h i g h l i g h t s • A new MPC suitable for closed-loop re-identification is proposed. • A re-identification needs to be developed in a closed-loop fashion, since the process cannot be stopped. • The main problem is the conflict between the control and identification objectives. • A generalization, from punctual stability to (invariant) set stability, is done to avoid the conflict. • The proposal could be potentially applied to real processes.
Recently, a linear Model Predictive Control (MPC) suitable for closed-loop re-identification was proposed, which solves the potential conflict between the persistent excitation of the system (necessary to perform a suitable identification) and the control, and guarantees recursive feasibility and attractivity of an invariant region of the closed-loop. This approach, however, needs to be extended to account for a proper robustness to moderate-to-severe model mismatches, given that re-identifications are necessary when the system is not close to the operating point where the current linear model was identified. In this work, new results on robustness are presented, and an exhaustive application of the new MPC suitable for closed-loop re-identification to a nonlinear polymerization reactor simulator is made to explore the difficulties arising from a real life identification. Furthermore, several closed-loop re-identification are performed in order to clearly show that the proposed controller provides uncorrelated input-output data sets, which together with the guaranteed stability, constitute the main controller benefit.
The main problem of a closed-loop re-identification procedure is that, in general, the dynamic control and identification objectives are conflicting. In fact, to perform a suitable identification, a persistent excitation of the system is needed, while the control objective is to stabilize the system at a given equilibrium point. However, a generalization of the concept of stability, from punctual stability to (invariant) set stability, allows for a flexibility that can be used to avoid the conflict between these objectives. Taking into account that an invariant target set includes not only a stationary component, but also a transient one, the system could be excited without deteriorating the stability of the closed-loop. In this work, a MPC controller is proposed that assures the stability of invariant sets at the same time that a signal suitable for closed-loop re-identification is generated. Several simulation results show the propose controller formulation properties.
Stationary process gains are critical model parameters for determining targets in commercial MPC technologies. Consequently, important savings can be reached by accessing an early prevention method capable of detecting whether the actual process moves away from the modeled dynamics, particularly by indicating when the process gains are no longer represented by those included in the model identified during commissioning stages. In this first approach, a subspace identification method is used under open-loop process condition to estimate the process gain matrix. The main reason for using the subspace identification (SID) method is that it works directly with raw data; it directly yields a multivariable state space model and has proved to be successful in dealing with multivariable processes and periodic batch-wise data collection. To detect significant changes in the estimator population, a monitoring sequence of hypothesis tests can be done through simple confidence limits directly on each gain estimator, or increasing the sensitivity by using the exponentially weighted moving average (EWMA) or the cumulative sum (CUSUM) algorithms. The objective of this aticle is to present a rational combination of inferential tools capable of detecting which gain of a multivariable model starts moving away from its original value. The anticipated knowledge of these events could provide a warning to process engineers and prevent targeting process conditions with wrong gain estimations. The regular follow-up of the gain matrix should also help to localize those dynamics needing an updating identification and reduce the frequency of time-consuming re-identification of the complete model.
Resumen: Model Predictive Control (MPC) is the most used advanced control strategy in the industries, mainly due to its capability to fulfill economic objectives, taking into account a dynamic simplified model of the plant, constraints, and stability requirements. In the last years, several economic formulations of MPC have been presented, which get over the standard setpoint-tracking formulation. The goal of this work is to provide, by means of application to a highly nonlinear plant, a comparison of different strategies, focusing mainly on economic optimality, computational burden, and economic performance.
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