# Effect of Process Dynamics on Loop Performance Tips

July 11, 2013
Most process engineers were not taught how process and equipment design affect loop dynamics and performance. Many of the more demanding control applications are the result poor process dynamics. Automation engineers can help bridge the gap and be able to intelligently discuss how plant design is affecting plant performance.

Most process engineers were not taught how process and equipment design affect loop dynamics and performance. Many of the more demanding control applications are the result poor process dynamics. Automation engineers can help bridge the gap and be able to intelligently discuss how plant design is affecting plant performance. The following perspective, overview, and recommendations can provide the understanding for better basic control and benefits from advanced control making the most of process knowledge.

Perspective

An increase in back mixed volumes is beneficial in terms of increasing the process time constant or decreasing the integrating process gain slowing down and attenuating load disturbances. In contrast, an increase in a plug flow volume (e.g. pipe and dip tube volume) or decrease in mixing (e.g. increase in turnover time) is detrimental in terms of increasing process dead time. A decrease in heat transfer coefficient will increase the secondary time constant presenting a problem in terms of slowing down corrective actions that is particularly problematic for integrating and runaway processes. Such insights are seen in the relationships and typical range of values for process gain, dead time, and time constants in the Process Dynamics Table

An essential realization for proper loop analysis is that time constants in series create dead time. These time constants can occur anywhere in the control loop. Multiple process time constants primarily arise from volumes in series and heat transfer surfaces.

In the first order plus dead time approximation (FOPDT), the largest time constant is singled out and a fraction of all other time constants is taken as dead time. For equal time constants, a fraction of the totalized time constants is used as dead time. The equations are for non-interacting time constants. Pairs of interacting time constants can be converted to non-interacting time constants.

The equivalent dead time from time constants in series is added to the pure dead time. If we are just looking at the process, the total is a process dead time. However, we need to include the dead time from the automation system to arrive at a total loop dead time that determines tuning and loop performance.

The process sources of pure dead time typically involve transportation or mixing delays.  Examples of transportation delays are composition or temperature changes propagating through a dip tube, extruder, pipeline, sheet line, static mixer, or any plug flow volume.

If the largest time constant is in the process downstream of load disturbances, the process time constant will act to slow down the excursion rate for these disturbances giving the PID controller time to catch up and correct for the load change. If the largest time constant is in the measurement or PID input signal, the disturbance seen by the PID is still slowed down but the actual process variable is not. The PID is seeing a filtered version of the real disturbance. The equations for estimating PID tuning and loop performance do not distinguish where the largest time constant is located. Consequently, the loop performance predicted must be corrected if the largest time constant is in the measurement or PID input signal.

The fraction of time constants not converted to dead time should be added to the largest time constant to give an open loop time constant. Open loop denotes the fact that the response being measured is for the PID controller output in manual, remote output or output tracking. The term "open loop" denotes no feedback action.

The process gain for composition and temperature control is a function of a flow ratio (e.g. ratio of manipulated flow to feed flow). The process gain for level and gas pressure is a function of the difference in flow going into and out of the volume. Plots of the process variable gain should be versus a flow ratio for composition and temperature and versus a flow difference for level and gas pressure.

The controller tuning depends upon the product of the valve or variable speed drive (VSD) gain, process gain, and measurement gain, termed the open loop gain. The open loop gain is dimensionless.

Note that the literature commonly calls the open loop gain a process gain; the open loop time constant a process time constant; and the total loop dead time a process dead time. The more descriptive terms he 6/14/2013 Control Talk Blog "Key Misunderstood Terms" serves as a reminder that the dynamics of the automation system, besides the process, affect tuning and loop performance.

For an integrating process, the product of the valve or VSD, process, and measurement gains is no longer dimensionless but has units of inverse time (e.g. 1/sec). Here the term open loop integrating process gain is used for the product.

A key concept important for a unified methodology is the approximation of a process with a large process time constant as a near-integrator so the tuning for integrating processes can be used. The response can be considered to be a near-integrator when the process time constant is larger than 4 times the total loop dead time.

The estimation of a secondary time constant can be important for tuning and loop analysis, particularly for integrating and runaway processes. For self-regulating processes, the secondary time constant is the second largest time constant in the loop. For an integrating process, it is also the second largest if you consider the integrating process gain can be equated to a large time constant in the near-integrator approximation. For a runaway process (open loop unstable process), the secondary time constant is also the second largest time constant because the largest time constant must be the positive feedback time constant for closed loop stability.

Overview

The dynamic response of processes can be categorized based on internal feedback within the process. If the process has negative feedback, the process is self-regulating and will eventually reach a steady state if there are no more disturbances or subsequent changes in PID output.  If the process has zero feedback, the process is integrating and will ramp for any unbalance in flows into and out of the volume. If the process has positive feedback, the process is runaway and can accelerate if left in manual long enough. In all cases, equipment limits, Safety Instrumented Systems, and relief devices may prevent the process from reaching a steady state or continuing to ramp or accelerate.

Processes with a dead time larger than the largest time constant are termed dead time dominant. While such processes are rare and often the result of a large time interval between analyzer updates, the tuning rules and loop performance change drastically. Consequentially, while there are 3 types of process responses, the self-regulating process is sub classified based on the ratio of the total loop dead time to the largest time constant creating a total of 4 types of dynamic responses. Self-regulating processes where the dead time to time constant ratio is less than ¼ are treated as lag dominant processes and can use the tuning rules for integrating processes. The remaining self-regulating processes use the self-regulating process tuning rules proven to be important as the process becomes dead time dominant.

Recommendations

•1.      To see the effect of process design on process dynamics, use the table and equations in the chapter to estimate the process gain, process time constants, and process dead time.

•2.      To see the effect of dynamics on tuning and loop performance, use the equations to estimate the ultimate gain and period depending upon whether the process is self-regulating, integrating, or runaway.

•3.      Convert lag dominant self-regulating and runaway processes to integrating processes and use integrating process tuning to prevent the start of oscillations from a reset time not being increased when a PID gain is decreased.

•4.      For near-integrating, integrating, and runaway processes, identify any significant secondary time constant (e.g. thermal lag from a heat transfer surface and thermowell for temperature control).

•5.      For runaway processes, make sure the PID gain is well above the limit for stability that is the inverse of the open loop gain. The open loop gain is the product of the manipulated variable gain (e.g. valve or variable speed drive gain), process gain, and the measurement gain.

•6.      For runaway processes, make sure the secondary time constant and total loop dead time are each significantly less than the primary process time constant to prevent closing of the window of allowable PID gains causing the process to be unstable for all tuning settings. To safely stay far enough away from a closed PID gain window, the largest possible secondary time constant and total loop dead time should each be less than 1/10 of the smallest possible primary process time constant determining positive feedback.

### Greg McMillan | Columnist

Greg K. McMillan captures the wisdom of talented leaders in process control and adds his perspective based on more than 50 years of experience, cartoons by Ted Williams and Top 10 lists.

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