In discrete-time control theory, the dead beat control problem consists of finding what input signal must be applied to a system in order to bring the output to the steady state in the smallest number of time steps.
For an Nth-order linear system it can be shown that this minimum number of steps will be at most N (depending on the initial condition), provided that the system is null controllable (that is can be brought to state zero by some input). The solution is to apply feedback such that all poles of the closed-loop transfer function are at the origin of the z-plane. (For more information about transfer functions and the z-plane see z-transform). Therefore the linear case is easy to solve. By extension, a closed loop transfer function which has all poles of the transfer function at the origin is sometimes called a dead beat transfer function.
For non-linear systems, dead beat control is an open research problem. (See Nesic reference below).
Dead beat controllers are often used in process control due to their good dynamic properties. They are a classical feedback controller where the control gains are set using a table based on the plant system order and normalized natural frequency.
The deadbeat response has the following characteristics:
- Zero steady-state error.
- Minimum rise time.
- Minimum settling time.
- Less than 2% overshoot/undershoot.
- Very high control signal output.
Famous quotes containing the words dead, beat and/or control:
“Whoever neglects the arts when he is young has lost the past and is dead to the future.”
—Sophocles (497–406/5 B.C.)
“There used to be two kinds of kisses. First when girls were kissed and deserted; second, when they were engaged. Now there’s a third kind, where the man is kissed and deserted. If Mr. Jones of the nineties bragged he’d kissed a girl, everyone knew he was through with her. If Mr. Jones of 1919 brags the same everyone knows it’s because he can’t kiss her any more. Given a decent start any girl can beat a man nowadays.”
—F. Scott Fitzgerald (1896–1940)
“We long for our father. We wear his clothes, and actually try to fill his shoes. . . . We hang on to him, begging him to teach us how to do whatever is masculine, to throw balls or be in the woods or go see where he works. . . . We want our fathers to protect us from coming too completely under the control of our mothers. . . . We want to be seen with Dad, hanging out with men and doing men things.”
—Frank Pittman (20th century)