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Controllable Pitch Propeller
Controllability is an important property of a control system and plays a crucial role in many regulation problems, such as the stabilization of unstable systems using feedback, tracking problems, obtaining optimal control strategies, or, simply prescribing an input that has a desired effect on the state. Controllability and observability are dual notions. Controllability pertains to regulating the state by a choice of a suitable input, while observability pertains to being able to know the state by observing the output (assuming that the input is also being observed). Broadly speaking, the concept of controllability relates to the ability to steer a system around in its configuration space using only certain admissible manipulations. The exact definition varies depending on the framework or the type of models dealt with. The following are examples of variants of notions of controllability that have been introduced in the systems and control literature: * State controllability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Control System
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation. The control system compares the value or status of the process variable (PV) being controlled with the desired value or setpoint (SP), and applies the difference as a control signal to bring the process variable output of the plant to the same value as the setpoint. For sequential and combinational logic, software logic, such as in a programmable logic controller, is used. Open-loop and closed-loop control Feedback control systems Logic control Logic control systems for indus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Rank (linear Algebra)
In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns. p. 48, § 1.16 This corresponds to the maximal number of linearly independent columns of . This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the " nondegenerateness" of the system of linear equations and linear transformation encoded by . There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics. The rank is commonly denoted by or ; sometimes the parentheses are not written, as in .Alternative notation includes \rho (\Phi) from and . Main definitions In this section, we give some definitions of the rank of a matrix. Many definitions are possible; see Alternative definitions for several of these. The column rank of is the dimension of the column space of , while the row rank of is the dimension of the row space of . A fundamental resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Reachability (controls)
In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s can reach a vertex t (and t is reachable from s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with s and ends with t. In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph. Any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component; therefore, in such a graph, reachability is symmetric (s reaches t iff t reaches s). The connected components of an undirected graph can be identified in linear time. The remainder of this article focuses on the more difficult problem of determining pairwise reachability in a directed graph (which, incidentally, need not be symmetric). Definition For a directed graph G = (V, E), with vertex set V and edge set E, the reachability relation of G is the transitive closur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Zero Dynamics
In mathematics, zero dynamics is known as the concept of evaluating the effect of zero on systems. History The idea was introduced thirty years ago as the nonlinear approach to the concept of transmission of zeros. The original purpose of introducing the concept was to develop an asymptotic stabilization with a set of guaranteed regions of attraction ( semi-global stabilizability), to make the overall system stable. Initial working Given the internal dynamics of any system, zero dynamics refers to the control action chosen in which the output variables of the system are kept identically zero. While, various systems have an equally distinctive set of zeros, such as decoupling zeros, invariant zeros, and transmission zeros. Thus, the reason for developing this concept was to control the non-minimum phase and nonlinear systems effectively. Applications The concept is widely utilized in SISO mechanical systems, whereby applying a few heuristic A heuristic or heuristic tec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Lie Bracket Of Vector Fields
In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X and Y on a smooth manifold M a third vector field denoted ,Y/math>. Conceptually, the Lie bracket ,Y/math> is the derivative of Y along the flow generated by X, and is sometimes denoted ''\mathcal_X Y'' ("Lie derivative of Y along X"). This generalizes to the Lie derivative of any tensor field along the flow generated by X. The Lie bracket is an R- bilinear operation and turns the set of all smooth vector fields on the manifold M into an (infinite-dimensional) Lie algebra. The Lie bracket plays an important role in differential geometry and differential topology, for instance in the Frobenius integrability theorem, and is also fundamental in the geometric theory of nonlinear control systems. V. I. Arnold refers to this as the "fisherman derivative", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Pitch (flight)
An aircraft in flight is free to rotate in three dimensions: ''Yaw (rotation), yaw'', nose left or right about an axis running up and down; ''pitch'', nose up or down about an axis running from wing to wing; and ''roll'', rotation about an axis running from nose to tail. The axes are alternatively designated as ''vertical'', ''lateral'' (or ''transverse''), and ''longitudinal'' respectively. These axes Moving frame, move with the vehicle and rotate relative to the Earth along with the craft. These definitions were analogously applied to spacecraft when the first crewed spacecraft were designed in the late 1950s. These rotations are produced by torques (or Moment (physics), moments) about the principal axes. On an aircraft, these are intentionally produced by means of moving control surfaces, which vary the distribution of the net Aerodynamics, aerodynamic force about the vehicle's center of gravity. Elevator (aeronautics), Elevators (moving flaps on the horizontal tail) produce pi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Yaw (flight)
An aircraft in flight is free to rotate in three dimensions: '' yaw'', nose left or right about an axis running up and down; ''pitch'', nose up or down about an axis running from wing to wing; and ''roll'', rotation about an axis running from nose to tail. The axes are alternatively designated as ''vertical'', ''lateral'' (or ''transverse''), and ''longitudinal'' respectively. These axes move with the vehicle and rotate relative to the Earth along with the craft. These definitions were analogously applied to spacecraft when the first crewed spacecraft were designed in the late 1950s. These rotations are produced by torques (or moments) about the principal axes. On an aircraft, these are intentionally produced by means of moving control surfaces, which vary the distribution of the net aerodynamic force about the vehicle's center of gravity. Elevators (moving flaps on the horizontal tail) produce pitch, a rudder on the vertical tail produces yaw, and ailerons (flaps on the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Aircraft
An aircraft ( aircraft) is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or the Lift (force), dynamic lift of an airfoil, or, in a few cases, direct Powered lift, downward thrust from its engines. Common examples of aircraft include airplanes, rotorcraft (including helicopters), airships (including blimps), Glider (aircraft), gliders, Powered paragliding, paramotors, and hot air balloons. Part 1 (Definitions and Abbreviations) of Subchapter A of Chapter I of Title 14 of the U. S. Code of Federal Regulations states that aircraft "means a device that is used or intended to be used for flight in the air." The human activity that surrounds aircraft is called ''aviation''. The science of aviation, including designing and building aircraft, is called ''aeronautics.'' Aircrew, Crewed aircraft are flown by an onboard Aircraft pilot, pilot, whereas unmanned aerial vehicles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Orientation (rigid Body)
In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement, in which case it may be necessary to add an imaginary translation to change the object's position (or linear position). The position and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its position does not change when it rotates. Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Car Analogy
The car analogy is a common technique, used predominantly in engineering textbooks, to ease the understanding of abstract concepts in which a car, its composite parts, and common circumstances surrounding it are used as analogs for elements of the conceptual systems. The car analogy can be seen elsewhere, in textbooks covering other subjects and at various educational levels, such as explaining regulation of human temperature. Uses of car analogies The efficiency of car analogies reside on their capacity to explain difficult concepts (usually due to their high abstraction level) on more mundane terms with which the target audience is comfortable, and with which many also have a special interest. Due to that, car analogies appear more often on works related to applied sciences and technology. In order to work, car analogies translate agents of action as the car driver, the seller, or police officers; likewise, elements of a system are referred as car pieces, such as wheels, motor, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Line (geometry)
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray (optics), ray of light. Lines are space (mathematics), spaces of dimension one, which may be Embedding, embedded in spaces of dimension two, three, or higher. The word ''line'' may also refer, in everyday life, to a line segment, which is a part of a line delimited by two Point (geometry), points (its ''endpoints''). Euclid's Elements, Euclid's ''Elements'' defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of geometry was established. ''Euclidean line'' and ''Euclidean geometry'' are terms introduced to avoid confusion with generalizations introduced since the end of the 19th century, such as Non-Euclidean geometry, non-Euclidean, Project ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Linearly Independent
In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space. Definition A sequence of vectors \mathbf_1, \mathbf_2, \dots, \mathbf_k from a vector space is said to be ''linearly dependent'', if there exist scalars a_1, a_2, \dots, a_k, not all zero, such that :a_1\mathbf_1 + a_2\mathbf_2 + \cdots + a_k\mathbf_k = \mathbf, where \mathbf denotes the zero vector. This implies that at least one of the scalars is nonzero, say a_1\ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |