Here we look at a myriad of metrics on process and control loop performance and show how to see through the complexity and diversity to recognize the commonality and underlying principles. We will see how dozens of metrics simplify to two classes each for the process and the loop. We also provide a concise view of how to compute and use these metrics and what affects them.
Let’s start with process metrics because while as automation engineers we are tuned into control metrics, our ultimate goal is improvement in the process and thus, process metrics. The improvement in profitability of a process comes down to improving process efficiency and/or capacity. Often these are interrelated in that an increase in process capacity is often associated with a decrease in process efficiency. Also an increase in the metrics for a particular part of a process may decrease the metrics for other parts of the process. The following example cited in the April 2017 Control Talk Column “An ‘entitlement’ approach to process control improvement” is indicative of the need to have metrics and an understanding for the entire process:
“In a recent application of MPC for thermal oxidizer temperature control that had a compound response complicating the PID control scheme, there was a $700K per year benefit clearly seen in reduced natural gas usage. However, the improvement also reduced steam make to a turbo-generator, reducing electricity generated by $300K per year. We reached a compromise of about $400K per year in net benefit because of lost electrical power generation from less steam to the turbo-generators. We spent many hours to align the benefit with measureable accounting for the natural gas reduction and the electrical purchases. Sometimes the loss of benefits is greater than expected. You need to be upfront and make sure you don’t just shift costs to a different cost area.”
Process efficiency can be increased by reducing energy use (e.g., electricity, steam, coolant and other utilities) and raw materials (e.g., reactants, reagents, additives and other feeds). The efficiency is first expressed as a ratio of the energy use per unit mass of product produced (e.g., kJ/kg) or energy produced (kJ/kJ) and then ideally in terms of ratio of cost to revenue by including the cost of energy used (e.g., $ per kJ) and the value of revenue for product produced (e.g., $ per kg) or energy produced (e.g., $ per kJ). The kJ of energy and kg and mass are running totals where the oldest value of mass flow or energy multiplied by a time interval between measurements is replaced in the total by the current value. A deadtime block can provide the oldest value. The time interval between measurements and the deadtime representative of the time period for the running total should both be chosen to provide a good signal to noise ratio. The deadtime block time period should also be chosen to help focus on the source of changes in process efficiency. For batch operations, the time period is usually the cycle time of a key phase in the batch and may simply be the totals at the end of the phase or batch. For continuous operations, I favor a time period that is an operator shift to recognize the key effect of operators on process performance. This time period is also suitable for evaluating other sources of variability, such as the effect of ambient conditions (day to night operation and weather) and feeds and recycle and heat integration (upstream, downstream and parallel unit operations). The periods of best operation can be used to as a goal to be possibly achieved by smarter instruments or better installations less sensitive to ambient conditions or smarter controls thru procedural automation or state based control as discussed in the in the Sept 2016 Control Talk Column “Continuous improvement of continuous processes”.
The metrics that affect process capacity are more diverse and complicated. Process capacity can be affected by feed rates, onstream time, startup time, shutdown time, maintenance time, transition time, spectrum of products and their value, recycle, and off spec product. An increase in off spec product that can be recycled can be taken as a loss in product capacity if the raw material feed rate is kept the same or taken as a loss in process efficiency if the raw material feed rate is increased. If the off spec product can be sold as a lower revenue product, the $ per kg must be correspondingly adjusted.
For batch operations, an increase in batch end point in terms of kg of product produced and a decrease in batch cycle time including time in-between batches can translate to an increase in process capacity. If a higher endpoint can be reached by holding or running the batch longer, there is a likely increase in process efficiency assuming a negligible increase in raw material but there may be an increase or decrease in process capacity. The optimum time to end a batch is best determined by looking at the rate of change of product formation (batch slope) and if necessary the rate of change of raw material and energy use to determine the optimum time to end the batch and move on. A deadtime block is again used to provide a fast update with a good signal to noise ratio to compute the slope of the batch profile and the prediction of batch end point. Of course whether downstream units for recovery and purification are able to handle an increase in batch capacity and their metrics must be included in the total picture. For example in ethanol production, a reduction in fermenter cycle time may not translate to an increase in process capacity because of limitations in distillation columns downstream or the dryer for recovery of dried solids byproduct sold as animal feed. For more on the optimization of batch end points see the Sept 2012 Control feature article “Getting the Most Out of your Batch”.
The metrics that indicate loop performance can be classified as load response and setpoint response metrics. The load response is often most important in that the desired setpoint response can be achieved for the best load response by the proper use of PID options. The load response should in nearly all cases be based on disturbances that enter as inputs to the process whereas many academic and model based studies are based on disturbances entering in the process output. For self-regulating processes where the process deadtime is comparable to or larger than the process time constant, the point of entry does not matter because the intervening process time constant does not appreciably slow down input disturbances in the time frame of the PID response (e.g., 2 to 4 deadtimes). However, most of the more interesting temperature and composition control loops in my career did not have a negligible process time constant and in fact had a near-integrating, true integrating or runaway open loop response.
The load metrics are peak error and integrated error. The peak error is the maximum excursion after a load upset. The integrated error is most often an absolute integrated error (IAE) but can be an integrated square error. If the response is non oscillatory, the integrated error and IAE are the same. There are also metrics indicative of oscillations such as settling time and undershoot. The ultimate and practical limits to peak error are proportional to the deadtime and inversely proportional to controller gain, respectively. The ultimate and practical limits to integrated error are proportional to the deadtime squared and the ratio of controller reset time to controller gain, respectively.
For setpoint metrics, there is the time to get close to setpoint, which I call rise time, important for process capacity. I am sure there is a better name because the metric must be indicative of the performance for an increase or decrease in setpoint. The other setpoint metrics are overshoot, undershoot and settling time that can affect process capacity and efficiency. The use of a setpoint lead-lag or PID structure that minimizes proportional and derivative action on setpoint changes can reduce overshoot, despite using good load disturbance rejection tuning. A setpoint lag equal to the reset time (no lead) corresponds to a PID structure of Proportional and Derivative on the Process Variable and Integral action on the Error (PD on PV and I on E).
See the Sept and Oct 2016 Control Talk Blogs “PID Options and Solutions - Part 1” and “PID Options and Solutions - Parts 2 and 3” for a discussion of loop metrics in great detail including when they are important and how to improve them. Also look at the presentation for the ISA Mentor Program WebExs “ ISA-Mentor-Program-WebEx-PID-Options-and-Solutions.pdf ”.
My last bit of advice is to ask your spouse for metrics on your marriage. Minimizing the deadtime while still having a good signal to noise ratio is particularly important. For men, the saying “Happy wife, happy life” I think would work the other way as well. I just need a rhyme.