The speedup of a plant’s response can cause loops to go from a smooth to an oscillatory response. In actual plants, the faster rate of change of a process variable important for product quality such a temperature or composition occurs for various changes in operating conditions. Principal sources of speed up in an actual plant are a smaller mass due to minimization of inventory or at the start of fed-batch operations, an increase in heat transfer coefficient from a cleaner surface or higher fluid flow, and an increase in catalyst activity from fresh catalyst or higher fluid flow. In virtual plants, an increase in integration step size in first principle models is used for simulation speedup so scenarios take minutes instead of hours to complete. This speedup of simulations is essential for training operators and developing/prototyping control strategies. The bottom line is that the product of two terms can be used to detect and prevent instability in plant speed up.
The first term as you might expect is dead time in seconds. The second term is the maximum ramp rate in % of PV scale per second divided the change in % PID output that caused the ramp. The ramp rate should reach a maximum in 4 dead times after the change in PID output. The change in output can be due to a remote or manual output change or a setpoint change. This second term is an integrating process open loop gain and has units of %/sec/% or 1/sec. The product of the two terms is dimensionless.
The temperature and composition response of nearly all liquid column, vessel, and tank volumes can be characterized by the product of these two terms. For continuous operations, the second term is effectively the self-regulating process open loop gain divided by the primary process time constant in a near-integrating response.
The maximum PID gain is inversely proportional to the product of these two terms; the product of the total loop dead time and the integrating process open loop gain. A simple check of this product during the speedup of a process can show whether the response will become oscillatory. Assuming the reset time is not too fast for slower operation, process speedup should not cause oscillations from integral action since the minimum reset time is proportional to the primary time constant and/or dead time that has been decreased during speedup. A simple check of whether the reset time is too small at the start for a given PID gain should be done since PID gain settings are often reduced without realizing the reset time must be proportionally increase. The PID gain multiplied by the reset time should be greater than the inverse of the integrating process open loop gain to prevent slow rolling oscillations with a period 10 times or more the ultimate period.
In the speedup of a virtual plant, an increase in integration step size will generally increase the integrating process open loop gain. If the virtual plant dead time is small enough that the product of the two terms is less than reset time divided by the PID gain, the response will be smooth. Most virtual plants don’t have as much dead time as actual plants. Also, automation system dead time in the virtual plant such as thermowell lags and analyzer cycle times can be decreased so the product does not exceed the maximum for plant stability. Note that process speedup normally does not affect the pipeline pressure and flow response except through changes in the origination and destination volume pressures. The speedup for gas volumes does not need to be anywhere near as fast as the liquid volume speedup because the gas volumes are already quite fast. Thus, the focus in a virtual plant is on the speedup of temperature and composition response of liquid volumes and the check is simple in terms of the product of two easily and quickly identifiable terms.