Hola Greg, one of the options you recommend for eliminating overshoot at setpoint changes is using a setppoint lead-lag setup. I cannot visualize the concept in my mind. In a Two Degrees of Freedom PID Structure you will have an idea of what beta and gamma do and where they are in the execution path.
For the Setpoint Lead-Lag setup I do not comprehend where the lead and where the lag act; in other words, what is led and what is lagged?
Gracias,
Héctor
Hi Hector
To get a setpoint Lead-Lag, the PID setpoint would be passed through a Lead-Lag function block. A Lead-Lag block is normally used for dynamic compensation of feedforward signals. For setpoint changes we are using this block to moderate the step in the PID output from the proportional mode, the bump from the derivative mode, and to prevent immediately driving the PID output past its final resting value. The tuning settings that reduce the peak and integrated errors from unmeasured step disturbances to the process input maximize the step and bump in the PID output for setpoint changes making the approach to setpoint faster but causing excessive setpoint overshoot. Preventing overshoot is important in many applications and reducing abrupt movements in the PID output that could upset other loops & systems is important in gas volumes and utility headers.
In the frequency domain, the lead is a zero and the lag is a pole. The Laplace transform shows that the numerator term for the zero has the same form as the denominator term for the pole. If the lead time equals the lag time, the numerator (zero) and denominator (pole) cancel out and the output equals the input. If the lead time is zero, the output is simply the filtered input where the lag time is the filter time. If the lead time is nonzero but less than the lag time, there is a small step in the block output followed by the exponential approach to the final value of the input set by the lag (filter) time. If the lead time is greater than the lag time, there is a spike in the output that is greater than the input followed by an exponential decay to the final value of the input set by the lag (filter) time.
If the lead time is zero and the lag time is set equal to the PID reset time, the response of the PID should be similar to a PD on PV and I on Error structure or a Two Degrees of Freedom (2DOF) structure with beta and gamma both equal to zero. This will prevent overshoot and provide a smooth and gradual change for both the PID output and PV. The time to reach setpoint (rise time) is much longer.
For bioreactors, gas furnaces and reactors, and plug flow systems (e.g. pipes, static mixers, extruders, sheet lines) a smooth approach with no overshoot is much more important than rise time. Bioreactor cells are very sensitive to abrupt changes and to a temperature or pH higher than optimum. Gas and plug flow volumes have no primary process time constant to filter out abrupt changes in PID output and reach a final value relatively quickly without having to make an abrupt change in the PID output.
For large well mixed liquid volumes, the increase in rise time for setpoint changes in startup, transitions, and batch operations can appreciably reduce process capacity. The response of these volumes for continuous operations is near-integrating and for batch operations is essentially true integrating. For both types of operations on these volumes, lambda integrating process tuning rules are used. The inherent approach to setpoint is very slow due to a large primary process time constant or slow integrating process gain making it necessary to have large sudden change in the PID output to get to a significantly different setpoint in minutes rather than hours.
If the lead time is set equal to 25% of the lag time, and the lag time is set equal to the reset time, you get a response with a good compromise between setpoint overshoot and rise time. Similar results can be obtained by a 2DOF structure with the beta equal to 0.5 and the gamma = 0.25. However, in my test results, the 2 DOF structure with any gamma setting > than zero resulted in some short term higher frequency oscillations in the PID output whereas with the Lead-Lag there was simply one bump. The 2DOF oscillations disappear quickly and may not exist for less aggressive tuning than what I used.
Since adding a Lead-Lag function block to all setpoint changes requires more effort than simply changing the PID structure to 2DOF, the 2DOF option may be better. Since you can achieve many of the other PID structures that have integral action by a simple change of the beta and gamma, one could say for flexibility, the 2DOF structure may be the future way to go.
You can go to DeltaV Books Online to find out more about the Lead-Lag block and PID structures.
Thank you for the question.
Greg
Greg is a retired Senior Fellow from Monsanto-Solutia and an ISA Fellow. Greg was inducted into the Control “Process Automation Hall of Fame” in 2001 and received the ISA Life Achievement Award in 2010.