BuildingSystems.Fluid.Actuators.Dampers.PressureIndependent

# .BuildingSystems.Fluid.Actuators.Dampers.PressureIndependent

Model for an air damper whose mass flow is proportional to the input signal

## Information

Model for an air damper whose airflow is proportional to the input signal, assuming that at `y = 1`, `m_flow = m_flow_nominal`. This is unless the pressure difference `dp` is too low, in which case a `kDam = m_flow_nominal/sqrt(dp_nominal)` characteristic is used.

The model is similar to BuildingSystems.Fluid.Actuators.Valves.TwoWayPressureIndependent, except for adaptations for damper parameters. Please see that documentation for more information.

#### Computation of the damper opening

The fractional opening of the damper is computed by

- inverting the quadratic flow function to compute the flow coefficient from the flow rate and the pressure drop values (under the assumption of a turbulent flow regime);
- inverting the exponential characteristics to compute the fractional opening from the loss coefficient value (directly derived from the flow coefficient).

The quadratic interpolation used outside the exponential domain in the function BuildingSystems.Fluid.Actuators.BaseClasses.exponentialDamper yields a local extremum. Therefore, the formal inversion of the function is not possible. A cubic spline is used instead to fit the inverse of the damper characteristics. The central domain of the characteritics having a monotonous exponential profile, its inverse can be properly approximated with three equidistant support points. However, the quadratic functions used outside of the exponential domain can have various profiles depending on the damper coefficients. Therefore, five linearly distributed support points are used on each side domain to ensure a good fit of the inverse.

Note that below a threshold value of the input control signal (fixed at 0.02), the fractional opening is forced to zero and no more related to the actual flow coefficient of the damper. This avoids steep transients of the computed opening while transitioning from reverse flow. This is to be considered as a modeling workaround (avoiding the introduction of an additional state variable) to prevent control chattering during shut off operation where the pressure difference at the damper boundaries can vary between slightly positive and negative values due to outdoor pressure variations.

## Revisions

- August 11, 2021, by Michael Wetter:
  Reformulated initial equation section to avoid warning in OPTIMICA about variable array index.
  This is for IBPSA #1513.
- June 10, 2021, by Michael Wetter:
  Changed implementation of the filter and changed the parameter `order` to a constant as most users need not change this value.
  This is for IBPSA #1498.
- April 6, 2020, by Antoine Gautier:
  Added the computation of the damper opening.
- December 23, 2019 by Antoine Gautier:
  Refactored as the model can now extend directly BuildingSystems.Fluid.Actuators.BaseClasses.PartialDamperExponential.
  This is for IBPSA #1188.
- March 21, 2017 by David Blum:
  First implementation.

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