The problem of guaranteeing stability from the entire null controllable region (NCR) for multi-input linear dynamical systems is addressed in the present manuscript. The proposed controller design is ...inspired by results for single input systems and generalized to multiple input systems. The approach relies on utilizing the level sets of the NCR as level sets of a Lyapunov function. A contractive constraint is incorporated into a model predictive control design, guaranteeing feasibility for any horizon length, and resulting in the NCR as the closed-loop stability region. The proposed method is illustrated using a simulation example.
This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be ...capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example.
This manuscript addresses the problem of determining input excitation for data driven model identification appropriate for cell culture bio-processes in general, and for an industrial bioreactor used ...for the production of monoclonal antibodies, in particular. The design space is set up to give us the operating parameters for the key objective of demonstrating the feasibility of using far more perturbations than typically done in bio process identification, although significantly less than other applications, to yield data rich enough for the purpose of data driven modelling (and subsequently, control). A proprietary mechanistic model developed by Sartorius for their Cellca cell line is first introduced to serve as a test bed, based on AMBR 250® (Sartorius registered trademark for integrated high throughput bioreactor systems). Subsequently, this test bed is used to address the question of determining the frequency of input perturbation sufficient to identify a data driven dynamic model. To this end, the test bed is used to generate data at various frequencies and a linear time invariant model identified. The predictive capability of the identified model is used to ascertain the frequency of changes in data generation such that the changes are acceptable from a biological standpoint, and yet generate sufficiently rich data. In particular, a frequency of perturbations at once every three days is found to balance these tradeoffs for the monoclonal antibody process under consideration. The results from the manuscript are meaningful both from a specific results standpoint (as illustrated by subsequent adoption by Sartorius), but also by providing a mechanism to ascertain such information for other bio-processes.
This paper addresses the problem of enabling the use of complex first principles model information as part of a linear Model Predictive Control implementation for improved control. This is achieved ...by building a hybrid model that uses an approximate implementation of a first principle model and a Subspace Identification (SID) State Space model to explain the error (the residual) between the first principle implementation and the process outputs. The key idea is to utilize the first principles model with the initial conditions consistent with a particular batch, but using a constant value of the control action. Thus, even though the first principles model may be intractable from an optimization perspective, the approximate implementation allows the hybrid model to be linear (in the control input), while allowing the nonlinear dependence on the initial conditions to be captured. The proposed hybrid model based MPC is compared against a previous hybrid model with 2 SID models and a single SID model on a fed batch crystallization process.
The paper demonstrates the improved performance achievable by the readily implementable proposed approach.
This paper addresses the problem of capturing the multiphase nature of a rotational molding process using subspace identification (SSID) to enable improved control. Existing SSID techniques are not ...designed to utilize any known, multiphase nature of a process in the model identification stage. This work adapts existing SSID methods to account for multiple phases by splitting the data into phases during the identification step and building a distinct SSID model for each phase while carefully connecting the individual models through the means of subspace states. This is achieved via a partial least-squares (PLS) model that relates the final states of the preceding phase to the initial states of the proceeding phase. This multiphase subspace identification (MPSSID) approach exploits the ability of SSID techniques for dynamic modeling of batch processes, which allows for model construction using batches of nonuniform length. In this work, the proposed approach is applied to the rotational molding process. For rotational molding, the final product quality is dependent on the temperature trajectory of the polymer inside the mold, and the process goes through visibly distinct phases that can be recognized when a specific temperature (not time) is reached. Data from past experiments are used to build the model and validate it, comparing the predictive ability of multiphase models to conventional one-phase models. Results demonstrate the ability of the multiphase models to better predict both the temperature trajectories and final product quality of validation batches.
In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by ...population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.
This work considers the problem of stabilization of nonlinear systems subject to constraints, uncertainty and faults in the control actuator. We first design a robust model predictive controller that ...allows for an explicit characterization of the set of initial conditions starting from where feasibility of the optimization problem and closed-loop stability is guaranteed. The main idea in designing the robust model predictive controller is to employ Lyapunov-based techniques to formulate constraints that (a) explicitly account for uncertainty in the predictive control law, without making the optimization problem computationally intractable, and (b) allow for explicitly characterizing the set of initial conditions starting from where the constraints are guaranteed to be initially and successively feasible. The explicit characterization of the stability region, together with the constraint handling capabilities and optimality properties of the predictive controller, is utilized to achieve fault-tolerant control of nonlinear systems subject to uncertainty, constraints, and faults in the control actuators. The implementation of the proposed method is illustrated via a chemical reactor example.
•A new model predictive controller with re-identification is proposed.•The proposed re-identification approach uses the past training data and current data as training data.•Closed-loop subspace ...identification is utilized for identification.•The accuracy of model prediction is monitored by the proposed model.
In this work, we address the problem of handling plant-model mismatch by designing a subspace identification based MPC framework that includes model monitoring and closed-loop identification components. In contrast to performance monitoring based approaches, the validity of the underlying model is monitored by proposing two indexes that compare model predictions with measured past output. In the event that the model monitoring threshold is breached, a new model is identified using an adapted closed-loop subspace identification method. To retain the knowledge of the nominal system dynamics, the proposed approach uses the past training data and current input, output and set-point as the training data for re-identification. A model validity mechanism then checks if the new model predictions are better than the existing model, and if they are then the new model is utilized within the MPC. The effectiveness of the proposed method is illustrated through simulations on a nonlinear polymerization reactor.
Latent Variable Model Predictive Control (LV-MPC) algorithms are developed for trajectory tracking and disturbance rejection in batch processes. The algorithms are based on multi-phase PCA models ...developed using batch-wise unfolding of batch data arrays. Two LV-MPC formulations are presented, one based on optimization in the latent variable space and the other on direct optimization over a finite vector of future manipulated variables. In both cases prediction of the future trajectories is accomplished using statistical latent variable missing data imputation methods. The proposed LV-MPCs can handle constraints. Furthermore, due to the batch-wise unfolding approach selected in the modeling section, the nonlinear time-varying behavior of batch processes is captured by the linear LV models thereby yielding very simple and computationally fast nonlinear batch MPC. The methods are tested and compared on a simulated batch reactor case study.
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