Control theory deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems:
Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument. This makes reasoning based upon cause and effect tricky, and it is necessary to analyze the system as a whole.
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential that is typically 100,000 times larger than the potential difference between its input terminals. Operational amplifiers had their origins in analog computers, where they were used to perform mathematical operations in linear, non-linear, and frequency-dependent circuits.
In electronics and control system theory, loop gain is the sum of the gain, expressed as a ratio or in decibels, around a feedback loop. Feedback loops are widely used in electronics in amplifiers and oscillators, and more generally in both electronic and nonelectronic industrial control systems to control industrial plant and equipment. The concept is also used in biology. In a feedback loop, the output of a device, process or plant is sampled and applied to alter the input, to better control the output. The loop gain, along with the related concept of loop phase shift, determines the behavior of the device, and particularly whether the output is stable, or unstable, which can result in oscillation. The importance of loop gain as a parameter for characterizing electronic feedback amplifiers was first recognized by Heinrich Barkhausen in 1921, and was developed further by Hendrik Wade Bode and Harry Nyquist at Bell Labs in the 1930s.
A Negative-feedback amplifier is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal. The applied negative feedback can improve its performance and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback.
Negative feedback occurs when some function of the output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances.
Positive feedback is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback. Both concepts play an important role in science and engineering, including biology, chemistry, and cybernetics.
In electronics, frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. For a linear system, doubling the amplitude of the input will double the amplitude of the output, and summing two inputs produces an output that is the sum of the two corresponding outputs to the individual inputs. In addition, if the system is time-invariant, then the frequency response also will not vary with time, and injecting a sine wave into the system at a given frequency will make the system respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation.
A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. It is an analog circuit with two inputs and and one output , in which the output is ideally proportional to the difference between the two voltages:
In an open-loop controller, also called a non-feedback controller, the control action from the controller is independent of the "process output", which is the process variable that is being controlled. It does not use feedback to determine if its output has achieved the desired goal of the input command or process "set point".
A feed forward, sometimes written feedforward, is an element or pathway within a control system that passes a controlling signal from a source in its external environment to a load elsewhere in its external environment. This is often a command signal from an external operator.
In electronics engineering, frequency compensation is a technique used in amplifiers, and especially in amplifiers employing negative feedback. It usually has two primary goals: To avoid the unintentional creation of positive feedback, which will cause the amplifier to oscillate, and to control overshoot and ringing in the amplifier's step response. It is also used extensively to improve the bandwidth of single pole systems.
The asymptotic gain model is a representation of the gain of negative feedback amplifiers given by the asymptotic gain relation:
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
In electronic amplifiers, the phase margin (PM) is the difference between the phase lag φ and -180°, for an amplifier's output signal at zero dB gain - i.e. unity gain, or that the output signal has the same amplitude as the input.
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the term, is a specialized flow graph, a directed graph in which nodes represent system variables, and branches represent functional connections between pairs of nodes. Thus, signal-flow graph theory builds on that of directed graphs, which includes as well that of oriented graphs. This mathematical theory of digraphs exists, of course, quite apart from its applications.
Parasitic oscillation is an undesirable electronic oscillation in an electronic or digital device. It is often caused by feedback in an amplifying device. The problem occurs notably in RF, audio, and other electronic amplifiers as well as in digital signal processing. It is one of the fundamental issues addressed by control theory.
Classical control theory is a branch of control theory that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback, using the Laplace transform as a basic tool to model such systems.
Feedforward is the provision of context of what one wants to communicate prior to that communication. In purposeful activity, feedforward creates an expectation which the actor anticipates. When expected experience occurs, this provides confirmatory feedback.
