MPC is the crown jewel of industrial process control. Originally conceived in the late 1970s as model predictive heuristic control, it works by using a process model to predict the future behavior of a plant, then optimizing a sequence of control moves over a receding horizon to steer the output toward its set point. This gives MPC three superpowers that conventional controllers lack: fast reference tracking, the ability to handle constraints on inputs and states, and a natural talent for multivariable processes and time delays. Over the decades, variants such as dynamic matrix control, generalized predictive control, and economic MPC have carried it into refineries, chemical plants, and power stations worldwide.

But MPC has an Achilles heel: its performance is only as good as its model. Researchers have long pointed out that in large-scale industrial systems it is rarely possible to find process models that are 100 percent accurate. Model parameters can be uncertain, the model structure itself can be wrong, and in thermal power plants the situation is especially dire. Superheated steam temperature, a vital operating parameter, illustrates the problem perfectly: its dynamic characteristics shift significantly with the operating condition of the unit, mechanistic modeling is difficult, and the accuracy of system identification cannot be guaranteed. As renewable energy penetration forces coal-fired units into deep peak-shaving operation, working conditions change frequently across a wide range, making the mathematical descriptions of thermal processes vary continuously.

Previous attempts to rescue MPC in this environment have taken two main routes. Robust MPC can tolerate model uncertainty, but its algorithms are too complex to implement on the distributed control systems (DCS) that run thermal power plants. The more common workaround is a hierarchical structure that pairs MPC with a basic PI or PID controller, so the MPC no longer depends directly on the process model. Yet even this approach stumbles, because designing the MPC requires identifying the closed-loop model of the PID-based system, and closed-loop identification is complex, time-consuming, and computationally expensive. Worse, thermal processes are contaminated by disturbances and measurement noise that deteriorate identification accuracy. An extended state observer (ESO)-based MPC strategy was proposed to sidestep identification, but when a coal-fired unit is running, it is impractical to test whether the plant has been fully compensated by the ESO, because the modified process is an open-loop unstable integral system.

The new solution, developed by Gengjin Shi, Miaomiao Ma, Donghai Li, Yanjun Ding, and Kwang Y. Lee, replaces both the PID and the ESO in the hierarchical structure with a reference model-based PID controller known as a desired dynamic equational (DDE) PID controller. The core idea is elegant: instead of identifying what the process actually does, the engineers specify what the closed loop should do. The DDE-PID is tuned so that its parameters are evaluated directly from the coefficients of a desired dynamic equation, typically a first- or second-order reference model with a chosen closed-loop bandwidth. If the tuning is appropriate, the closed-loop output tracks the response of this reference model with an integral absolute error no larger than 10 percent, an overshoot below 1 percent, no obvious oscillation, and an unsaturated actuator.

Here is where the technical magic happens. When the DDE-PID is well-tuned, its reference model becomes a strong assumption that the closed loop behaves like the specified dynamic equation, and that assumption can serve as the design model for the MPC. The MPC in the upper layer of the hierarchy is then designed entirely from this known reference model, in state-space form, discretized at the same sample time as the DCS, with a quadratic optimization problem solved over a prediction horizon and a control horizon set to one for simplicity and safety. No accurate process model, no closed-loop identification, no open-loop unstable compensation to verify. Meanwhile, the DDE-PID itself descends from a nonlinear robust controller with a disturbance observer, the Tornambè controller, so it brings a built-in capacity to estimate and reject unmeasured external disturbances that the MPC alone cannot touch.

The team validated the approach, abbreviated MPC-DDE, against two widely recognized industrial PID tuning methods, the Skogestad internal model control PID and the approximated maximum-sensitivity integral gain optimization PID, across six typical thermal process models representing subsystems such as low-pressure heaters, superheated steam temperature, high-pressure heaters, and boiler drums. The results were striking. Across most models, MPC-DDE achieved the shortest settling time and the smallest integral absolute errors for both reference tracking and disturbance rejection. On a drum-level integral process, for instance, MPC-DDE posted a settling time of 2.02 seconds and a tracking error of 0.710, compared with 15.26 seconds and 3.133 for SIMC-PID. Crucially, plain MPC could not reject unmeasured disturbances on processes with integrators, while MPC-DDE handled them effortlessly through the disturbance observer embedded in the DDE-PID.

Robustness, the make-or-break property for variable working conditions, was tested with Monte Carlo simulations of 1,000 trials per model, perturbing plant coefficients within plus or minus 10 percent. The scatter plots told a clear story: MPC-DDE’s scatters were more intensive and closer to the origin than those of MPC, SIMC-PID, and AMIGO-PID, indicating stronger robustness and better dynamic performance. The researchers explain this by noting that the DDE-PID is equivalent to a control structure with state feedback and a disturbance observer, giving it a strong ability to handle model uncertainties, and because the DDE-PID absorbs plant perturbations, the design model of the MPC varies little. The team also applied MPC-DDE to the power loop of a recognized nonlinear fluidized-bed combustor model under five different steady-state operating conditions, where the Vinnicombe gap measurement confirmed that nonlinearity grows with load, and MPC-DDE again delivered the smallest disturbance rejection errors against fuel feed, primary air flow, and coal quality disturbances.

The decisive test came in the field. On 11 August 2022, the researchers implemented MPC-DDE on the secondary air system of a 330 MW in-service unit at Shenxi Power Plant in Shenyang, Liaoning Province, China. The secondary air flow, regulated by two blowers, determines combustion efficiency and NOx emissions, and its command is computed in real time from load, main steam pressure, and fuel feed. Because open-loop step tests are forbidden during safe operation, the MPC could not be designed from an identified process model, making this exactly the scenario MPC-DDE was built for. With the unit load varying between 140 and 175 MW, the average tracking error of the secondary air dropped from 12.97 per second under the original field-tuned PI controller to 6.18 per second under MPC-DDE, a reduction of more than half, while the controller covered a wider load and command range than either the PI or the DDE-PI alone.

The implications reach far beyond one air system in one plant. As power grids absorb ever more wind and solar generation, coal-fired units are being pushed into frequent deep peak-shaving duty, and controllers must remain stable and accurate while the plant’s own dynamics shift beneath them. The authors’ conclusion is candid about the method’s limits: MPC-DDE is not suitable for processes with large relative delay, where the ratio of time delay to time constant is high, because the DDE-PID output cannot then track the desired dynamic response accurately. But within its domain, the strategy offers something rare in industrial control: the optimization power of MPC, the disturbance rejection of a robust observer-based controller, and a tuning procedure simple enough for the distributed control systems already installed in power plants. The team’s future work includes an auto-tuning toolbox, extensions to multivariable systems, and pairing the DDE-PID reference model with other model-based strategies such as H-infinity controllers and linear quadratic regulators, suggesting that the model-free MPC may soon spread across the thermal power industry.

Subject of Research: A process-model-free method for model predictive control via a reference model-based proportional-integral-derivative controller with application to a thermal power plant

Article Title: A process-model-free method for model predictive control via a reference model-based proportional-integral-derivative controller with application to a thermal power plant

Article References: Shi, G., Ma, M., Li, D., Ding, Y., & Lee, K. Y. (2023). A process-model-free method for model predictive control via a reference model-based proportional-integral-derivative controller with application to a thermal power plant. Frontiers in Control Engineering, 4, Article 1185502. https://doi.org/10.3389/fcteg.2023.1185502

Image Credits: AI Generated

DOI: 10.3389/fcteg.2023.1185502

Keywords: process-model-free, method, model, predictive, control, reference, model-based, proportional-integral-derivative, controller, application, thermal, power