# Logic Control

## Introduction

The basic form of logic control arises from the analysis of the operating mechanism of the controller, and the resulting control rules can be logically described by a pan-Boolean algebra.

The stability of the system can be analyzed by the deviation of the language trajectory consisting of nine points on the deviation change graph.

The difference between logic control, traditional control and fuzzy control is:

The traditional control theory is based on differential equations to achieve automatic control;

Both fuzzy control and logical control are based on conceptual control.

The differences between them are:

The fuzzy control is carried out according to the fuzzy set theory proposed by L. A Chad and the corresponding definition operation;

Logical control is performed according to the laws obeyed by the generalized Boolean algebra.

The recurrence law of the fuzzy set is not established, and the remnant law of the generalized Boolean algebra is established;

The definition of non-operations is different in the two systems.

The difference between logic control and fuzzy control with correction factor is:

One uses mathematical analytic expressions to represent control rules or output responses, while the other uses a semi-boolean algebraic expression to represent control rules or output responses that conform to human thinking.

## Basic logical relationship

Logical “AND” relationship

The logical AND can be compared to the effect of two switches connected in series to power a lamp.

For example, if there are two people who express their opinions on something, they can use this simple voting circuit.

There is a switch in front of each person, and the two switches are connected in series to receive a light.

Only when two people put the switch in the on state, the light will be on.

When the light is on, it means that both A and B agree.

Usually the bathroom and the kitchen share a water heater. Whether [bathing] or “washing the dishes” can make the water heater supply hot water. From the two valves, this is the logical “OR” relationship.

Hot water can be obtained by any of the two conditions, not necessarily all.

Logical OR relationship

The logical “OR” relationship can also be compared with the circuit, which is the effect of two switches connected in parallel to the same xenon lamp.

If the switches in front of the two people are connected in parallel, as long as any one of them puts the switch in the on state, the light will be on.

Bright means that at least one of A and B agrees (maybe both agree).

Logical “Non” relationship

In addition, there is a logical “non-” relationship, then it is not meant.

As long as the definition of a certain condition is reversed, it means “no”.

For example [no fire extinguishing] is “non” [extinguishing].

Then, [stop water] is also “not” [no water stop].

For the circuit, the [pass] and [off] of the switch are reversed, and it becomes a “non-” relationship.

This binary logic is ubiquitous in nature.

## Control System

The basic form of logic control arises from the analysis of the operating mechanism of the controller, and the resulting control rules can be logically described by a pan-Boolean algebra.

Logical control is performed according to the laws obeyed by the generalized Boolean algebra.

A control system is a management system consisting of a control subject, a control object, and a control medium with its own goals and functions.

The control system means that it can hold and change any amount of interest or variable within a machine, mechanism or other device in the desired manner.

The control system is also implemented to bring the controlled object to a predetermined ideal state.

The control system causes the controlled object to tend to a desired steady state.

## There are several classification methods for control systems

1. According to different control principles, the automatic control system is divided into open loop control system and closed loop control system.

Open loop control system

In the open-loop control system, the system output is only controlled by the input, and the control accuracy and the characteristics of suppressing interference are relatively poor.

In an open-loop control system, a logic control based on timing is called a sequential control system;

It consists of a sequence control device, a detection component, an actuator, and a controlled industrial object.

Mainly used in the control of machinery, chemicals, material handling and transportation processes, as well as robots and production automation lines.

Closed loop control system

The closed-loop control system is based on the feedback principle. By using the deviation of the output and the expected value to control the system, better control performance can be obtained.

The closed loop control system is also called the feedback control system.

1. According to the classification of given signals, the automatic control system can be divided into constant value control system, follow-up control system and program control system.

Constant value control system

The set value is constant, and the system output is required to approach the system with the desired value with a certain precision.

For example, the automatic control system such as temperature, pressure, flow rate, liquid level and motor speed in the production process belongs to a constant value system.

Follow-up control system

The given value changes as a function of the unknown time, requiring the output to follow the change in the given value.

Such as the radar antenna system that follows the satellite.

Program control system

The given value changes as a function of time.

Such as program-controlled machine tools.

## Basic logic control

There are many types of logic control, such as fuzzy logic control, basic logic control, and combinational logic control.

Here is a brief introduction to basic logic control.

The basic logic control is generated from the analysis of the operating mechanism of the controller of the single loop control system in the classical control theory.

It is based on the control of the generalized Boolean algebra, which is a two-dimensional logic control that is controlled according to the deviation of the controlled parameters of the system and the variation of the deviation.

The control based on the generalized Boolean algebra is derived from fuzzy control.

It abstracts the logical relationship of the system according to people’s control experience and intuitive thinking, and then abstracts this thinking process, using symbols to classify the input variables and influencing factors of the system according to the production experience, based on the theory of pan-Boolean algebra. , to derive a set of logical expressions describing the system.

Then use the formula of the general logic diagram or the multi-boolean algebra to simplify the logic expression, and obtain a simplified logic control rule with clear causal relationship and obvious logic meaning.

It can handle many control problems in industrial production, especially systems with multiple variables and multiple influencing factors, and the mathematical model of the system is difficult to determine.

According to the nine cases of variation of deviation and deviation, five kinds of control rules that vary with the output of the system in the vicinity of the expected value are formed to form a basic logic controller.

Its essence is to imitate human thinking and macroscopic behavioral functions.

The basic idea of basic logic control is to use the computer to simulate human logic thinking and imitate human control behavior in the control process, and to identify the feature information provided by the dynamic characteristics of the control system as much as possible.

After inference, the control strategy is determined or transformed online to effectively control the object lacking the mathematical model.

In order to better simulate human logical thinking, imitate human control behavior, and use computer technology to achieve logic control, more variables must be sought to describe the dynamic characteristics of the control system.  