• Control Theory

    Date: 2010.04.19 | Category: Uncategorized | Response: 0

    Control theory is an interdisciplinary branch of engineering and mathematics, that deals using the behavior of dynamical programs. The sought after output of the program is known as the reference. When one or additional output variables of your process need to have to follow a certain reference over time, a controller manipulates the inputs with a technique to obtain the sought after impact on the output of the technique.

    Overview

    Control principle is

    * a concept that deals with influencing the behavior of dynamical systems
    * an interdisciplinary subfield of science, which originated in engineering and mathematics, and evolved into use because of the social sciences, like psychology, sociology and criminology.

    [edit] An example

    Take into account an automobile’s cruise handle, which can be a device intended to sustain a constant automobile rate; the preferred or reference velocity, offered through the driver. The program in this situation is the car or truck. The method output will be the car or truck speed, and the control variable will be the engine’s throttle position which influences engine torque output.

    A primitive solution to implement cruise restrain is merely to lock the throttle placement when the driver engages cruise regulate. Nevertheless, on mountain terrain, the car will slow down proceeding uphill and accelerate going downhill. In fact, any parameter various than what was assumed at pattern time will translate into a proportional error within the output velocity, such as exact mass of the automotive, wind resistance, and tire pressure. This kind of controller is known as an open-loop controller due to the fact there’s no direct connection among the output of the system (the vehicle’s velocity) along with the actual conditions encountered; that may be to say, the process doesn’t and can not compensate for unexpected forces.

    In the closed-loop handle program, a sensor monitors the output (the vehicle’s speed) and feeds the information with a pc which continuously adjusts the regulate input (the throttle) as important to maintain the restrain error with a minimum (that is, to retain the ideal speed). Feedback on how the program is basically performing makes it possible for the controller (vehicle’s on board personal computer) to dynamically compensate for disturbances on the technique, such as alterations in slope in the ground or wind speed. An perfect feedback regulate method cancels out all errors, successfully mitigating the results of any forces that may well or may well not arise throughout operation and producing a response from the system that perfectly matches the user’s wishes. In reality, this can’t be achieved due to measurement mistakes within the sensors, delays within the controller, and imperfections inside handle input.
    [edit] History
    Centrifugal governor in the Boulton & Watt engine of 1788

    Although manage techniques of various types date back to antiquity, a more formal analysis on the field began with a dynamics analysis on the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868 entitled On Governors.[1] This described and analyzed the phenomenon of “hunting”, in which lags inside the system can lead to overcompensation and unstable behavior. This generated a flurry of interest within the topic, throughout which Maxwell’s classmate Edward John Routh generalized the results of Maxwell for the general class of linear systems.[2] Independently, Adolf Hurwitz analyzed technique stability using differential equations in 1877. This result is called the Routh-Hurwitz theorem.[3][4]

    A notable application of dynamic handle was inside area of manned flight. The Wright Brothers made their first successful test flights on December 17, 1903 and were distinguished by their ability to regulate their flights for substantial periods (far more so than the ability to produce lift from an airfoil, which was known). Restrain of the airplane was needed for safe flight.

    By World War II, control concept was an important part of fire-control programs, guidance devices and electronics. The Space Race also depended on accurate spacecraft manage. However, manage principle also saw an increasing use in fields just like economics.
    [edit] People in devices and regulate
    Main article: People in devices and regulate

    Many active and historical figures made significant contribution to manage theory, which includes, for example:

    * Alexander Lyapunov (1857–1918) from the 1890s marks the beginning of stability principle.
    * Harold S. Black (1898–1983), invented the concept of negative feedback amplifiers in 1927. He managed to develop stable negative feedback amplifiers within the 1930s.
    * Harry Nyquist (1889–1976), developed the Nyquist stability criterion for feedback methods within the 1930s.
    * Richard Bellman (1920–1984), developed dynamic programming since the 1940s.
    * Andrey Kolmogorov (1903–1987) co-developed the Wiener-Kolmogorov filter (1941).
    * Norbert Wiener (1894–1964) co-developed the Wiener-Kolmogorov filter and coined the term cybernetics from the 1940s.
    * John R. Ragazzini (1912–1988) introduced digital control along with the z-transform in the 1950s.
    * Lev Pontryagin (1908–1988) introduced the maximum principle and the bang-bang principle.

    [edit] Classical manage theory

    To avoid the problems in the open-loop controller, handle theory introduces feedback. A closed-loop controller uses feedback to regulate states or outputs of the dynamical process. Its name comes from the information path from the process: process inputs (e.g. voltage applied to an electric motor) have an impact on the process outputs (e.g. velocity or torque with the motor), that is measured with sensors and processed through the controller; the result (the restrain signal) is used as input towards the process, closing the loop.

    Closed-loop controllers have the following advantages over open-loop controllers:

    * disturbance rejection (for example unmeasured friction in a very motor)
    * guaranteed performance even with model uncertainties, when the model structure won’t match completely the real process along with the model parameters are not exact
    * unstable processes can be stabilized
    * reduced sensitivity to parameter variations
    * improved reference tracking performance

    In some systems, closed-loop and open-loop control are used simultaneously. In such systems, the open-loop handle is termed feedforward and serves to further improve reference tracking performance.

    A common closed-loop controller architecture could be the PID controller.
    [edit] Closed-loop transfer function

    The output with the program y(t) is fed back through a sensor measurement F for the reference value r(t). The controller C then takes the error e (difference) in between the reference and also the output to change the inputs u on the method under manage P. This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller.

    This is called a single-input-single-output (SISO) restrain technique; MIMO (i.e. Multi-Input-Multi-Output) programs, with far more than one input/output, are common. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite-dimensional (typically functions).