Model-following process control

All feedback controllers are designed to eliminate errors between the process variable and setpoint. Model-following controllers do so by forcing the process variable to reach the setpoint along a specified trajectory. The user defines the desired trajectory by creating a mathematical model that represents an idealized process—a process that would be easier to control if it could somehow ...


All feedback controllers are designed to eliminate errors between the process variable and setpoint. Model-following controllers do so by forcing the process variable to reach the setpoint along a specified trajectory.

The user defines the desired trajectory by creating a mathematical model that represents an idealized process—a process that would be easier to control if it could somehow be substituted for the real one. The controller then measures the model’s output rather than the actual process variable and tries to drive the model’s output toward the setpoint along the desired trajectory.

Doing so achieves specified closed-loop behavior for the idealized process, but does nothing for the actual process. A second controller is required to simultaneously force the actual process variable to match the model’s output, thereby forcing the actual process to mimic idealized process behavior. If both controllers can achieve their respective objectives, the actual process variable will end up following the desired trajectory toward the setpoint.

How it works

The graphic shows how such “model-following” can be accomplished with two PID loops. In the bottom loop (blue), the main PID controller applies its corrective efforts (the “model control signal”) to the model as if it were a real process. The model’s output is then fed back and subtracted from the setpoint to generate the error signal that feeds into the main controller.

The model control signal is also applied to the real process with the addition of a “correcting signal” generated by the top loop (orange). The error signal for this “correcting loop” is the difference between the model’s output and actual process variable. That difference is fed into the “correcting controller” to generate the correcting signal, which is added to the model control signal. That sum then serves as the corrective effort applied to the actual process.

The user tunes the “model controller” in the bottom loop to achieve a desired trajectory in response to a setpoint change. This exercise is fairly straightforward since the behavior of the idealized process is already known, having been defined by the user. Any number of loop-tuning rules could be used to translate gains and time constants of the idealized process model into tuning parameters for the model controller. (See “Loop Tuning Fundamentals,” Control Engineering , July 2003).

Tuning tradeoff

Tuning the correcting controller in the top loop is trickier, especially if gains and time constants of the real process are unknown or time-varying. The correcting loop is also subject to real-world load disturbances, plus artificial disturbances caused by the model control signal.

Process, Software, Controllers

The model controller in the blue loop applies its efforts to both the model and the actual process. The correcting controller in the orange loop applies an additional corrective effort to the actual process. The model controller tries to drive the model output toward the setpoint, while the correcting controller tries to drive the process variable toward the model output.

On the other hand, the correcting controller should not require precise tuning if the user-defined model is at least somewhat similar to the actual process. If that is the case, the model control signal will cause the actual process variable to match the model’s output reasonably well all by itself. Only a relatively small correcting signal will be required, so the correcting controller’s tuning should be relatively unimportant.

The correcting controller will need to make dramatic moves only if the user-defined model differs significantly from the actual process, causing the process variable to differ significantly from the model’s output. More detailed mathematical analysis and/or trial-and-error would be required to tune the correcting controller to handle large deviations.

Robust applications

In spite of this tradeoff, model-following controllers have proven particularly useful for applications where robustness is required, since they tend to be less sensitive to variations in behavior of the controlled process than traditional single-loop control strategies. The user-defined trajectory feature is also beneficial for servo control problems where eliminating error between the setpoint and process variable is only half the battle. The path that the process variable takes en route to the setpoint must also be controlled to avoid excessively oscillatory closed-loop behavior.

Several variations on the basic model-following control strategy have been proposed, including a technique recently published by Professor Krzysztof Pietrusewicz, Institute of Control Engineering , Szczecin University of Technology, and editor for Control Engineering Poland . See the on-line extra linked to this article under January 2007 at : “Model-Following Control. Robustness and quality at the same time?” The experiments discussed in the paper are outlined above.

Author Information

Vance VanDoren, Ph.D., P.E., is consulting editor for Control Engineering . He can be reached at .

Experiments in model-following control

Model-following control can promote robustness and quality, says Krzysztof Pietrusewicz, a professor at the Institute of Control Engineering, Szczecin University of Technology. Pietrusewicz, also an editor for Control Engineering Poland , tested a strategy with experiments described in his December 2006 paper “Model-Following Control: Robustness and quality at the same time? Is it possible?” Such improvements could have broad impact, he suggests, since almost 95% of industrial applications are based on the well-known proportional-integral-derivative (PID) control algorithm. Nearly 90% of Canadian sawmills use PI controllers, and PID has been a mainstay of control engineering practice for nearly 60 years because of simplicity and value, Pietrusewicz contends.

His experiments optimized oxide content in a steam boiler using a programmable logic controller (PLC) and MFC/IMC (model-following control/internal model control) software with nonlinear corrective control using fuzzy-logic. Structure offered shows substantial robustness to plant parameter changes, he says, such as varying time-delay. The MFC/IMC system offers an effective alternative to control algorithms employed so far and can be implemented on PLCs and programmable automation controllers (PACs), Pietrusewicz says. The experiment used a plant with an MFC/IMC system with constant parameters, scaling factors of controllers, and internal model of the controlled plant, instead of a gain-scheduled PID control.

Plant parameters were changed to test robustness and sensitivity to disturbances of two-loop control structures containing a model of the controlled plant and two PID controllers, says Pietrusewicz. Results were used to compare properties of the proposed structure with properties of classic control system structure with one feedback loop. The oxide content optimization system prevents oxide levels in the combustion chamber from decreasing during the burning process. Oxide content of less than 2% causes boiler shutdown for safety reasons and because of efficiency loss in the burning process.

In the experiments, robustness and control performance for the perturbed plant time-delay and time constant (in the presence of load disturbances, assuming constant parameters of both controllers) were compared with the classic control system with PID controllers tuned for each steam demand point. The setpoint of oxide content was varied from 4% (2,000) to 2.5% (1,000). Plant load has been treated as a perturbation. The main controller has been tuned in experimental conditions with 75% of burner power. After plant output and control signals were logged, the nominal model and model controller were derived. The corrective controller uses nonlinear PID with fuzzy logic. Results show that using model-following control can provide robustness and quality at the same time, Pietrusewicz suggests.

Mark T. Hoske, Control Engineering

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