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:
“I held it truth, with him who sings
To one clear harp in diverse tones,
That men may rise on stepping-stones
Of their dead selves to higher things.”
—Alfred Tennyson (1809–1892)
“When I was a kid I used to tell myself the moon was a silver gong and if I could climb high enough to beat on it with both hands all my wishes would come true.”
—John Dos Passos (1896–1970)
“The child knows only that he engages in play because it is enjoyable. He isn’t aware of his need to play—a need which has its source in the pressure of unsolved problems. Nor does he know that his pleasure in playing comes from a deep sense of well-being that is the direct result of feeling in control of things, in contrast to the rest of his life, which is managed by his parents or other adults.”
—Bruno Bettelheim (20th century)