In part 3 we start a list of the essential concepts needed to understand what is most important and what to do to help make a loop meet process objectives. The concepts are presented in the broadest possible terms to provide a perspective that can be used in a wide spectrum of process control applications. This list and recommended best practices will be featured in a future article coauthored with Michel Ruel and Jacques Smuts "What Every Engineer Needs to Know about Process Control"
Essential Concepts for Process Control
- Deadtime is detrimental. Deadtime delays the ability of the control loop to see a change and get the correction to the right point in the process to correct for a disturbance or achieve a new setpoint. The ultimate limit to the peak and integrated error is proportional to the deadtime and deadtime squared, respectively. Deadtime compensators can help deal with deadtime and get closer to the ultimate limits to errors by allowing more aggressive tuning but are extremely sensitive to overestimates of the deadtime.
- Deadtime is variable. Process deadtime originates from transportation delays and mixing delays that vary with residence time. For temperature loops, thermal lags in series that vary with heat transfer coefficient become effectively deadtime. The delays from residence time and the equivalent thermal lags increase as flow is decreased. Deadtime also originates from sensor lags (e.g. thermowell and electrode) that vary with process conditions and valve deadband or resolution that increases as the rate of change of the controller output decreases.
- Time constants in series cause deadtime. The fraction of a small time constant that becomes equivalent deadtime increases as the small to large time constant ratio decreases. For small time constants, I simply take them as equivalent deadtime since estimates of deadtime tend to be low except at low operating rates.
- A process time constant downstream of disturbance is beneficial. A large process time constant will filter out variability from disturbances and control actions including limit cycles. A large process time constant slows down excursions and gives the PID time to act. The ultimate limit to peak and integrated errors are both inversely proportional to this process time constant for a lag dominant process. A large process time constant is generally associated with a back mixed volume with a large residence time. For perfect mixing, nearly all the residence time becomes a process time constant. The largest time constant must be in the process. If the largest time constant is in the measurement, the PID sees an attenuated version of the actual process variations. The peak error of the filtered process variable may look better and controller gain setting can be increased fooling engineers into thinking a large signal filter is beneficial.
- A secondary time constant is particularly detrimental. The second largest time constant is termed a secondary time constant. This time constant slows down correction if in the manipulated variable path into the process or slows down recognition if in the measurement. Integrating processes and runaway processes are especially sensitive to a secondary time constant. The secondary time constant should be decreased wherever possible by better mixing and heat transfer and faster valves and measurements. In general, the rate time should be increased by an amount about equal to the secondary time constant.
- Most loops have a nonlinear open loop gain. The open loop gain is the product of the valve, process, and measurement gains. The valve gain is the slope of the installed flow characteristic, which varies with pressures and inherent flow (trim) characteristic. A secondary flow loop is desirable to isolate this nonlinearity from the process loop. The process gain for temperature and composition control is generally inversely proportional to feed flow but also varies with feed conditions and operating conditions including setpoint. The measurement gain is generally constant but is inversely proportional to the span of the PID scale. Gain scheduling, signal characterization, and adaptive control are solutions for nonlinearities that cannot be abated by better design and control. As control gets tighter, less of an operating point nonlinearity, such as pH, is seen by the loop.
- Tuning can take advantage of design proficiencies and help deal with design deficiencies until fixed. The ultimate limit to performance is only reached if the PID is tuned tightly. A sluggishly tuned PID will perform as badly as a loop with more deadtime. Thus, better performance from investments in improving the dynamics by better instrument, mechanical, and process design is only achieved if the loop is well tuned. The minimum peak error for lag dominant loop is inversely proportional to the controller gain. The minimum integrated error is proportional to the integral time and inversely proportional to the controller gain assuming a non-oscillatory response as discussed in the InTech article "PID tuning rules." If a process has poor dynamics, the PID can be detuned to deal with the problem until fixed. Tuning should not be used as a cover up but only as a short term fix until the source of the problem is addressed.
- Process objectives determine the degree of transfer of variability from the process variable to the manipulated variable. While minimum peak and integrated error is important for reactor and column temperature control, it is undesirable for surge tank level control. For surge tanks, the transfer of variability is reduced as much as possible with the objective being to keep the level within alarm limits. For interacting loops, the transfer of variability to the manipulated variable may be moderated for the least important loop. For optimization, the transfer of variability may be increased for an approach to an undesirable condition and decreased for the opposite direction. A compressor surge controller should take faster action on an approach to the surge curve to protect the compressor against a loss in efficiency and the disruption of severe oscillations from surge to downstream users. A pH controller on a waste pH stream must take much faster action for a decrease in pH to prevent undissociated Hydrofluoric acid (HF) from decreasing glass electrode efficiency and possibly killing the electrode from HF attack of the glass. A pH controller on a bioreactor should react slower to a decrease in pH to prevent unnecessary addition of the base sodium bicarbonate that increases cell osmotic pressure and cell death rate. A primary control loop in a cascade control system may need to slow down the rate of change of the manipulated setpoint of a secondary loop to prevent the primary loop from outrunning the secondary loop causing a burst of oscillations.
We continue this series with a list of best practices in Parts 4 and 5. We then finally move on to additional questions from Brian Hrankowsky.