Economic model predictive control (EMPC) has attracted significant attention in recent years and is recognized as a promising advanced process control method for next‐generation smart manufacturing. It has the potential to not only improve economic performance but also significantly increase computational complexity. Model approximation has been a standard approach for reducing computational complexity in process control. In this work, we perform a study on three types of representative model approximation methods applied to EMPC, including model reduction based on available first‐principle models (e.g., proper orthogonal decomposition), system identification based on input–output data (e.g., subspace identification) that results in an explicitly expressed mathematical model, and neural networks based on input–output data. A representative algorithm from each model approximation method is considered. Two processes that are very different in dynamic nature and complexity were selected as benchmark processes for computational complexity and economic performance comparison, namely, an alkylation process and a wastewater treatment plant. The strengths and drawbacks of each method are summarized according to the simulation results, with future research direction regarding control‐oriented model approximation proposed at the end.

Water scarcity is an urgent issue to be resolved and improving irrigation water-use efficiency through closed-loop control is essential. The complex agro-hydrological system dynamics, however, often pose challenges in closed-loop control applications. In this work, we propose a two-layer neural network (NN) framework to approximate the dynamics of the agro-hydrological system. To minimize the prediction error, a linear bias correction is added to the proposed model. The model is employed by a model predictive controller with zone tracking (ZMPC), which aims to keep the root zone soil moisture in the target zone while minimizing the total amount of irrigation. The performance of the proposed approximation model framework is shown to be better compared to a benchmark long-short-term-memory model for both open-loop and closed-loop applications. Significant computational cost reduction of the ZMPC is achieved with the proposed framework. To handle the tracking offset caused by the plant-model-mismatch of the proposed NN framework, a shrinking target zone is proposed for the ZMPC. Different hyper-parameters of the shrinking zone in the presence of noise and weather disturbances are investigated, of which the control performance is compared to a ZMPC with a time-invariant target zone.

Water scarcity is an urgent issue to be resolved and improving irrigation water-use efficiency through closed-loop control is essential. The complex agro-hydrological system dynamics, however, often pose challenges in closed-loop control applications. In this work, we propose a twolayer neural network (NN) framework to approximate the dynamics of the agro-hydrological system. To minimize the prediction error, a linear bias correction is added to the proposed model. The model is employed by a model predictive controller with zone tracking (ZMPC), which aims to keep the root zone soil moisture in the target zone while minimizing the total amount of irrigation. The performance of the proposed approximation model framework is shown to be better compared to a benchmark long-short-term-memory (LSTM) model for both open-loop and closed-loop applications. Significant computational cost reduction of the ZMPC is achieved with the proposed framework. To handle the tracking offset caused by the plantmodel-mismatch of the proposed NN framework, a shrinking target zone is proposed for the ZMPC. Different hyper-parameters of the shrinking zone in the presence of noise and weather disturbances are investigated, of which the control performance is compared to a ZMPC with a time-invariant target zone.

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