The Feedback Loop and Process Dynamics

The loop

A measurement of the process variable is compared with a setpoint. The difference is the error. A controller acts on that error to produce an output, which moves a final control element, which changes the process, which changes the measurement. That circle is the feedback loop, and everything in it affects the result.

It follows that a badly performing loop can be caused by the sensor, the transmitter, the wiring, the controller, the valve, the process itself, or the interaction of the loop with other loops. Reaching for the tuning constants first is the most common mistake in process control.

Process gain

Process gain is the change in the process variable produced by a given change in controller output, expressed in consistent units. A high-gain process responds strongly to a small output change and needs a low controller gain; a low-gain process needs the opposite.

Crucially, process gain is often not constant. A valve's installed characteristic, a non-linear process such as pH or level in a spherical vessel, and changes in throughput all change the gain. A loop tuned at one operating point can be sluggish at another and unstable at a third, which is why loops that were "fine last year" oscillate after a production change.

Dead time

Dead time is the delay between an output change and any measurable response. It comes from transport delay in pipes, mixing time, analyser cycle time, measurement lag and scan rates.

Dead time is the fundamental limit on control performance. During dead time the controller is acting blind, and if it acts aggressively it will have over-corrected before it sees anything. The larger the ratio of dead time to process time constant, the lower the achievable performance and the more conservatively the loop must be tuned. Reducing dead time — moving a sensor closer, speeding an analyser, increasing scan rate — improves control more than any amount of tuning.

Time constant and process types

• Self-regulating — the process settles at a new steady state after a change. Most flow, temperature and pressure loops.
• Integrating — the process variable keeps changing until the imbalance is removed. Level in a vessel with a fixed outflow is the classic case; it needs a different tuning approach and usually much less integral action.
• Runaway — an exothermic reactor, where the response accelerates. These need specialist attention and robust protection.

Typical loop speeds

Flow loops are fast, noisy and have almost no dead time, so they use low gain and fast integral. Pressure loops on gas are fast; on liquid they are very fast. Level loops are integrating and usually want slow, gentle control. Temperature loops are slow with significant lag. Composition loops have large dead time from analyser cycles. Recognising which type you are dealing with narrows the tuning problem enormously before any test is run.