Parallel and Series Algorithms

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, 

is set to zero, there is no difference between the controller action of the parallel and the series algorithm with only P and I action  

This chapter presented a flow diagram of a PID feedback control loop with the process streams and instrument lines labeled. The proportional, integral, and derivative actions of the controller were defined mathematically and described for the example in the diagram. 

How much does the controller output change if a proportional-only controller gain is 5 and the process variable changes by 5% of its span  

For a PI controller with a proportional band of 25% and a reset rate of 0.05 repeats per minute, what is the proportional gain of the controller and how many minutes will it take to change the controller output the same amount as the gain for a fixed amount of error  

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