Nael H. El-Farra

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control ☆

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints. We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time for which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.

Bounded robust control of constrained multivariable nonlinear processes

Abstract This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.

Quasi-decentralized model-based networked control of process systems

Abstract This paper develops a quasi-decentralized control framework for plants with distributed, interconnected units that exchange information over a shared communication network. In this architecture, each unit in the plant has a local control system that communicates with the plant supervisor – and with other local control systems – through a shared communication medium. The objective is to design an integrated control and communication strategy that ensures the desired closed-loop stability and performance for the plant while minimizing network utilization and communication costs. The idea is to reduce the exchange of information between the local control systems as much as possible without sacrificing stability of the individual units and the overall plant. To this end, dynamic models of the interconnected units are embedded in the local control system of each unit to provide it with an estimate of the evolution of its neighbors when measurements are not transmitted through the network. The use of a model to recreate the interactions of a given unit with one of its neighbors allows the sensor suite of the neighboring unit to send its data in a discrete fashion since the model can provide an approximation of the unit’s dynamics. The state of each model is then updated using the actual state of the corresponding unit provided by its sensors at discrete time instances to compensate for model uncertainty. By formulating the networked closed-loop plant as a hybrid system, an explicit characterization of the maximum allowable update period (i.e., minimum cross communication frequency) between each control system and the sensors of its neighboring units is obtained in terms of the degree of mismatch between the dynamics of the units and the models used to describe them. The developed control strategy is illustrated using a network of interconnected chemical reactors with recycle.

Integrating robustness, optimality and constraints in control of nonlinear processes

Abstract This work focuses on the development of a unified practical framework for control of single-input–single-output nonlinear processes with uncertainty and actuator constraints. Using a general state-space Lyapunov-based approach, the developed framework yields a direct nonlinear controller design method that integrates robustness, optimality, and explicit constraint-handling capabilities, and provides, at the same time, an explicit and intuitive characterization of the state-space regions of guaranteed closed-loop stability. This characterization captures, quantitatively, the limitations imposed by uncertainty and input constraints on our ability to steer the process dynamics in a desired direction. The proposed control method leads to the derivation of explicit analytical formulas for bounded robust optimal state feedback control laws that enforce stability and robust asymptotic reference-input tracking in the presence of active input constraints. The performance of the control laws is illustrated through the use of a chemical reactor example and compared with existing process control strategies.

Brief Analysis and control of parabolic PDE systems with input constraints

This paper develops a general framework for the analysis and control of parabolic partial differential equations (PDE) systems with input constraints. Initially, Galerkins method is used for the derivation of ordinary differential equation (ODE) system that capture the dominant dynamics of the PDE system. This ODE systems are then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed-loop stability in the presence of constraints. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator. The theoretical results are used to stabilize an unstable steady-state of a diffusion-reaction process using constrained control action.

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.

Model-based control of particulate processes

In this work, we present an overview of recently developed methods for model-based control of particulate processes. We primarily discuss methods developed in the context of our previous research work and use examples of crystallization, aerosol and thermal spray processes to motivate the development of these methods and illustrate their application. Specifically, we initially discuss control methods for particulate processes which utilize suitable approximations of population balance models to design nonlinear, robust and predictive control systems and demonstrate their application to crystallization and aerosol processes. Finally, we discuss the issues of control problem formulation and controller design for high-velocity oxygen-fuel (HVOF) thermal spray processes and close with few thoughts on unresolved research challenges on control of particulate processes.

Predictive control of crystal size distribution in protein crystallization

This work focuses on the modelling, simulation and control of a batch protein crystallization process that is used to produce the crystals of tetragonal hen egg-white (HEW) lysozyme. First, a model is presented that describes the formation of protein crystals via nucleation and growth. Existing experimental data are used to develop empirical models of the nucleation and growth mechanisms of the tetragonal HEW lysozyme crystal. The developed growth and nucleation rate expressions are used within a population balance model to simulate the batch crystallization process. Then, model reduction techniques are used to derive a reduced-order moments model for the purpose of controller design. Online measurements of the solute concentration and reactor temperature are assumed to be available, and a Luenberger-type observer is used to estimate the moments of the crystal size distribution based on the available measurements. A predictive controller, which uses the available state estimates, is designed to achieve the objective of maximizing the volume-averaged crystal size while respecting constraints on the manipulated input variables (which reflect physical limitations of control actuators) and on the process state variables (which reflect performance considerations). Simulation results demonstrate that the proposed predictive controller is able to increase the volume-averaged crystal size by 30% and 8.5% compared to constant temperature control (CTC) and constant supersaturation control (CSC) strategies, respectively, while reducing the number of fine crystals produced. Furthermore, a comparison of the crystal size distributions (CSDs) indicates that the product achieved by the proposed predictive control strategy has larger total volume and lower polydispersity compared to the CTC and CSC strategies. Finally, the robustness of the proposed method (achieved due to the presence of feedback) with respect to plant-model mismatch is demonstrated. The proposed method is demonstrated to successfully achieve the task of maximizing the volume-averaged crystal size in the presence of plant-model mismatch, and is found to be robust in comparison to open-loop optimal control strategies.