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# What is rate-predictive control?

05 August 2019

### A new non-PID control algorithm, rate-predictive control (RPC), is adaptive to changes in process gain. This is helpful, says Allan Kern, given the difficult history of loop tuning, auto-tuning, and model maintenance.

##### Rate-predictive control (RPC) uses a pre-set move rate, and tapers the move based on the PV’s predicted (apparent or already manifest) value. Courtesy: APC Performance LLC

Most people in the process control business accept that the proportional-integral-derivative (PID) algorithm, for all its idiosyncrasies, is unlikely to ever be replaced as industry’s standard for single-loop control. A recently patented invention called rate-predictive control (RPC) compels academic and practical interest from several standpoints. RPC is:

• A new and novel control algorithm (not a PID variation) with notable advantages.
• Adaptive to process gain changes, a landmark development, given industry’s long and difficult history of loop tuning, auto-tuning, model maintenance, and related challenges.
• Well-suited as a model-less feedback multivariable control algorithm, which is something that remains otherwise lacking today. A follow-up article will discuss multivariable control.

How does RPC work?
RPC is simpler and more intuitive than PID. The key to understanding RPC is perceiving its simple mechanism, and not necessarily to plumb its math. However, its math is simpler than PID or model-based control.

The graphic illustrates how RPC works. At time zero, the setpoint is increased by 10%. In response, RPC begins increasing the output at a pre-set move rate (1% per second, in this example). During each controller execution, RPC calculates the ongoing process variable (PV) rate-of-change and predicted future value. As the predicted value reaches the setpoint, the moves are tapered and halted so the PV ultimately settles exactly on target based on first-order process dynamics.

RPC prediction time is a tuning parameter set in a manner similar to PID integral time (or Lambda) and is often equal to or somewhat longer than the actual 63% process time constant (T63) to provide a smooth and reliable approach to setpoint with little or no overshoot or oscillation.

The pre-set move rate is selected based on experience and safe operating practice and can be thought of as a process speed limit or safe driving habit, although RPC is not limited to one speed. The move rate can be dynamically adjusted to meet various control performance criteria. For example, a move rate multiplier can be applied when constraint limits are exceeded, and the move rate is dynamically adjusted within the RPC taper band.

As the prediction approaches the setpoint, the degree of rounding in the output trend is a function of the RPC taper band. The taper band serves to reduce the move rate as the predicted value approaches the setpoint, so that the move rate goes to zero as the error goes to zero.

This is analogous to how an operator, when controlling in manual mode, would reduce step size as the setpoint is approached. The RPC taper band results in reliable control behavior in the face of real-life nonidealities such as variance in process response, deadtime, inverse response, etc.

RPC is affected by deadtime in essentially the same way as PID and to the same extent, so deadtime dominant loops (deadtime >> T63) remain a special challenge. However, RPC dynamic deadtime control is a novel technique that can improve control of deadtime dominant control loops.

It can be seen intuitively that the RPC mechanism is inherently adaptive to changes in process gain. For example, if process gain becomes larger, the process response will be larger, the prediction vectors will extend farther, and moves will be tapered and halted correspondingly sooner so the PV settles right on target. By the same reasoning, RPC is inherently adaptive to changes in the pre-set move rate, so that it can be manually tuned at will or dynamically adjusted to meet various high-performance criteria.

Several process control advantages in RPC are worth noting. RPC is inherently adaptive to changes in process gain. This is significant for an industry where the terms tuning, retuning and detuning have found roughly equal usage. Auto-tuning has come up far short of industry’s hopes and expectations. A model-based control has become perhaps best known for its high model-maintenance.

These experiences collectively stem from the same root cause – frequently and dynamically changing process gains that can benefit from an inherently adaptive method.

RPC also is inherently adaptive to changes in the move rate, which means the move rate can be manually tuned at will for desired loop performance, or dynamically adjusted, using built-in ancillary RPC features to achieve various high-performance criteria.

RPC is more responsive to incipient error and more stable as the PV returns to setpoint because it uses the predicted (apparent or already manifest) value of the PV and not just the current value.

For example, a conventional PID controller might see a small incipient error whereas RPC might see a larger error and make a much larger move sooner by taking the PV rate-of-change and predicted value into account. For the same reason, RPC is more stable and reliable as the PV returns to setpoint with little or no unwanted overshoot or oscillation. To control system operators, RPC looks identical to conventional PID controllers – it has PV, setpoint, output and mode – so it can be seamlessly adopted in an operations and control system environment. RPC is easier and more intuitive to learn and tune for control engineers.

Other tuning applications
RPC is versatile and can be tuned for other types of performance. For example, classic error-minimization or quarter-amplitude-damping can be provided by using a high move rate and short prediction time. RPC (like PID) works “as is” for integrating and non-integrating variables. For loops where there is effectively a very high “speed limit,” (not uncommon in single-loop control, but rare in multivariable control) a large move rate can be combined with a wide taper band to provide a large response when far from setpoint, tapering to a safe speed as the setpoint is approached.

RPC is ‘model-less,’ which is another way of saying it is inherently adaptive. It does not use a process model (nor does it attempt to ‘roll its own,’ such as with auto-tuning or adaptive modelling). RPC relies on gain direction only, which is equivalent to PID control action (direct or reverse), or the sign of the gain (positive or negative). Gain direction is the most fundamental and immutable aspect of any model.

RPC uses process response time (T63), but this can be tuned intuitively (like integral time, Lambda or closed-loop response time), rather than in detail (as in model-based control). RPC performance is mildly impacted by variation in actual T63.

Gain direction and approximate speed of response are the minimum information necessary for effective control of any loop. More detailed model information can be put to further advantage, but it also introduces more cost, risk and maintenance. From this standpoint, RPC provides a prudent and robust compromise among simplicity, performance, and reliability.

Allan Kern is owner and consultant with APC Performance.