Self-exciting Oscillation
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Self-exciting Oscillation
Self-oscillation is the generation and maintenance of a periodic motion by a source of power that lacks any corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefore distinct from forced and parametric resonators, in which the power that sustains the motion must be modulated externally. In linear systems, self-oscillation appears as an instability associated with a negative damping term, which causes small perturbations to grow exponentially in amplitude. This negative damping is due to a positive feedback between the oscillation and the modulation of the external source of power. The amplitude and waveform of steady self-oscillations are determined by the nonlinear characteristics of the system. Self-oscillations are important in physics, engineering, biology, and economics. History of the subject The study of self-oscillators dates back to Robert Willis, George Biddell Airy, James Cle ...
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Self Excited Oscillation
The self is an individual as the object of that individual’s own reflective consciousness. Since the ''self'' is a reference by a subject to the same subject, this reference is necessarily subjective. The sense of having a self—or ''selfhood''—should, however, not be confused with subjectivity itself. Ostensibly, this sense is directed outward from the subject to refer inward, back to its "self" (or itself). Examples of psychiatric conditions where such "sameness" may become broken include depersonalization, which sometimes occurs in schizophrenia: the self appears different from the subject. The first-person perspective distinguishes selfhood from personal identity. Whereas "identity" is (literally) sameness and may involve categorization and labeling, selfhood implies a first-person perspective and suggests potential uniqueness. Conversely, we use "person" as a third-person reference. Personal identity can be impaired in late-stage Alzheimer's disease and in other neu ...
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Philippe Le Corbeiller
Philippe Emmanuel Le Corbeiller (January 11, 1891 – July 24, 1980) was a French-American electrical engineer, mathematician, physicist, and educator. After a career in France as an expert on the electronics of telecommunications, he became a professor of applied physics and general education at Harvard University. His most important scientific contributions were in the theory and applications of nonlinear systems, including self-oscillators. Career in France Son of author and politician Jean-Maurice Le Corbeiller and his wife Marguerite Dreux, Philippe entered the École Polytechnique in 1910, training there in engineering and the mathematical sciences. During World War I he served in the French Signal Corps, earning the '' croix de guerre'' and joining the staff of Marshal Ferdinand Foch. After the war, Le Corbeiller worked on telegraphy and radio systems. In 1926 he completed a doctorate in mathematics from the Sorbonne. His dissertation was on the arithmetic t ...
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Hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect. Hysteresis can be found in physics, chemistry, engineering, biology, and economics. I ...
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Thermostat
A thermostat is a regulating device component which senses the temperature of a physical system and performs actions so that the system's temperature is maintained near a desired setpoint. Thermostats are used in any device or system that heats or cools to a setpoint temperature. Examples include building heating, central heating, air conditioners, HVAC systems, water heaters, as well as kitchen equipment including ovens and refrigerators and medical and scientific incubators. In scientific literature, these devices are often broadly classified as thermostatically controlled loads (TCLs). Thermostatically controlled loads comprise roughly 50% of the overall electricity demand in the United States. A thermostat operates as a "closed loop" control device, as it seeks to reduce the error between the desired and measured temperatures. Sometimes a thermostat combines both the sensing and control action elements of a controlled system, such as in an automotive thermostat. T ...
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Tire
A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), traction on the surface over which the wheel travels. Most tires, such as those for automobiles and bicycles, are pneumatically inflated structures, which also provide a flexible cushion that absorbs shock as the tire rolls over rough features on the surface. Tires provide a footprint, called a contact patch, that is designed to match the weight of the vehicle with the bearing strength of the surface that it rolls over by providing a bearing pressure that will not deform the surface excessively. The materials of modern pneumatic tires are synthetic rubber, natural rubber, fabric, and wire, along with carbon black and other chemical compounds. They consist of a tire tread, tread and a body. The tread provides Traction (engineering), traction ...
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Speed Wobble
Wobble, shimmy, tank-slapper, speed wobble, and even death wobble are all words and phrases used to describe a quick (4–10 Hz) oscillation of primarily just the steerable wheel(s) of a vehicle. Initially, the rest of the vehicle remains mostly unaffected, until translated into a vehicle yaw oscillation of increasing amplitude producing loss of control. Vehicles that can experience this oscillation include motorcycles and bicycles, skateboards, and, in theory, any vehicle with a single steering pivot point and a sufficient amount of freedom of the steered wheel, including that which exists on some light aircraft with tricycle gear where instability can occur at speeds of less than ; this does not include most automobiles. The initial instability occurs mostly at high speed and is similar to that experienced by shopping cart wheels and aircraft landing gear. Theory Sustained oscillation has two necessary components: an underdamped second- or higher-order system and a ...
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Wheel
A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction with axles, allow heavy objects to be moved easily facilitating movement or transportation while supporting a load, or performing labor in machines. Wheels are also used for other purposes, such as a ship's wheel, steering wheel, potter's wheel, and flywheel. Common examples are found in transport applications. A wheel reduces friction by facilitating motion by rolling together with the use of Axle, axles. In order for wheels to rotate, a Moment (physics), moment needs to be applied to the wheel about its axis, either by way of gravity or by the application of another external force or torque. Using the wheel, Sumer, Sumerians invented a device that spins clay as a potter shapes it into the desired object. Terminology The English word '':wi ...
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Rail Transport
Rail transport (also known as train transport) is a means of transport that transfers passengers and goods on wheeled vehicles running on rails, which are incorporated in tracks. In contrast to road transport, where the vehicles run on a prepared flat surface, rail vehicles ( rolling stock) are directionally guided by the tracks on which they run. Tracks usually consist of steel rails, installed on sleepers (ties) set in ballast, on which the rolling stock, usually fitted with metal wheels, moves. Other variations are also possible, such as "slab track", in which the rails are fastened to a concrete foundation resting on a prepared subsurface. Rolling stock in a rail transport system generally encounters lower frictional resistance than rubber-tyred road vehicles, so passenger and freight cars (carriages and wagons) can be coupled into longer trains. The operation is carried out by a railway company, providing transport between train stations or freight customer ...
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Closed-loop Transfer Function
A closed-loop transfer function in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the plant under control. Overview 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, images, or other types of data streams. An example of a closed-loop transfer function is shown below: The summing node and the ''G''(''s'') and ''H''(''s'') blocks can all be combined into one block, which would have the following transfer function: : \dfrac = \dfrac G(s) is called feedforward transfer function, H(s) is called feedback transfer function, and their product G(s)H(s) is called the Open loop transfer function. Derivation We define an intermediate signal Z (also known as error signal) shown as follows: Using this figure we write: : Y(s) = G(s)Z(s) : Z(s) =X(s) ...
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Nyquist Stability Criterion
In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a dynamical system. Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although the number of each type of right-half-plane singularities must be known). As a result, it can be applied to systems defined by non- rational functions, such as systems with delays. In contrast to Bode plots, it can handle transfer functions with right half-plane singularities. In addition, there is a natural generalization to more complex systems with multiple inputs and multiple outputs, such as control systems for airplan ...
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Routh–Hurwitz Stability Criterion
In control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as time goes on. The Routh test is an efficient recursive algorithm that English mathematician Edward John Routh proposed in 1876 to determine whether all the roots of the characteristic polynomial of a linear system have negative real parts. German mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix, and showed that the polynomial is stable if and only if the sequence of determinants of its principal submatrices are all positive. The two procedures are equivalent, with the Routh test providing a more efficient way to compute the Hurwitz determinants ( ...
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Mechanical Equilibrium
In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity, the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity, that particle is in static equilibrium. S ...
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