Control theory in control systems engineering is a subfield of mathematics that deals with the control of continuously operating dynamical systems in engineered processes and machines. The objective is to develop a control model for controlling such systems using a control action in an optimum manner without delay or overshoot and ensuring control stability. To do this, a controller with the requisite corrective behavior is required; this controller monitors the controlled process variable, compares it with the reference or set point. 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 studied are controllability and observability; this is the basis for the advanced type of automation that revolutionized manufacturing, aircraft and other industries. This is feedback control, continuous and involves taking measurements using a sensor and making calculated adjustments to keep the measured variable within a set range by means of a "final control element", such as a control valve.

Extensive use is made of a diagrammatic style known as the block diagram. In it the transfer function known as the system function or network function, is a mathematical model of the relation between the input and output based on the differential equations describing the system. Control theory dates from the 19th century, when the theoretical basis for the operation of governors was first described by James Clerk Maxwell. Control theory was further advanced by Edward Routh in 1874, Charles Sturm and in 1895, Adolf Hurwitz, who all contributed to the establishment of control stability criteria. Although a major application of control theory is in control systems engineering, which deals with the design of process control systems for industry, other applications range far beyond this; as the general theory of feedback systems, control theory is useful. Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868, entitled On Governors.

A centrifugal governor was used to regulate the velocity of windmills. Maxwell described and analyzed the phenomenon of self-oscillation, in which lags in the system may lead to overcompensation and unstable behavior; this generated a flurry of interest in the topic, during which Maxwell's classmate, Edward John Routh, abstracted Maxwell's results for the general class of linear systems. Independently, Adolf Hurwitz analyzed system stability using differential equations in 1877, resulting in what is now known as the Routh–Hurwitz theorem. A notable application of dynamic control was in the area of manned flight; the Wright brothers made their first successful test flights on December 17, 1903 and were distinguished by their ability to control their flights for substantial periods. Continuous, reliable control of the airplane was necessary for flights lasting longer than a few seconds. By World War II, control theory was becoming an important area of research. Irmgard Flügge-Lotz developed the theory of discontinuous automatic control systems, applied the bang-bang principle to the development of automatic flight control equipment for aircraft.

Other areas of application for discontinuous controls included fire-control systems, guidance systems and electronics. Sometimes, mechanical methods are used to improve the stability of systems. For example, ship stabilizers are fins mounted beneath emerging laterally. In contemporary vessels, they may be gyroscopically controlled active fins, which have the capacity to change their angle of attack to counteract roll caused by wind or waves acting on the ship; the Space Race depended on accurate spacecraft control, control theory has seen an increasing use in fields such as economics and artificial intelligence. Here, one might say that the goal is to find an internal model that obeys the good regulator theorem. So, for example, in economics, the more a trading model represents the actions of the market, the more it can control that market. In AI, an example might be a chatbot modelling the discourse state of humans: the more it can model the human state, the better it can manipulate the human.

These last two examples take the narrow historical interpretation of control theory as a set of differential equations modeling and regulating kinetic motion, broaden it into a vast generalization of a regulator interacting with a plant. Fundamentally, there are two types of control loops: closed loop control. In open loop control, the control action from the controller is independent of the "process output". A good example of this is a central heating boiler controlled only by a timer, so that heat is applied for a constant time, regardless of the temperature of the building; the control action is the timed switching on/off of the boiler, the process variable is the building temperature, but neither is linked. In closed loop control, the control action from the controller is dependent on feedback from the process in the form of the value of the process variable. In the

Raymond Allen Draper was an American jazz tuba player. Draper attended the Manhattan School of Music in the mid-1950s; as a leader, he recorded his first album, Tuba Sounds, with a quintet. His second album, The Ray Draper Quintet featuring John Coltrane, was recorded at the age of 17 with slight changes in his quintet, including John Coltrane. Imprisoned over his drug use, after his release in the late 1960s, Draper formed the first jazz rock fusion band composed of established jazz musicians of the day; this preceded Miles Davis's Bitches Brew, recognized as the first jazz rock fusion group and recording by two years. Original band members included George Bohanon on trombone, Hadley Caliman on tenor sax, John Duke on upright bass, Paul Lagos on drums and Tom Trujillo on guitar; this band, after its first live performance at Hollywood's Whisky a Go Go - where it shared the bill with Nazz - was offered numerous record deals and booked solid at rock venues for the rest of the year. Draper began using heroin again, whereupon the more experienced band members quit, except for the youngest member, guitarist Tom Trujillo and his landlord, Chuck Gooden.

This led to a search for new members and hirings that included San Diego trumpeter Don Sleet and Ernie Watts. After two years of searching and many personnel changes, including getting clean from drugs, Draper brought drummer Paul Lagos back, along with saxophonist Richard Aplanalp, trumpeter Phil Wood, bassist Ron Johnson; this new group was named Red Beans and Rice, named after their favorite meal cooked by Draper's first wife, Cassondra. This group appeared on bills with some of the day's headlining groups including Jimi Hendrix, Chicago Transit Authority, Jethro Tull, Gil Scott Heron, they went on to record the album produced by Jackie Mills titled Red Beans and Rice Featuring Sparerib Ray Draper on Epic Records. But when the band saw that Draper and his manager Forrest Hamilton had put only Draper's picture on the cover, the whole group quit and Draper was on his own once more. After this, he got hooked back on heroin and he sporadically performed and recorded but he was no longer able to recreate the band sound with other players.

He left California and spent a couple years in London before returning to New York in the hopes of becoming clean once again. He remarried and had two children and Hakim, with his second wife, continuing to compose for other musicians. In 1982, coming out of a bank, he was held up by a gang of juveniles; the 13-year-old leader of the gang shot him. Draper had been clean of drug use and had been working on a composition, found in his attaché case upon his death. 1957: Tuba Sounds 1957: The Ray Draper Quintet featuring John Coltrane 1958: A Tuba Jazz, reissued as John Coltrane album, Like Sonny 1968: Red Beans and Rice With Sonny Criss Sonny's Dream With Brother Jack McDuff Who Knows What Tomorrow's Gonna Bring? With Jackie McLean Jackie McLean & Co. Strange Blues Fat Jazz With Max Roach Max Roach + 4 at Newport Deeds, Not Words Award-Winning Drummer With Archie Shepp There's a Trumpet in My Soul With Dr. John The Sun, Moon & Herbs Ray Draper at Discogs

South Korean boy group Shinee have received several awards and nominations for their music work. The group was formed by SM Entertainment in 2008 and released their first full-length album, The Shinee World, on August 28, 2008, which won the Newcomer Album of the Year at the 23rd Golden Disk Awards; the first single released from the album was "Sanso Gateun Neo" and won first place on M Countdown on September 18, 2008 making it the group's first win on Korean music shows since debut. Their second album Lucifer produced two singles, "Lucifer" and "Hello". For their outstanding choreography the group was nominated for the Best Dance Performance Award at the Mnet Asian Music Awards in 2010. Lucifer won the Disk Bonsang Award at the 25th Golden Disk Awards as well as the Popularity Award. On March 21, 2012 the group released their fourth EP Sherlock for which the group was awarded another Disk Bonsang Award at the 27th Golden Disc Awards and the Bonsang Award at the 22nd Seoul Music Award. Following the success of the lead single it was nominated for Song of the Year at the 2012 Mnet Asian Music Awards.

Following Shinee's successful promotions for their third Korean studio album —, divided into two parts, the group was crowned Artist of the Year at the Melon Music Awards in 2013 — one of the biggest award ceremonies in the country, which hand out prizes based on digital sales and online votes. The group has gained various recognitions for their fashion style like the Ceci Asia Icon Award at the 28th Golden Disk Awards as well as for their unique dance performances winning the Best Dance Performance Award at the Mnet Asian Music Awards three times in a row; the group got awarded the Communication Design Award Package at the Red Dot Design Award several times for their album design