lecture note 7 discrete event control1 discrete event control contents 1. introduction 2. state...

Lecture note 7 discrete event control 1

Discrete Event Control

CONTENTS

1. Introduction

2. State Diagram

3. Boolean Logical Equation


Discrete Event Control

Concept

Representation

DEC controller design

DEC controller implementation


Discrete Event Control: introduction

DEC: All control variables are discrete variables, and their change is

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.

Figure 1DiscreteEventControl system


Figure 2

Introduction

Figure 3

Level Limit Switch LLS

Controller Input valve Tank

Level of Water


We need a method to represent system dynamics, i.e. control system (including both plant and controller).

However, in a discrete event driven system, plant (transient) dynamics is ignored. This means that when the valve is open, the water level seems to rise to a level instantly.

Therefore, the control system for a discrete event driven system reduces to the controller only.

goal controller plant plant output

State and state diagram is the method to represent system dynamics.

Introduction


State Diagram States: indicators that system changes

State Variables: assign a name to each independent class of states.

EX 1: Switch. The switch is a state variable. It has two states (1, 0),

where 1=on and 0=off.

State change has a cause.

State diagram (Fig. 4, Fig. 5) represents the state change with cause;I

n 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


State diagram

Example system

Figure 4

Figure 5


State Diagram

System has input, output, and itself.

Fluid is a part of the system or total system.

System itself includes components, e.g., valve, pump.

System itself is represented by a set of state variables.

The total system has fluid and device, and the device manipulates the fluid.

Level of the fluid in the tank is the output of the plant (e.g., tank) or the plant control system (including both the plant and controller) and the input to the controller.

In the time continuous system, the goal or reference variable such as L (in the tank example) is an input to the control system, while the level of the fluid is the output of the control system.


State Diagram: how to identify the state variable

Control system(X: state variable)

Level of fluid: LLS

Remain to see what is X and what is the output (to controller).


State Diagram


Level of fluid: LLS

X: state variable: valve.

Output (for controller): X as well.

So we have: output = state variable of the system


State Diagram

It is noted that the two circles represent different states of one 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:

Pump


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


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 the tank 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 and LLS=0, or keep

the pump on if it is already on and the valve is open and LLS=0.

4. Turn the pump off if it is on and LLS=1, or keep the pump off if

LLS=1.


State Diagram

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.


State Diagram

Figure 6

Put all state variables of the system in one circle


State Diagram

Fig. 7 shows another way to represent the state diagram

for EX 2. The features of Fig. 7 are:

Each node represents one state variable with its value or

state.

A state variable can be the cause of changes for other

state variables.


State Diagram

Fig. 7

Remark:

The meaning that the pump can never be on if the valve is closed is not represented by the state diagram.

This shows a limitation of the state diagram


State Diagram


Level of fluid: LLS

X1: state variable: pump

X2: state variable: valve

Output (for controller): X1, X2

So we have: output = state variable


State Diagram: Summary


I

I: a vector of inputs (for controller)

O: a vector of outputs (for controller)

X: a vector of state variables

I and O are in general function of X. In a special case, O=X or I=X.

O


State Diagram: Summary

1. State diagram involves logical variables that take 0 or 1 as their values. State diagram has nodes and edges.

2. Each edge represents one cause or event for the state change in the corresponding nodes. The cause is also a representation of the logical variables. For instance, in Fig. 7, the cause can be written as: X2=1 and LLS =0.

3. The state diagram has some limitation to express the meaning of the 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 of another way

to represent the controller or control system.


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).


Boolean Logic Equation – operational property

1. A+B means that either A or B is true. Examples: A+B=0 when A=0 and B=0. A+B=1 otherwise.

2. AB means that both A and B are true. Examples: AB=1 when A=1 and B=1. AB=0 otherwise.

3. Not operation, by A

1A

0A

when A=0

when A=1

lecture note 7 discrete event control1 discrete event control contents 1. introduction 2. state...

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