Control algorithm from time-series

The simplest algorithm for a PID controller is the sum of Equations 8.1, 8.2, and 8.3 as shown in Equation 8.4. This is common in computer-based control systems, and all three control actions are considered to be operating in parallel. However, many industrial analog controllers and microprocessor DCS (distributed control system) controllers use a capacitance lag (filter) of about 0.05 to 0.10 in series with the process variable signal to reduce the effect of derivative action from setpoint changes and from short time constant noise described earlier. When the derivative time constant,... 

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