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The low-pass filter is used to create a smoother flow of a point. Take for example a setpoint here which goes first from 14 to 20°C and then back down. The filter smoothens the flow of the setpoint.The internal working of the low pass filter is based on the principle of a time constant as characteristic of a decaying exponential function. An input step-profile that goes from 0 to 1 instantaneously at t=0s, will reach 63.21% (1-e-1) at t=𝜏 with 𝜏
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The idea behind the smoothening is known as exponential smoothing (or exponential moving average). The update rule is typically written as:
where:
An is the new running average (or filtered value) at time step n.
An−1 is the previous running average.
xn is the expected output for the current timestamp, which is smoothed to An
α is a smoothing factor between 0 and 1. In Hysopt, alpha is built in a way that the Control Delay equals the time constant.
In Hysopt, you can define a separate time constant for an upramping change and a downramping change.
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The example below shows the output of a low pass filter with a Control delay of 0.5h (1800s). After exactly 1 time constant, the value of 63% is reached.
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This component is very useful when it comes to valves and energy centers to create a more sensible, smoother behavior.