Chapter 1: Feedback

An example of feedback is when the outputs of a system are used as inputs for the same system, creating a circuit or loop as part of a chain of cause-and-effect relationships. When this happens, we might say that the system feeds back onto itself. When considering feedback systems, it is important to use caution when dealing with the concept of cause and effect:

Reasoning about simple causal relationships in a feedback system is challenging because the first system impacts the second system, and the second system effects the first system, which results in a circular argument. Because of this, using reasoning that is based on cause and effect may be difficult, and it is essential to investigate the system as a whole.

-?Karl Johan Åström and Richard M.Murray, Feedback Systems: An Introduction for Scientists and Engineers

The concept of feedback had begun to enter economic theory in Britain by the 18th century, but at that time, it was not recognized as a universal abstraction, and as a result, it did not have a name. Self-regulating mechanisms have been around since antiquity, and they began to enter economic theory in Britain.

Since the 17th century, centrifugal governors have been used in windmills in order to manage the distance and pressure between the millstones. Following a recommendation from his business colleague Matthew Boulton, James Watt created his first centrifugal governor in the year 1788. This particular governor was intended for use in the steam engines that they produced. The earliest steam engines utilized a motion that was solely reciprocating, and they were utilized for pumping water. This was an application that was able to tolerate variations in the working speed; however, the utilization of steam engines for other applications required more precise control of the speed.

James Clerk Maxwell published the influential work "On governors" in 1868. This study is now generally regarded as a classic in the field of feedback control theory. This study made a seminal contribution to the fields of control theory and the mathematics of feedback.

As early as the 1860s, people in the United States were already using the verb phrase "to feed back," which means "to return to an earlier point in a mechanical process.", The study of circular causal feedback systems was at the heart of the progression of cybernetics from the 1940s forward.

There has been substantial debate throughout the course of time over which definition of feedback is the most accurate. According to the cybernetician Ashby (1956), mathematicians and theorists who are interested in the principles of feedback systems favor the notion of "circularity of action," as it maintains the theory's simplicity and consistency. [Citation needed] Feedback should be a purposeful impact for individuals who have more practical goals, and it should come through a link that is more palpable.

[Those Who Engage in Practical Experimentation] Take Issue With the Mathematicians' Definition, pointing out that this would need them to admit that feedback was there in the conventional pendulum would be one way to do this.

between its location and its momentum-a "feedback" that is created between the two, from the standpoint of actual application, is a little bit mysterious.

In response to this, the mathematician retorts that if feedback is only deemed to be there when there is a physical wire or nerve to represent it, then this argument is invalid, then the theory becomes chaotic and riddled with irrelevancies.:?54?

Ramaprasad (1983), who focuses on the applications of feedback in management theory, defines it in a generic sense as "...knowledge concerning the gap between the actual level and the reference level of a system parameter" that is used to "change the gap in some manner." He stresses the point that the information in and of itself does not constitute feedback until it is acted upon.

Positive feedback is the term used to describe the situation in which the signal that is fed back from the output is in phase with the signal that is being fed in.

Negative feedback: If the signal feedback is of opposite polarity or out of phase by 180° with respect to input signal, The term for this kind of input is "negative feedback.".

The graphic might illustrate a cruise control system in a vehicle, for instance, that matches a goal speed such as the speed limit. This would be an illustration of negative feedback. The automobile itself serves as the controlled system, and its inputs include not just the torque produced by the engine but also the gradient of the road as it changes (the disturbance). A speedometer is used to determine the current speed of the vehicle. The deviation of the actual speed from the desired speed, as determined by the speedometer, is the source of the error signal (set point). This measured mistake is evaluated by the controller, which then commands the accelerator to be adjusted, which in turn commands the engine to receive more gasoline (the effector). The feedback, which is the ensuing change in engine torque, interacts with the torque that is exerted by the changing road grade to decrease the error in speed, so reducing the disruption to the road.

Before World War II, the concepts of "positive" and "negative" feedback were initially used to the phenomenon. In the 1920s, when the regenerative circuit was first developed, the concept of positive feedback was already well-established in the scientific community. The groundbreaking work that first detailed the use of negative feedback in electronic amplifiers was completed in 1934 by Harold Stephen Black. According to the claims of Black:

The gain of the amplifier is increased by positive feed-back, whilst the gain is decreased by negative feed-back.

According to Mindell (2002), there was an increase in ambiguity over the terminology not long after this:

...Friis and Jensen had drawn the same difference between "positive feed-back" and "negative feed-back" as Black had made, depending not on the sign of the feedback in and of itself, but rather on the influence that it has on the gain of the amplifier.

In contrast, Nyquist and Bode, when they developed their ideas based on Black's work, referred to the phenomenon as "something with the sign inverted" when discussing negative feedback.

Black had trouble convincing others of the utility of his invention in part because confusion existed over basic matters of definition.:?121?

Even before the terms were applied, James Clerk Maxwell described several different kinds of "component motions" associated with the centrifugal governors that were used in steam engines. He differentiated between those that lead to a continual increase in a disturbance or the amplitude of an oscillation, and those that lead to a decrease of the same. This was done even before the terms were applied.

The phrases "positive feedback" and "negative feedback" are defined differently depending on the field of study one looks at.

the modification of the difference between the reference value and the actual value of a parameter, depending on whether or not the difference is growing (positive) or shrinking (negative) (negative).

the emotional connotation that the action or result that narrows the gap has on the receiver or observer, either in terms of being pleased (with a positive connotation) or dissatisfied (with a negative connotation). However, even within a single field, an example of feedback might be labeled either positive or negative, depending on how values are assessed or referenced. [Case in point:].

This misunderstanding could occur due to the fact that feedback can serve either an informative or a motivating function, and it often consists of both a qualitative and a quantitative component. According to Connellan and Zemke's (1993) definition of it:

The quantitative input we get informs us how many and how many of anything there are.

The qualitative comments let us know how well we're doing, bad or indifferent.:?102?

Many feedback looped systems cannot be simply labeled as either positive or negative. This is particularly the case when there are numerous feedback loops present in the system. While basic systems may sometimes be defined as being of one or the other kind, this is not always the case.

When there are simply two components coupled together in such a way that they influence one another, Important and relevant information on the qualities of the whole may be gleaned from the properties of the feedback.

When the number of pieces, however, increases to even as little as four,, if the actions of each one have an effect on the other three, If so, then twenty different circuits may be found inside them; and knowing the properties of all the twenty circuits does not give complete information about the system.:?54?

Positive and negative feedback may be dominant at various frequencies or different places in the state space of a system. In general, feedback systems can have multiple signals given back, and the feedback loop usually contains combinations of positive and negative feedback.

Bipolar feedback is a word that was made up to describe biological systems in which both positive and negative feedback systems may interact with one another. This means that the output of one system can impact the input of another system, and vice versa.

Some feedback systems may exhibit highly complicated behaviors, such as chaotic behaviors in non-linear systems. Other feedback systems, on the other hand, have considerably more predictable behaviors, such as those utilized in the construction and design of digital feedback systems.

Digital...