# Logic Control

## Introduction

The foundation of logic control stems from the examination of the controller’s functioning mechanism, and the resulting control rules can be logically represented using Boolean algebra.

The stability of the system can be analyzed through the deviation of the nine-point language trajectory on the deviation change graph.

The distinction between logic control, traditional control, and fuzzy control is as follows:

Traditional control theory relies on differential equations to attain automatic control, while both fuzzy control and logical control are based on conceptual control. The differences between these two are:

Fuzzy control operates based on the fuzzy set theory introduced by L.A. Zadeh and its corresponding definition and operation, while logical control is performed according to the laws of generalized Boolean algebra.

The fuzzy set lacks a recurrence law, while the generalized Boolean algebra has a remnant law, and the two systems have different definitions for non-operations.

The difference between logic control and fuzzy control with a correction factor is that one utilizes mathematical analytical expressions to depict control rules or output responses, while the other uses semi-Boolean algebraic expressions that align with human reasoning to represent control rules or output responses.

## Basic logical relationship

The Logical “AND” Relationship

The logical “AND” can be compared to the functioning of two switches connected in series to power a light. For instance, if two people are expressing their opinions, they can use this simple voting circuit. Each person has a switch and the two switches are connected in series to power the light. Only when both people turn their switches on, the light will turn on. This means that both A and B agree.

An example of the logical “AND” relationship can be seen in the shared water heater used by the bathroom and kitchen. To have hot water, either bathing or washing dishes must be taking place. Both conditions must be met for the water heater to supply hot water.

The Logical “OR” Relationship

The logical “OR” relationship can be compared to the effect of two switches connected in parallel to a xenon lamp. If the switches in front of the two people are connected in parallel, the light will turn on as long as either person turns their switch on. This means that at least one of A and B agrees, or both may agree.

The Logical “Non” Relationship

There is also a logical “non-” relationship, which means the opposite of the defined condition. For example, “no fire extinguishing” is the “non” of “extinguishing.” Similarly, “stop water” is the “non” of “no water stop.” In a circuit, the “pass” and “off” of a switch are reversed, creating a “non-” relationship.

This type of binary logic is present throughout nature.

## Control System

The foundation of logic control comes from analyzing the operating mechanism of the controller and expressing the resulting control rules using Boolean algebra. Logical control follows the laws of generalized Boolean algebra.

A control system is a management system composed of a control subject, control object, and a control medium that serves specific goals and functions. The purpose of a control system is to regulate and adjust any desired variables or quantities within a machine, mechanism, or device.

The control system is designed to bring the controlled object to a desired, ideal state and maintain it at a steady state. By doing so, the control system ensures that the controlled object operates as intended.

## There are several classification methods for control systems

(1) Automatic control systems can be divided into two categories based on different control principles: open loop control systems and closed loop control systems.

Open Loop Control System

In an open loop control system, the output is solely controlled by the input, and its control accuracy and ability to suppress interference is limited. A type of logic control that operates based on timing is called a sequential control system in an open loop control system. It consists of a sequence control device, detection component, actuator, and the industrial object being controlled. This type of control system is mainly used in controlling machinery, chemicals, material handling and transportation processes, as well as robots and production automation lines.

Closed Loop Control System

The closed loop control system operates based on the feedback principle. By using the deviation of the output from the desired value, the system can be better controlled. This type of control system is also referred to as a feedback control system and offers improved control performance compared to the open loop control system.

(2) Automatic control systems can also be classified based on the type of input signal they receive into constant value control systems, follow-up control systems, and program control systems.

Constant Value Control System

In a constant value control system, the set value is constant, and the system is expected to approach the desired value with a certain degree of precision. Examples of this type of control system include temperature, pressure, flow rate, liquid level, and motor speed in the production process.

Follow-up Control System

In a follow-up control system, the input value changes as a function of an unknown time and the system output is expected to follow these changes. An example of this type of control system is a radar antenna system that follows a satellite.

Program Control System

In a program control system, the input value changes as a function of time. Examples of this type of control system include program-controlled machine tools.

## Basic logic control

There are several types of logic control, including fuzzy logic control, basic logic control, and combinatorial logic control. In this brief introduction, we’ll focus on basic logic control.

Basic logic control is derived from the analysis of single loop control systems in classical control theory. It operates based on generalized Boolean algebra, a two-dimensional logic control that adjusts according to deviations in controlled parameters and changes in those deviations.

The control method based on generalized Boolean algebra originates from fuzzy control. It abstracts the logical relationships of the system based on human control experience and intuition. This thinking process is then symbolized to classify input variables and influencing factors of the system, using the theory of pan-Boolean algebra. This leads to a set of logical expressions that describe the system.

The logic expression is then simplified through the use of general logic diagrams or multi-Boolean algebra to produce a simplified logic control rule with clear causality and logic meaning. This approach can effectively handle control problems in industrial production, especially in systems with multiple variables and factors and a difficult-to-determine mathematical model.

By examining the nine cases of deviation and deviation variation, five control rules that vary based on the system’s output near expected values are established to form a basic logic controller. Its aim is to mimic human thinking and macroscopic behavioral functions.

The fundamental principle of basic logic control is to use a computer to imitate human logic and control behavior in the control process. The computer identifies as much feature information from the control system’s dynamic characteristics as possible, and then determines or updates the control strategy online to effectively control objects without a mathematical model.

To better simulate human thinking and control behavior, and to achieve logic control through computer technology, it is necessary to consider more variables to describe the dynamic characteristics of the control system.

Professional Insights