Control Of Nonlinear Process Systems Research Articles

Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results

This paper discusses recent developments in the data-based modeling and control of nonlinear chemical process systems using sparse identification of nonlinear dynamics (SINDy). SINDy is a recent nonlinear system identification technique that uses only measurement data to identify model dynamical systems in the form of first-order nonlinear differential equations. In this work, the challenges of handling time-scale multiplicities and noisy sensor data when using SINDy are addressed. Specifically, a brief overview of novel methods devised to overcome these challenges are described, along with modeling guidelines for using the proposed techniques for process systems. When applied to two-time-scale systems, to overcome model stiffness, which leads to ill-conditioned controllers, a reduced-order modeling approach is proposed where SINDy is used to model the slow dynamics, and nonlinear principal component analysis is used to algebraically “slave” the fast states to the slow states. The resulting model can then be used in a Lyapunov-based model predictive controller with guaranteed closed-loop stability provided the separation of fast and slow dynamics is sufficiently large. To handle high levels of sensor noise, SINDy is combined with subsampling and co-teaching to improve modeling accuracy. The challenges of modeling and controlling large-scale systems using noisy industrial data are then addressed by using ensemble learning with SINDy. After summarizing the advances, a nonlinear chemical process is used to provide an end-to-end demonstration of process modeling using sparse identification with guidelines for chemical engineering practitioners. Finally, several future research directions for the incorporation of SINDy into process systems engineering are proposed.

Adaptive output‐feedback Lyapunov‐based model predictive control of nonlinear process systems

SummaryThis work addresses the problem of output feedack control of nonlinear uncertain systems via adaptive Lyapunov‐based model predictive control design. To this end, at every control implementation, a moving horizon mechanism is first utilized to generate current estimates of the uncertainty and states. The model with the current estimated uncertainty is then used in a Lyapunov‐based model predictive controller to achieve uncertainty rejection. The key ideas are explained through an illustrative example and the application demonstrated on a networked reactor‐separator process subject to measurement noise and uncertainty.

Lyapunov‐based offset‐free model predictive control of nonlinear process systems

AbstractThis work considers the problem of control of nonlinear systems subject to uncertainty. To this end, a Lyapunov‐based robust model predictive controller (MPC) design is integrated with a moving horizon based offset‐free mechanism to enable improved closed–loop performance. Simulation results are presented to illustrate the key ideas of the proposed design.

Economic model predictive control of nonlinear process systems using empirical models

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J, 61: 816–830, 2015

Real‐time economic model predictive control of nonlinear process systems

Closed‐loop stability of nonlinear systems under real‐time Lyapunov‐based economic model predictive control (LEMPC) with potentially unknown and time‐varying computational delay is considered. To address guaranteed closed‐loop stability (in the sense of boundedness of the closed‐loop state in a compact state‐space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite‐time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed‐loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed‐loop stability under the real‐time LEMPC strategy is analyzed and specific stability conditions are derived. The real‐time LEMPC scheme is applied to a chemical process network example to demonstrate closed‐loop stability and closed‐loop economic performance improvement over that achieved for operation at the economically optimal steady state. © 2014 American Institute of Chemical Engineers AIChE J, 61: 555–571, 2015

Economic model predictive control of nonlinear process systems using Lyapunov techniques

AbstractIn this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

AbstractIn this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010

Distributed model predictive control of nonlinear process systems

AbstractThis work focuses on a class of nonlinear control problems that arise when new control systems which may use networked sensors and/or actuators are added to already operating control loops to improve closed‐loop performance. In this case, it is desirable to design the pre‐existing control system and the new control system in a way such that they coordinate their actions. To address this control problem, a distributed model predictive control method is introduced where both the pre‐existing control system and the new control system are designed via Lyapunov‐based model predictive control. Working with general nonlinear models of chemical processes and assuming that there exists a Lyapunov‐based controller that stabilizes the nominal closed‐loop system using only the pre‐existing control loops, two separate Lyapunov‐based model predictive controllers are designed that coordinate their actions in an efficient fashion. Specifically, the proposed distributed model predictive control design preserves the stability properties of the Lyapunov‐based controller, improves the closed‐loop performance, and allows handling input constraints. In addition, the proposed distributed control design requires reduced communication between the two distributed controllers since it requires that these controllers communicate only once at each sampling time and is computationally more efficient compared to the corresponding centralized model predictive control design. The theoretical results are illustrated using a chemical process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Enhanced stability regions for model predictive control of nonlinear process systems

AbstractThe problem of predictive control of nonlinear process systems subject to input constraints is considered. The key idea in the proposed approach is to use control‐law independent characterization of the process dynamics subject to constraints via model predicative controllers to expand on the set of initial conditions for which closed–loop stability can be achieved. An application of this idea is presented to the case of linear process systems for which characterizations of the null controllable region (the set of initial conditions from where closed–loop stability can be achieved subject to input constraints) are available, but not practically implementable control laws that achieve stability from the entire null controllable region. A predictive controller is designed that achieves closed–loop stability for every initial condition in the null controllable region. For nonlinear process systems, while the characterization of the null controllable region remains an open problem, the set of initial conditions for which a (given) Lyapunov function can be made to decay is analytically computed. Constraints are formulated requiring the process to evolve within the region from where continued decay of the Lyapunov function value is achievable and incorporated in the predictive control design, thereby expanding on the set of initial conditions from where closed–loop stability can be achieved. The proposed method is illustrated using a chemical reactor example, and the robustness with respect to parametric uncertainty and disturbances demonstrated via application to a styrene polymerization process. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Robust model predictive control of nonlinear process systems: Handling rate constraints

This work considers the problem of stabilization of control affine nonlinear process systems subject to constraints on the rate of change and magnitude of control inputs in the presence of uncertainty. We first handle rate constraints within a soft constraints framework. A new robust predictive controller formulation that minimizes rate constraint violation while guaranteeing stabilization and input constraint satisfaction from an explicitly characterized stability region is designed. We then derive conditions that allow for guaranteed satisfaction of hard rate constraints. Subsequently, a predictive controller is designed that ensures rate constraints satisfaction when the required conditions are satisfied, relaxing them otherwise to preserve feasibility and robust stability. The implementation of the proposed predictive controllers is illustrated via a chemical reactor example.

Application of minimum crest factor multisinusoidal signals for “plant-friendly” identification of nonlinear process systems

Abstract Guidelines for specifying the design parameters of minimum crest factor multisine signals generated per the approach of Guillaume et al. are presented. These guidelines are evaluated in the identification and control of nonlinear process systems. The minimum crest factor multisine signals offer some distinct advantages over both Schroeder phased multisine signals and multi-level Pseudo-Random Sequences (multi-level PRS) with respect to “plant-friendliness” considerations. These signals can be used to reduce the effects of nonlinearity in obtaining an Empirical Transfer Function Estimate (ETFE). As an example, the ETFE of a Rapid Thermal Processing (RTP) reactor simulation is presented. The effectiveness of the minimum crest factor multisine signals is also discussed and illustrated in the identification and control of a simulated continuous stirred tank reactor using “Model-on-Demand” estimation and Model Predictive Control. Since the performance of the “Model-on-Demand” estimator is highly dependent upon the quality of the identification data, the CSTR case study provides a compelling example of the usefulness of the proposed design procedure.