Nonlinear systemIn mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
State-space representationIn control engineering, model based fault detection and system identification a state-space representation is a mathematical model of a physical system specified as a set of input, output and variables related by first-order (not involving second derivatives) differential equations or difference equations. Such variables, called state variables, evolve over time in a way that depends on the values they have at any given instant and on the externally imposed values of input variables.
Nonlinear filterIn signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage R(t) at any moment is the square of the input voltage r(t); or which is the input clipped to a fixed range [a,b], namely R(t) = max(a, min(b, r(t))).
Linear approximationIn mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that where is the remainder term.
Binomial approximationThe binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that It is valid when and where and may be real or complex numbers. The benefit of this approximation is that is converted from an exponent to a multiplicative factor. This can greatly simplify mathematical expressions (as in the example below) and is a common tool in physics. The approximation can be proven several ways, and is closely related to the binomial theorem.
Single-input single-output systemIn control engineering, a single-input and single-output (SISO) system is a simple single-variable control system with one input and one output. In radio, it is the use of only one antenna both in the transmitter and receiver. SISO systems are typically less complex than multiple-input multiple-output (MIMO) systems. Usually, it is also easier to make an order of magnitude or trending predictions "on the fly" or "back of the envelope". MIMO systems have too many interactions for most of us to trace through them quickly, thoroughly, and effectively in our heads.
Linear systemIn systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.
Mixing (process engineering)In industrial process engineering, mixing is a unit operation that involves manipulation of a heterogeneous physical system with the intent to make it more homogeneous. Familiar examples include pumping of the water in a swimming pool to homogenize the water temperature, and the stirring of pancake batter to eliminate lumps (deagglomeration). Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components or phases. Modern industrial processing almost always involves some form of mixing.
Continuous stirred-tank reactorThe continuous stirred-tank reactor (CSTR), also known as vat- or backmix reactor, mixed flow reactor (MFR), or a continuous-flow stirred-tank reactor (CFSTR), is a common model for a chemical reactor in chemical engineering and environmental engineering. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. The mathematical model works for all fluids: liquids, gases, and slurries.
Chemical reactorA chemical reactor is an enclosed volume in which a chemical reaction takes place. In chemical engineering, it is generally understood to be a process vessel used to carry out a chemical reaction, which is one of the classic unit operations in chemical process analysis. The design of a chemical reactor deals with multiple aspects of chemical engineering. Chemical engineers design reactors to maximize net present value for the given reaction.
Anti-tank warfareAnti-tank warfare originated from the need to develop technology and tactics to destroy tanks during World War I. Since the Allies deployed the first tanks in 1916, the German Empire developed the first anti-tank weapons. The first developed anti-tank weapon was a scaled-up bolt-action rifle, the Mauser 1918 T-Gewehr, that fired a 13.2 mm cartridge with a solid bullet that could penetrate the thin armor of tanks of the time and destroy the engine or ricochet inside, killing occupants.
TankA tank is an armoured fighting vehicle intended as a primary offensive weapon in front-line ground combat. Tank designs are a balance of heavy firepower, strong armour, and good battlefield mobility provided by tracks and a powerful engine; usually their main armament is mounted in a turret. They are a mainstay of modern 20th and 21st century ground forces and a key part of combined arms combat.
