Dead beat
Encyclopedia
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:
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
, 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
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...
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
Z-transform
In mathematics and signal processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation....
). 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
Process control
Process control is a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range...
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.