Limited integrator

Integrates its input, starting from 0, and stops integrating at ±Integral limit.

  • signal
  • Gradara equations
  • 2 ports
  • 1 parameter
BlockLimited integratorKindintegratorLibraryContinuous

Description

Integrates its input, starting from 0, and stops integrating at ±Integral limit. Use it for integral action that must not wind up.

At the limit, integration stops only while the input pushes further out; an input of the other sign brings the output back immediately.

Example

Step responses A unit step through a first-order filter, a second-order system, an integrator, and a delay; a ramp through a derivative.

Step at 0.1 sFirst orderSecond orderIntegratorDelay 0.3 sRamp, slope 2Derivative
In Gradara, select a Limited integrator block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:StepLow-pass filterRampDerivativeSecond-orderTransport delay

Ports

Inputs 1

  • usignal

    Input signal, the rate of change of the output.

Outputs 1

  • ysignal

    Output signal, the limited integral of u.

Parameters

  • Integral limitlimit8

    ≥ 0.01

    Symmetric bound on the output: the output stays within ±limit. At least 0.01.

Equations

Modelica
dx/dt = 0 if (x ≥ limit and u > 0) or (x ≤ −limit and u < 0)
dx/dt = u otherwise
y = x, with x = 0 at time 0

Implementation

The block’s Modelica model
Real x(start=0, fixed=true);
der(x) = if (x >= limit and u > 0) or (x <= -limit and u < 0) then 0 else u;
y = x;

Assumptions and limitations

  • The limit is always active and symmetric; there is no unlimited setting. Set a large limit to approximate a plain integrator.
  • The initial value is always 0, and there is no reset input.

Used in

These larger examples use it too. Open them from Examples in the app.

  • PMSM · Field-oriented control

See also

Select a block in Gradara and press F1 to open its page offline.