of fluid: LLS
Remain to see what is X and whatis output.
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State diagram
Figure 4
Figure 5
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State Diagram
Control system
(X: state variable)
Level of fluid: LLS
X: state variable: valve
Output: X as well
So we have: output = X
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State Diagram
It is noted that the two circles represent different states ofone state variable (i.e., valve). The system in EX 1 has
only one state variable.
EX 2: In EX 1, if we introduce also the pump in the
system. In particular, there is a piece of knowledge:
when the valve is closed the pump must be off. We can
sum up the desired control actions as follows:
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State Diagram
State variables: X1: pump; X2: valve.
X1: X1=0: pump off
X1=1: pump on
X2: X2=0: valve is closed
X2=1: valve is open
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State Diagram (for controller)
1. Open the valve if it is closed and the level of liquid in the
tank is less than the desired level L (LLS=0), or keep
the valve open if LLS=0.
2. Close the valve if it is open and the level of liquid in thetank is equal to or greater than the desired level L
(LLS=1), or keep the valve closed if LLS=1.
3. Turn the pump on if it is off and the valve is open andLLS=0, or keep the pump on if it is already on and the
valve is open and LLS=0.
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State Diagram
4. Turn the pump off if it is on and LLS=1, or keep the pumpoff if LLS=1.
The above expressions of control action can be represented
by two state variables, namely X1 (for pump) and X2 (for
valve)
X1=0, X2=0 (pump off, valve closed)
X1=0, X2=1 (pump off, valve open)
X1=1, X2=1 (pump on, valve open)
Fig.6 shows the state diagram for EX 2.
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State Diagram
Figure 6
Put all state variables
of the system in onecircle
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State Diagram
Fig. 7 shows another way to represent the state
diagram for EX 2. The features of Fig. 7 are:
1. Each node represents one state variable with its
value.
2. A state variable can be the cause of changes for
other state variables.
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State Diagram
Fig. 7The meaningthat the pump
can never be on
if the valve is
closed has notbeen
represented by
the state
diagram. This
shows some
limitation of the
state diagram
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State Diagram
Control system
(X: state variable)
Level of fluid: LLS
X1: state variable: pump
X2: state variable: valve
Output: X1, X2
So we have: output = X
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State Diagram: Summary
Control system
(X: state variable)I
I: a vector of inputs
O: a vector of outputs
X: a vector of state variablesI and O are in general function of X. In a special
case, O=X or I=X.
O
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State Diagram: Summary
1. State diagram involves logical variables that take 0 or 1 as theirvalues. State diagram has nodes and edges.
2. Each edge represents one cause or event for the state change inthe corresponding nodes. The cause is also a representation of thelogical variables. For instance, in Fig. 7, the cause can be writtenas: X2=1 and LLS =0.3. The state diagram has some limitation to express the meaning ofthe desired control action.
A formal way or mathematical way to represent the meaning:
If X2=1 AND LLS=0, X1 changes from 0 to 1. This desire
leads us to think of Boolean algebra. The idea is to think
another way to represent the controller or control system.
The next will discuss Boolean algebra.
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Boolean Logic Equations
Boolean Logic Equations
Let A and B be binary variables; that is, A, B=0, or 1.
When A =1 (B=1) means that A is true (resp., B is true).A =0 (B=0) means that A is false (resp., B is false).
(1) A+B means that either A or B is true
A+B=0 when A=0 and B=0
A+B=1 otherwise
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Boolean Logic Equation
(2) AB means that both A and B are true
AB=1 when A=1 and B=1
AB=0 otherwise
(3) Not operation, byA
1A
0A
when A=0
when A=1