(456b) Adaptive Model Predictive Control with Recursive Subspace Identification

Iman Hajizadeh, Mudassir Rashid, Ali Cinar

Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL, USA
(Corresponding author: cinar@iit.edu)

Control of chemical processes with time-varying parameters and nonlinear dynamics is challenging. The presence of stochastic disturbances, random measurement noises and unknown time-varying delays can make the problem more complex. A time-invariant model cannot describe the dynamic behaviour of these processes accurately and an offline-tuned controller cannot perform satisfactorily when the process is subjected to major disturbances^1,2.

In this work, we propose a data-driven recursive subspace identification approach and an adaptive model predictive control (AMPC) with a comprehensive controller performance assessment system (CPAS). To obtain an accurate and reliable time-varying model of the process, we extended the optimized version of the recursive predictor-based subspace identification method to better handle stochastic disturbances, measurement noises, and variable delays^3–5. This is done by incorporation of constraints on the fidelity and accuracy of the identified models, correctness of the sign of the input-to-output gains, and the integration of heuristics to ensure stability of the recursively identified models. Then, an AMPC is designed using this recursively updated model to handle constraints on the manipulated variables and outputs as well as any safety limits of the process⁶. To make the controller more efficient for mitigating the effects of unknown disturbances, the controller parameters are modified using information from a feature extraction method that can detect significant changes based on the rate and shape of variations in the outputs in real-time. Furthermore, to monitor the performance of the AMPC and retune the controller parameters, we also propose a detailed CPAS to evaluate the closed-loop performance on-line based on predefined performance indices in different time windows.

We have tested our proposed techniques for an artificial pancreas (AP) system where the model of glucose-insulin dynamics in people with type 1 diabetes is the underlying system. This process has all the aforementioned challenges in the modelling and controller design. The nonlinearities and time-varying changes of blood glucose dynamics, the occurrence of nonstationary disturbances, time-varying delays on measurements and insulin infusion, and noisy data from sensors provide challenges for the AP. Furthermore, an AP system is challenged by several factors such as meals, exercise, sleep and stress (MESS) that may have significant effects on glucose dynamics in the body⁷.

The FDA approved UVa/Padova metabolic simulator is used to design and test closed-loop algorithms for the AP⁸. This simulator has a set of virtual patients with type 1 diabetes on which to run the in-silico experiments. The results based on new developed techniques show an excellent performance in increasing the average percentage of time spent in the target range (Blood Glucose Concentration [BGC] ∈ [70, 180] mg/dL) by 12 % and reducing the mean and standard deviation of BGC by 10 and 5 mg/dL, respectively. The average maximum value of BGC was reduced by 17 mg/dL without any significant change in the average minimum value of BGC (a decrease of 0.5 mg/dL) and the injected insulin (manipulated variable) (an increase of 0.5 Unit of insulin per day). These outcomes demonstrate a significant improvement in the AP control system and their potential to be used in developing a fully automated AP that can function without any manual information and accommodate major disturbances to the BGC, such as MESS.

References

1. Schäfer J, Cinar A. Multivariable MPC system performance assessment, monitoring, and diagnosis. J Process Control. 2004;14(2):113-129.
2. Ljung L, Söderström T. Theory and Practice of Recursive Identification. Electr Eng. 1983;4:541.
3. Houtzager I, van Wingerden J-W, Verhaegen M. Recursive predictor-based subspace identification with application to the real-time closed-loop tracking of flutter. IEEE Trans Control Syst Technol. 2012;20(4):934-949.
4. Hajizadeh I, Rashid M, Cinar A. Ensuring Stability and Fidelity of Recursively Identified Control-Relevant Models. In: The 18th IFAC Symposium on System Identification. Stockholm, Sweden; 2018 (Accepted).
5. Hajizadeh I, Rashid M, Turksoy K, et al. Multivariable recursive subspace identification with application to artificial pancreas systems. IFAC-PapersOnLine. 2017;50(1):886-891.
6. Rashid M, Hajizadeh I, Cinar A. Plasma Insulin Cognizant Predictive Control for Artificial Pancreas. In: The American Control Conference. Milwaukee, WI; 2018 (Accepted).
7. Cinar A, Turksoy K. Advances in Artificial Pancreas Systems: Adaptive and Multivariable Predictive Control. Springer; 2018.
8. Dalla Man C, Micheletto F, Lv D, Breton M, Kovatchev B, Cobelli C. The UVa/Padova type 1 diabetes simulator: new features. J Diabetes Sci Technol. 2014;8(1):26-34.