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Control Theory
Control theory is a field of mathematics that deals with the control system, 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 theory, stability; often with the aim to achieve a degree of Optimal control, optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or Setpoint (control system), set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are con ...
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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 There are two common classes of control action: open loop and closed loop. ...
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PID Control
A proportional–integral–derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller continuously calculates an ''error value'' e(t) as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms (denoted ''P'', ''I'', and ''D'' respectively), hence the name. In practical terms, PID automatically applies an accurate and responsive correction to a control function. An everyday example is the cruise control on a car, where ascending a hill would lower speed if constant engine power were applied. The controller's PID algorithm restores the measured speed to the desired speed with minimal delay and overshoot by increasing the power output of the engine in a controlled manner. The fi ...
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Irmgard Flügge-Lotz
Irmgard Flügge-Lotz, née Lotz (16 July 1903 – 22 May 1974) was a German-American mathematician and aerospace engineer. She was a pioneer in the development of the theory of discontinuous automatic control, which has found wide application in hysteresis control systems; such applications include guidance systems, electronics, fire-control systems, and temperature regulation. She became the first female engineering professor at Stanford University in 1961 and the first female engineer elected a Fellow of the American Institute of Aeronautics and Astronautics. Early life and education Lotz was born in Hamelin, Germany on 16 July 1903. She was encouraged at an early age to pursue technical subjects by her mother, whose family had been involved in construction for several generations. She often visited construction sites with her uncle and attended half-price matinee shows for technical films. After her father, Osark, a travelling journalist, was drafted for military ser ...
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World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies of World War II, Allies and the Axis powers. World War II was a total war that directly involved more than 100 million Military personnel, personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Air warfare of World War II, Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the Atomic bombings of Hiroshima and Nagasaki, only two nuclear weapons ever used in war. World War II was by far the List of wars by death toll, deadliest conflict in hu ...
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Routh–Hurwitz Theorem
In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left half-plane. Polynomials with this property are called Hurwitz stable polynomials. The Routh-Hurwitz theorem is important in dynamical systems and control theory, because the characteristic polynomial of the differential equations of a stable linear system has roots limited to the left half plane (negative eigenvalues). Thus the theorem provides a test to determine whether a linear dynamical system is stable without solving the system. The Routh–Hurwitz theorem was proved in 1895, and it was named after Edward John Routh and Adolf Hurwitz. Notations Let ''f''(''z'') be a polynomial (with complex coefficients) of degree ''n'' with no roots on the imaginary axis (i.e. the line ''Z'' = ''ic'' where ''i'' is the imaginary unit and ''c'' is a real number). Let us define P_0(y) (a polynomial of degree ''n'') and P_1(y) (a nonzero polynomia ...
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Edward John Routh
Edward John Routh (; 20 January 18317 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematise the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory. Biography Early life Routh was born of an English father and a French-Canadian mother in Quebec, at that time the British colony of Lower Canada. His father's family could trace its history back to the Norman conquest when it acquired land at Routh near Beverley, Yorkshire. His mother's family, the Taschereau family, was well-established in Quebec, tracing their ancestry back to the early days of the French colony. His parents were Sir Randolph Isham Routh (1782–1858) and his second wife, Marie Louise Taschereau (1810–1891). Sir Randolph was Commissary General of ...
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Self-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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Centrifugal Governor
A centrifugal governor is a specific type of governor with a feedback system that controls the speed of an engine by regulating the flow of fuel or working fluid, so as to maintain a near-constant speed. It uses the principle of proportional control. Centrifugal governors, also known as "centrifugal regulators" and "fly-ball governors", were invented by Christiaan Huygens and used to regulate the distance and pressure between millstones in windmills in the 17th century. In 1788, James Watt adapted one to control his steam engine where it regulates the admission of steam into the cylinder(s), a development that proved so important he is sometimes called the inventor. Centrifugal governors' widest use was on steam engines during the Steam Age in the 19th century. They are also found on stationary internal combustion engines and variously fueled turbines, and in some modern striking clocks. A simple governor does not maintain an exact speed but a speed range, since under increasi ...
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Boulton And Watt Centrifugal Governor-MJ
Boulton may refer to: * Boulton (surname) * Boulton, Derby, England See also * Boulton Paul Aircraft Ltd, aircraft manufacturer * Boulton and Watt Boulton & Watt was an early British engineering and manufacturing firm in the business of designing and making marine and stationary steam engines. Founded in the English West Midlands around Birmingham in 1775 as a partnership between the Eng ..., partnership between Matthew Boulton and James Watt * Bolton (other) * * {{disambig ...
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Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as mathematical model, modeling, statistics, and mathematical optimization, optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the Maxima and minima, maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in mil ...
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Process Control
An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. It is implemented widely in industries such as automotive, mining, dredging, oil refining, pulp and paper manufacturing, chemical processing and power generating plants. There is a wide range of size, type and complexity, but it enables a small number of operators to manage complex processes to a high degree of consistency. The development of large industrial process control systems was instrumental in enabling the design of large high volume and complex processes, which could not be otherwise economically or safely operated. The applications can range from controlling the temperature and level of a single process vessel, to a complete chemical processing plant with several thousand control loops. History Early process control breakthr ...
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