Stochastic controlStochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise.
State-transition matrixIn control theory, the state-transition matrix is a matrix whose product with the state vector at an initial time gives at a later time . The state-transition matrix can be used to obtain the general solution of linear dynamical systems. The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form where are the states of the system, is the input signal, and are matrix functions, and is the initial condition at .
Adaptive controlAdaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.
Variable capacitorA variable capacitor is a capacitor whose capacitance may be intentionally and repeatedly changed mechanically or electronically. Variable capacitors are often used in L/C circuits to set the resonance frequency, e.g. to tune a radio (therefore it is sometimes called a tuning capacitor or tuning condenser), or as a variable reactance, e.g. for impedance matching in antenna tuners. In mechanically controlled variable capacitors, the distance between the plates, or the amount of plate surface area which overlaps, can be changed.
H-infinity methods in control theoryH∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. H∞ techniques have the advantage over classical control techniques in that H∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of H∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled.
Robust controlIn control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors. The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness, prompting research to improve them.
Nonlinear controlNonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, feedforward, or signal filtering. The system to be controlled is called the "plant".
Phase detectorA phase detector or phase comparator is a frequency mixer, analog multiplier or logic circuit that generates a signal which represents the difference in phase between two signal inputs. The phase detector is an essential element of the phase-locked loop (PLL). Detecting phase difference is important in other applications, such as motor control, radar and telecommunication systems, servo mechanisms, and demodulators. Phase detectors for phase-locked loop circuits may be classified in two types.
Closed-loop transfer functionIn control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback control loop on the input signal to the plant under control. The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, , or other types of data streams.
Surface acoustic waveA surface acoustic wave (SAW) is an acoustic wave traveling along the surface of a material exhibiting elasticity, with an amplitude that typically decays exponentially with depth into the material, such that they are confined to a depth of about one wavelength. SAWs were first explained in 1885 by Lord Rayleigh, who described the surface acoustic mode of propagation and predicted its properties in his classic paper. Named after their discoverer, Rayleigh waves have a longitudinal and a vertical shear component that can couple with any media like additional layers in contact with the surface.
