Feedback

• Type of physical science: Feedback, Electromagnetism, Electrical circuits, Amplification, Classical physics
• Field of study: Electromagnetism

Feedback is the technique or process by which a part of the output of a system is added to the system's input. If the signal fed back subtracts from the system input, it is called "negative" feedback and results in more predictable control or improved performance of the system. If it adds to the system input, the resulting "positive" feedback could result in oscillations or system instability. In effect, feedback results in a closed-loop system in which cause and effect have a mutual dependence.

Overview

Feedback is one of the most fascinating concepts of technology, dating back centuries. Historical examples include the use of floating valves to cause automatic draining of Roman aqueducts, the Japanese use of hydraulic oscillators to ward off birds from fields, and the employment of axle vanes to detect wind direction and orient windmills in seventeenth century Holland. Feedback is also an inherent part of many nonphysical systems, encompassing fields as varied as biology, human physiology, political economy, and sociology. For example, in his classic 1776 treatise Inquiry into the Nature and Causes of the Wealth of Nations, Adam Smith provided three examples of well-defined social-feedback mechanisms: wages, population, and general supply and demand. The concept of feedback is also implicit in the process of natural selection, by which nature checks and corrects irregularities and deficiencies before they reach conspicuous levels. On another basic level, feedback is an essential element in human communications to minimize misunderstanding or "noise" (it should be noted, however, that the popular connotations of "positive" and "negative" in this context differ from the definitions that follow; true negative feedback, for example, involves self-correction, not merely a reaction or response).

The evolution of tools proceeded from simple mechanical devices such as the wheel and the lever to powered machines that do not require human strength to operate. The control of the latter still required human intervention, until techniques were developed for true automation. An early example of a programmable machine was the automatic loom devised by Joseph-Marie Jacquard in 1801. In this machine, holes punched in steel plates—much like the punched cards used in the early days of the digital computer—determined the complex textile patterns. A major advance in automation occurred at the beginning of the Industrial Revolution with James Watt's incorporation of the flyball governor in his steam engine. The governor was connected to the engine shaft and operated by increasing or decreasing the steam inlet valve opening in response to any drop or rise in engine speed as a result of load changes, thereby maintaining a constant speed without recourse to continual manual adjustment. Numerous inventions followed, but they invariably lacked adequate theoretical understanding of the concept involved. The first mathematical formulation of feedback systems might be traced to James Clerk Maxwell's 1868 analysis of the flyball governor. The true beginnings of modern automatic feedback control theory, however, had to await developments in electronics early in the twentieth century.

A pioneer in recognizing the importance of feedback was Harold Black of Bell Labs, who was hard at work developing circuit techniques to reduce the distortion of signals in telephone repeaters. Repeaters are electronic amplifiers introduced periodically in telephone lines—such as the then-newly installed transcontinental link between New York and San Francisco—to compensate for transmission losses. Yet, these early amplifiers based on vacuum tubes also distorted the voice signals considerably as a result of the non-ideal characteristics of these "active" or amplifying devices. On one of his morning ferry crossings to work in 1927, Black came up with the idea of feeding back a part of the output electrical signal to the input such that it subtracted from the input. The elementary block diagram and the equation he wrote down on the margins of his morning newspaper still constitute the basis of a general feedback system. Dramatic improvements in the performance of electronic amplifiers resulted from the application of Black's idea, and World War II accelerated the development of feedback control systems with simultaneous advances in theory. Black himself was quick to recognize the general applicability of his feedback concept, so much so that his first patent cited as many as 164 applications. Incidentally, the use of the term "negative feedback" to describe this automatic control process began with this early work of Black and fellow engineers at Bell Labs.

The influence of feedback on system performance can be readily understood using the schematic block diagram shown above for an electronic amplifier. The diagram consists of two elements or blocks: a forward element containing an active or amplifying device (for example, a vacuum-tube or transistor amplifier) with a gain A, and a feedback element B that attenuates the output before it adds it to the system input via a comparator or summing junction. The amplifier multiplies the signal at its input by gain A, where A is much greater than 1; but A is not a constant and is sensitive to power-supply voltages, temperature, and aging of components. In contrast, the feedback element is only an attenuator (that is, B is less than 1) and hence can be built of highly precise "passive" components such as electrical resistors. By summing up the components on the input side (that is, Input minus B times Output), it can be readily shown from the diagram that the overall gain of the system with feedback Afb is given by.

Here the output and input may represent electrical voltages or currents. If A and B are both positive numbers, the feedback shown represents negative feedback since the signal fed back subtracts from the control input. If the "loop-gain" AB is much greater than unity, then the unity term in the denominator can be neglected, and now Afb = (A/AB) = (1/B), independent of A. Since B is a precise constant by design, a primary result of negative feedback has been gain stability, regardless of fluctuations in the gain A of the active element.

The schematic block diagram (Figure 1) illustrated above may represent not simply an electronic amplifier but any control system—electrical, mechanical, electromechanical, hydraulic, or a combination of these. The achievement of a precise gain with negative feedback means that the actual output of the system—say, the turning of the wing flaps of an airplane, or the speed of an automobile under cruise control—will be very nearly the desired output. In contrast, an "open-loop" system with only the amplifier A (and no feedback B) would exhibit considerable deviation of the actual output from the desired value as well as possible drift (change with time) as a result of the variability of A. An example of an open-loop system is the Jacquard loom referred to above, in which there is no provision for correcting any discrepancy between the design template and the actual patterns formed on the fabric.

Negative feedback has other useful effects in addition to constancy of gain. Any disturbances occurring in the system, such as noise or signal distortion showing up on the output side of the amplifier, will also be fed back negatively to the input, thereby canceling out a great part of the disturbance. Examination of the above equation will show that noise and distortion will be reduced by the factor (1 + AB) relative to an equivalent system without feedback. Thus, the fidelity of the amplified signal is improved--the effect sought by Black for his telephone repeater amplifiers. Another important consequence of negative feedback is increased speed of response or bandwidth, again by the factor (1 + AB). Thus, the loop gain (the product AB) is an important index of performance of a feedback control system and in general should have values much greater than unity.

Most practical feedback systems are more complex than that illustrated in Figure 1 and have multiple blocks, inputs, and outputs. There may also be several feedback loops incorporated within a system. In addition, the blocks may have terms that depend on frequency, temperature, and other parameters. A variety of elegant mathematical techniques have been developed to analyze the stability and speed of response of feedback systems, as well as to improve them by suitable incorporation of compensator elements. In spite of all the complexity, the basic motive behind negative feedback remains the same: self-correction or self-regulation for improved performance.

Feedback control system theory and practice have evolved well beyond the simple regulation of speed in James Watt's steam engine. Among the advances are optimal control, adaptive control, and artificial intelligence. The former two deal with the added task of defining an appropriate index of performance for the process of interest, and then operating in such a manner as to optimize the performance. Adaptive control has the further feature that it operates under conditions of continuously changing and unpredictable environment, which must be constantly monitored with separate sensors and a suitably tailored control strategy. In effect, this means that the parameters of the control system blocks (such as A and B in Figure 1) themselves will have to change or "adapt" to the specific operating conditions. Artificial intelligence in control deals with programming a computer so that it exhibits characteristics commonly associated with human reasoning, in effect creating a pseudo-human interface in the feedback process. Parenthetically, one may think of human interference in an open-loop system as completing the loop through a feedback process. Yet, the timescale of human reflexes (typically fractions of a second) is much longer than that of electronic (billionths of a second or shorter) and other components, so an automatic control system invariably offers performance unmatched by purely human control.

The systems discussed so far involve signals that are continuous, or "analog." With the rapid strides made by computer processors and memory chips, computation is no longer an expensive proposition, so a single digital controller can replace several analog ones. Computer terminals and keyboards now replace knobs and meters, systems have also become very flexible, since changing system parameters involves nothing more than altering a computer's instructions (or "rewriting the software"). The home thermostat may be thought of as a simple digital control system, as it operates on an on/off basis depending on the fluctuations in room temperature above and below the setting.

It is also possible to have systems in which the feedback is positive, that is, the signal fed back is added to the input. This sets up a regenerative process in which any disturbance increases the signal fed back, which then increases the output and again raises the fed-back signal, and this process causes instability. Positive feedback is thus undesirable for system control. However, positive feedback can be used to generate repetitive waveforms, such as a sinusoidal alternating voltage or current; a system designed with such an intent is called an "oscillator." An oscillator operates with the AB product set to -1, so that the gain Afb becomes infinity; in effect, there is an output with no input. This is the very function of an oscillator or waveform generator. A laser is another example; lasers employ positive optical feedback to generate coherent radiation.

Applications

Feedback control systems abound in all facets of modern life. The home thermostat is an elementary example, with a bimetallic strip (welded or bonded strips of two different metals having different thermal expansion) that bends in response to a temperature rise in the room and opens an electrical contact once the set temperature is reached. The heating source—electric or gas—is now turned off, and the thermal inertia of the room keeps the temperature around the desired value. When the temperature drops again as a consequence of the inevitable loss of heat, the bimetallic strip bends in the opposite direction and closes the electrical contact, thereby turning on the heat source. Note that the error signals involved here are of the on/off type, so the basic thermostat is an example of what is called a discrete-time feedback control system.

Radio and television receivers have feedback built in for a variety of reasons. Since the strength of the radio or video signal received by the antenna can fluctuate greatly, an automatic gain control (AGC) circuit is built into most receivers to avoid annoying fluctuations or "fading." Feedback is also included in the output power stages of amplifiers to reduce distortion as described earlier. More sophisticated feedback techniques are used in instrumentation and measurements for synthesis of oscillations of precise frequency (phase-locked loop or PLL) and recovery of very low-level signals buried in noise.

Feedback is also widely used in many home and office machines, for example to position a digital-computer magnetic-storage tape under the recording/reading head or to position a read-out laser beam over the grooves etched on a compact disc. An interesting biomedical application intended for diabetics is an implanted automatic insulin-delivery system that monitors blood-sugar variations with time and injects the right amount of insulin into the body.

The automobile is another domain in which there is increasing use of feedback control. Cruise control and interior climate-control systems are elementary examples, but more sophisticated schemes involve the use of "active" suspensions whereby the stiffness of the material is automatically adjusted according to the terrain, thus offering a smoother ride. This is an example of adaptive control, in which the system parameters themselves are set by first sensing the environment.

Modern aviation and space exploration would be impossible without control and guidance systems, though at a level of sophistication much higher than in a home appliance. In these and large industrial applications including robotic control, the proper execution of a function requires error-sensing feedback. Such systems, classified as "servomechanisms," may include digitally controlled machine tools, satellite-tracking antennas, automatic navigation systems, and antiaircraft gun-control systems. The feedback block diagram holds for servomechanisms also, but now the input represents the control or command signal, such as the desired position of an antenna, while the fed-back signal represents the actual position. Any difference between the two becomes an "error" signal that is amplified to correct the actual position of the controlled device. It is important to note that there will always be a finite but tiny error signal in a servo system.

Feedback can also be employed to cancel out unwanted signals or noise. For example, active suppression of ambient noise can be achieved by first picking up the noise with a microphone as an input and then inverting it before feeding to the loudspeaker. The original noise and that out of the speaker are now out of phase, or cancel each other. Such active sound mufflers are of great value to people who have to work in noisy environments. A similar system is also in use for suppressing mechanical vibration, as needed in instruments such as the scanning tunneling microscope that provides atomic-scale resolution.

Future evolution of feedback control points toward the development of the so-called "smart" or responsive structures and materials that, in a manner analogous to that of living organisms, adjust their properties in response to the environment as well as external input. This is accomplished by linking the electrical, mechanical, magnetic and other physical properties of these materials. For example, piezoelectric materials generate an electrical voltage in response to mechanical pressure, and vice versa, so they can be used to fabricate sensors and actuators in situ. In effect, the material itself constitutes a tailored feedback-control system. Applications include "smart skins" on aircraft surfaces for effective control of turbulence.

Context

One might wonder how the seemingly simple concept of negative feedback offers so much in the design of automatic control systems. The improvements in performance are truly spectacular, yet it should not be construed that something is obtained for nothing. The feedback equation clearly shows that the closed-loop gain Afb is much less than the open-loop gain A. There is thus a big drop in the control gain of the system, but what is achieved in this trade-off is gain stability; a large, variable gain is sacrificed for a low but constant gain. The attendant increase in the bandwidth of the system means that feedback does not alter the gain-bandwidth product, which, rather than gain itself, is a true figure of merit for comparing different systems.

Feedback, apart from being a designed-in effect in human-made control systems, also occurs in nature. The ability of a threatened animal to respond with multiple physical changes—the "fight or flight" reaction—involves automatic changes in the organism's endocrine system. The adaptive response of animals to malnutrition, in which the thyroid secretion is lowered to reduce the metabolic rate and hence the energy intake, is another example. Yet another instance occurs in the field of enzymology, in which the catalytic activity of an enzyme is inhibited by a product of the reaction sequence. This feedback inhibition mechanism prevents the accumulation of the product in a cell beyond an optimal amount. Once the product has been utilized or broken down, the reaction resumes.

On the atomic level, the transport of free electrons in a crystalline solid is influenced by the periodicity of atoms in the lattice. The result is that the electron behaves as if it had an "effective" mass different from the "free-space" mass (mass in vacuum). This could be seen as an instance of naturally occurring feedback interaction with the periodic atomic potential. Often, the effective mass is smaller than the free-space mass, thus improving the speed of response of a solid-state device such as a transistor. More recent advances in semiconductor materials call for synthesis of new structures in which the effective mass is designed in; these are the so-called semiconductor superlattices.

Feedback, in essence, represents a natural or artificial mechanism or process whereby the desired effect or outcome is forced back to constitute a part of the stimulus applied to the system. Self-correction and self-regulation are thus the hallmarks of (negative) feedback.

Principal Terms

CLOSED-LOOP SYSTEM: A system in which the output has an effect on the net input in such a manner as to maintain a desired output value

FEEDBACK FACTOR: The fraction of the output fed back to add to or subtract from the input

FREQUENCY: The number of oscillations occurring during a unit of time; the unit of frequency is hertz (Hz), defined as one oscillation per second

DISTORTION: Undesirable alteration of the shape of a signal; distortion usually results from nonlinear system characteristics

GAIN: The ratio of strength (typically, voltage, current, or power) of the output signal to that of the input signal

INPUT: The stimulus or signal applied to activate a system; in a feedback system, one can distinguish between a reference, or "gross," input applied externally and the "actuating" input, which represents the difference between the reference and feedback signals

NOISE: Any of the naturally occurring fluctuations in physical measurables (such as voltage or current) that interfere with signals

OPEN-LOOP SYSTEM: A system in which the output has no effect on the input

OUTPUT: The response of a system to the input

SIGNAL: Any time-dependent, information-bearing entity such as voltage, current, or displacement

SYSTEM: A combination of components designed to achieve a function not possible with any of the individual parts; a system may be natural or synthesized and can include physical, biological, organizational, and other entities

Bibliography

Bennett, S. A History of Control Engineering, 1800-1930. Peter Peregrinus, 1979.

Bennett, S. A History of Control Engineering, 1930-1955. Peter Peregrinus, 1993.

Kuo, B. C. Automatic Control Systems. 6th ed. Prentice-Hall, 1991.

"Magnetic Force Feedback: Explained." Iris Dynamics, 1 Nov. 2022, irisdynamics.com/articles/magnetic-force-feedback. Accessed 21 Jan. 2025.

Waldhauer, F. D. Feedback. John Wiley & Sons, 1982.