AUTOMATED SYSTEMS Linear systems 1st lesson 4^ ELT A Multimedia technicians: Lorenzo Bianchini Paolo G. De Maio

Automated processes are regulated by time but, as you know sometimes we will work inside frequency domain

System theory The birth of a mathematical theory capable of analyzing complex systems allowed the field of research to be extended to natural systems Biological systems Economic systems Physics sistems Social systems

What is a system? A portion of reality whose behavior can be described by the evolution along the time of a set of variable quantities (called output) as a function of a set quantities that can be modified from the outside (called input)

From 1st year lessons the following definitions are evolved as follows: System a combination of components that act together to perform a function not possible with any individual parts. The word System is interpreted to include physical, biological, organizational, and other entities which can be represented through a common mathematical symbolism. The formal name system engineering can also be assigned to this definition of the word System. Thus, the study of feedback control systems is essentially a study of an important aspect of systems engineering and its application.

Static and dynamic systems A system is “static” if the outputs depend only on the inputs of the same instant. A system is “dynamic” if the outputs depends not only on the inputs in that very instant, but also on the past inputs, meaning the system has a memory whose description is given by a set of variables called “state”

The art of automatic control systems permeates life in all advanced societies today. Such systems act as a catalyst in promoting progress and development.

One of the earliest automated systems was Hero’s devices for opening the doors of a Temple, the command input was lighting a fire upon the altar

The devices was probably actuated when the Ruler and his entourage started to ascend the Temple steps, and so time was a fundamental variable to calculate obviously we can consider it an open loop system.

Systems in which the output quantity has no effect upon the input quantity are called “Open loop control system” Input output Open loop system

For example, we go to a banquet in, say, 100 BC For example, we go to a banquet in, say, 100 BC. A bowl of wine sits on a center table with a spigot above it. The guests dip wine from the bowl. As the level drops, wine magically begins flowing from the spigot to refill the bowl.   Inside, hidden from view, is a ball-and-cock float-valve, just like the one in your toilet. It's pure feedback control. It senses, compares, and corrects the liquid level by itself, without human intervention.

That sort of thing was common in the Hellenistic world. One of the first feedback devices was the water-clock flow regulator. The 3rd-century BC engineer Ktsebios made the ancient water-clock into an accurate timekeeper by inventing a float stopper to regulate a constant flow of water into the indicator tank.

The concept of self-correction is what democracy is all about. Experience of some ancient Hellenistic engineers bore its fruit after 1800 years. The feedback concept was right at the heart of 18th-century revolution (not only industrial). The concept of self-correction is what democracy is all about. Think about this: The concept of self-correction is what democracy is all about.

Closed loop implies that the action resulting from the comparison between the output quantities and input quantities acts in order to maintain the output at the desired value

James Watt’s flyball governor for controlling speed, developed in 1788, can be considered the first feedback control system not involving human being.

Watt's governor was a superb example of feedback control Watt's governor was a superb example of feedback control. Feedback controllers, mechanisms that sense a discrepancy and correct it, are absolutely shot through our world today. We go through hardly an hour of any day without using feedback devices float valves in our toilets, thermostats in our rooms, pressure-control valves and carburetion electronics in our cars etc.. Water mills flow governor

As you know, the desired performance characteristic of a system, may be specified, for example, in terms of the transient response to a unit step-function input. Last year, we studied basic mathematical tools to analyze systems in time domain (state matrices) and in frequency, or better, complex variable “s” (Laplace transform).

Industrial- process temperature- control system

Industrial- process temperature- control system Ref e Temp Temp G G + + - - H

Industrial- process temperature- control system G H

In general terms: Open loop: Faster requires perfect knowledge about the system Closed loop: Slower can deal with a wide class of problems

In the next two years, while deepening the study of control systems in analog domain, we’ll discover that the two previous sentences are not completely true. The closed loop can cause problems of system instability. We will spend many lessons in analyzing these phenomena in Time or Frequency domain.