- PI controller
control engineering, a PI Controller (proportional-integral controller) is a feedback controller which drives the plant to be controlled with a weighted sum of the error (difference between the output and desired set-point) and the integral of that value. It is a special case of the common PID controllerin which the derivative (D) of the error is not used.
The controller output is given by :where is the set-point error.
Advantages of a Proportional Plus Integral Controller
The integral term in a PI controller causes the steady-state error to be zero.
PI Controller Model
A PI controller can be modelled easily in software such as
Simulinkusing a "flow chart" box involving Laplace operators::where: = proportional gain: = integral gain
Finding a value for G
Setting a value for is often a trade off between decreasing overshoot and increasing settling time.
Finding a value for
Finding a proper value for is an iterative process.
1) Set a value for from the optimal range.
2) View the Nichols Plot for the open-loop response of the system. Observe where the response curve crosses the 0dB line. This frequency is known as the cross-over frequency ().
3) The value of can be calculated as:
4) Decreasing decreases the phase margin, however it eliminates a greater proportion of the steady-state errors.
Disadvantages of a Proportional Plus Integral Controller
The problem with using a PI controller is that it introduces a phase-lag. This means that on a Nichols Plot, the stability margin (the phase margin) decreases. So careful design considerations with respect to the gain must be considered.
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