(564f) Fault-Tolerant Economic Model Predictive Control with Empirical Process Models

Actuator faults in the chemical process industries, which prevent the control signal from being able to impact the actuator output, are a problem that has been addressed through a variety of detection and fault-tolerant control methods in the literature (e.g., [1], [2]). Model-based fault-tolerant control designs are needed that can incorporate empirical process models because many industrial control designs are developed based on empirical models. Linear empirical models are common, and a variety of methods for identifying linear empirical models exist (e.g., subspace model identification methods [3]). Due to the widespread use of linear empirical models in advanced control designs such as model predictive control (MPC) in industry, development of a methodology for handling actuator faults in such controllers is necessary. This is particularly important since an empirical model developed from data corresponding to the case that all inputs are varying (i.e., no fault has occurred) may no longer be accurate after a fault prevents one of the inputs from varying because the data corresponding to the case that an actuator output is fixed was not incorporated in the data used to develop the original empirical model corresponding to the case without faults.

In this work, we develop an approach for accounting for actuator faults in MPC based on empirical models by utilizing an error-triggering procedure to initiate on-line updates of the empirical model based on significant prediction error due to the fault, assuming that it is known which actuator has experienced a fault. The methodology presented is developed in the context of economic model predictive control (EMPC) with empirical models [4] due to the potential of this control design to dictate time-varying process operation by computing a time-varying input trajectory, which may cause it to compute inputs that persistently excite the process dynamics so that routine process operating data can be utilized for the on-line model identification procedure. Specifically, the implementation strategy of the EMPC is updated after a fault to either incorporate the value of the faulty actuator output within the empirical model (reducing the number of decision variables) when the value at which the faulty actuator output is fixed is known, or, when the value of the faulty actuator output is not known, the EMPC continues to solve for all inputs but only implements those for the non-faulty actuators. A moving horizon error detector computes the relative prediction error in all process outputs throughout a prediction horizon and initiates model re-identification when this error exceeds a pre-specified threshold [5], where the new model identified after a fault has one less input since the faulty actuator output is no longer available to be adjusted by the EMPC. A chemical process example demonstrates the effectiveness of the proposed strategy at compensating for the actuator fault compared to utilizing a single empirical model throughout the time of operation despite the faults. It also demonstrates that the moving horizon error detector is effective at determining the necessity of updating the empirical model after a fault, so that the model is only changed within the control design when significant prediction error is detected.

[1] Lao L, Ellis M, Christofides PD. Proactive fault-tolerant model predictive control. AIChE Journal. 2013;59:2810-2820.

[2] Mhaskar P, Gani A, El-Farra NH, McFall C, Christofides PD, Davis JF. Integrated fault-detection and fault-tolerant control of process systems. AIChE Journal. 2006;52:2129-2148.

[3] Van Overschee P, De Moor B. Subspace Identification for Linear Systems: Theory, Implementation, Application; Kluwer Academic Publishers: Boston, Massachusetts, 1996.

[4] Alanqar A, Ellis M, Christofides PD. Economic model predictive control of nonlinear process systems using empirical models. AIChE Journal. 2015;61:816-830.

[5] Alanqar A, Durand H, Christofides PD. Error-triggered on-line model identification for model-based feedback control. AIChE Journal. 2017;63:949-966.