Did you know all loops today use cascade control? Do you understand how cascade control can correct for lower loop disturbances before they affect the upper loop and can make the upper loop faster? Do you know what to do to keep the system from oscillating if the lower loop is too slow or has insufficient rangeability? The fixes are quite simple.
In cascade control the output of an upper loop PID is the setpoint to a lower loop PID. While the discussion often centers on a single cascade, there can be multiple cascades. If you consider that a valve positioner is a really a digital valve controller (DVC) and in this DVC there may be cascade control where the output of a position controller is the setpoint for a relay travel or actuator pressure controller, you could have a triple cascade with just a flow controller. If you consider a reactor temperature controller whose output is the setpoint of a jacket temperature controller whose output is the setpoint of a flow controller whose output is the setpoint of a DVC, you have a quintuple cascade. Since today's control valves have positioners, every loop has a cascade control system and most have multiple cascades.
Here we will use the terms “higher” and “lower” to denote the relative position in the cascade control system. Higher loops are typically associated with quality control (e.g. composition, pH, and temperature control) and inventory control (e.g. gas pressure and level). Given that cascade loops are much more common than realized, we need to be aware of when and how they can help and the potential problems. The upper loop is often termed the primary loop and the lower loop termed the secondary loop. While the primary loop may enclose the primary process time constant and the secondary loop may enclose the secondary process time constant this is not necessarily the case. To avoid confusion as in the location or subscripting of process time constants, we will refer to the primary loop the upper loop and the secondary loop the lower loop.
For cascade control to be effective a lower loop must be faster than the loop immediately above it that is the source of its setpoint. There is an unofficial cascade rule that a lower loop must be 4 times faster than an upper loop. While stated in terms of a single cascade, the rule is applicable as you progress to higher loops. We will focus here on a single cascade with an upper and a lower loop.
By faster, we mean the total loop dead time of the lower loop must be smaller than for the upper loop. After the dead time, the rate of change of the lower loop must be greater than for the upper loop. For self-regulating processes this corresponds to the largest open loop time constant in a lower loop being smaller than the largest open loop time constant in the upper loop. For integrating processes, the open loop integrating process gain for the lower loop must be greater than the open loop integrating process gain for the upper loop. The ultimate limit to the peak error decreases as the ratio of the lower to upper loop dead time decreases and the ratio of the lower to upper loop rate of change increases.
If the cascade rule is violated, peak error and integrated error suffers but oscillations can be prevented by tuning the lower loop faster and the upper loop slower. Here the closed loop time constant of the lower and upper loops are made smaller and larger, respectively. Alternately, the external reset feedback of the lower loop process variable to the upper loop PID can prevent the burst of oscillations when an upper PID tries to change the setpoint of a lower PID faster than the lower loop can respond.
Lower loops can make the upper loop process gain more linear, compensate for lower disturbances before they appreciably affect the upper process, deal with valve stiction and backlash on a faster more direct basis, and offer flow feedforward (e.g. flow ratio control) when the lower loop is flow. If the lower loop does not give these advantages and is not as fast as needed, the cascade loop might best be abandoned in favor of a single loop with the rate time set equal to the lower loop process time constant.
In the days of analog electronic controllers and pneumatic positioners, the cascade rule was violated by putting a positioner on a fast loop (e.g. liquid pressure and flow). Volume boosters were recommended based on Nyquist plot studies. There were several factors not considered invalidating this guidance. The net result is that positioners are recommended on all control valves.
Cascade control has the interesting property of converting a detrimental dynamic term in a single loop to a beneficial term in a cascade loop. If you consider the original single loop, a lower time constant can seriously degrade performance either taken as an increase in dead time in self-regulating processes or even worse as a time constant in integrating and runaway processes. If a lower loop is created enclosing the lower time constant, this time constant is effectively removed from the upper loop and becomes the largest time constant in the lower loop. The larger the lower time constant, the larger the PID gain allowable in the upper loop by decreasing the total dead time and in the lower loop by increasing the time constant to dead time ratio. The upper loop becomes faster (ultimate period smaller) and better able to deal with upper loop disturbances.
The greatest improvement is seen for disturbances that are inputs to the lower process. Potentially the lower loop can correct for them before these disturbances affect the upper loop. Lower flow loops can correct for pressure disturbances before they affect the upper loop. Lower jacket temperature loops can correct for changes in coolant temperature before they affect a reactor temperature loop.
As the process time constant in the upper loop increases and the lower loop dead time decreases, the lower loop period decreases and the filtering action of short term transients by the upper process time constant increases. In fact, lower loops tuned for an oscillatory response may provide the best disturbance rejection for upper loop process time constants that are more than 10 times the lower loop dead time. An interesting unexpected example is the tuning of a DVC in a temperature loop to be oscillatory by the addition of integral action in the DVC. The fast oscillations (e.g. 2 second period) in the DVC, filtered by large time constant (e.g. 60 minutes) in the temperature loop are less than the resolution limit of the sensor. These oscillations are preferable to an offset in the DVC that will show up in the temperature. However such tuning will wear out the valve. The better solution is a valve with a much smaller stick-slip (resolution and threshold sensitivity limit) and hence smaller offset.
The upper loop has a smaller ultimate period than the original single loop. The lower loop can also isolate nonlinearities from the upper loop. Flow loops isolate the nonlinearity of the installed characteristic. Jacket and coil temperature loops isolate the process nonlinearity where the process gain and dead time increase as the jacket flow decreases as well as valve nonlinearities and discontinuities at the split range point from the transition from heating to cooling and vice versa. These loops can also enforce temperature limits to prevent hot or cold spots on heat transfer surfaces particularly important for crystallizers and bioreactors.
If the cascade rule is obeyed, the upper PID gain and rate time can be increased and the reset time decreased. Consequently, the cascade loop can better handle disturbances that originate in the upper loop than in the original single loop.
We can make the lower loop faster by making the measurement, controller or final control element faster. For measurements this corresponds to decreasing the delay and lag of the sensor (e.g. thermowell or electrode) and of the transmitter (e.g. damping and wireless default update rate). For controllers, this means decreasing the PID execution time and signal filter. For final control elements (e.g. valves and variable speed drives) this translates to decreasing the deadband, resolution, and threshold sensitivity limits. It also means keeping speed control in the variable frequency drive rather than moving it to the DCS so the controller execution is faster. For valves we need to decrease the pre-stroke dead time and stroking time. For Variable speed drives, we need to increase the allowable rate of change of speed.
The upper closed loop time constant or arrest time (lambda) should be about 4 times greater than the lower loop lambda. If this cannot be done by making the lower loop faster, it can be done by tuning the upper loop lambda to be larger.
The addition of a lower flow loop enables flow feedforward. A watch-out is whether the flow measurement has enough rangeability. Magnetic flow meters have good turndown (e.g. 50 to 1) and Coriolis meters have great turndown (e.g. 200 to 1). Differential head may get too noisy and vortex meters signals may drop out at low flows in which case logic needs to be added to the cascade loop to switch to a flow measurement computed from valve or variable speed drive position.
Variable speed drives with negligible deadband and setpoint rate limits may be necessary for polymer pressure control to prevent a serious violation of the cascade rule. Polymer pressure control often needs to be tight to maintain polymer properties. Polymer pressure process dynamics are faster than valve dynamics.
Process flow diagrams, analysis, metrics, and simulations (e.g. steady state and dynamic) all depend upon getting the flows right. Lower flow loops improve process operation and process control improvement.