Nonlinear Control Framework Research Articles

Optimal control of an epidemic model with a saturated incidence rate

In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by a competitive Gauss–Seidel like implicit difference method.

UAV Formation Flight Based on Nonlinear Model Predictive Control

We designed a distributed collision‐free formation flight control law in the framework of nonlinear model predictive control. Formation configuration is determined in the virtual reference point coordinate system. Obstacle avoidance is guaranteed by cost penalty, and intervehicle collision avoidance is guaranteed by cost penalty combined with a new priority strategy.

Presentation of Malaria Epidemics Using Multiple Optimal Controls

An existing model is extended to assess the impact of some antimalaria control measures, by re‐formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. The optimality system is solved numerically by a competitive Gauss‐Seidel‐like implicit difference method. Finally, numerical simulations of the optimal control problem, using a set of reasonable parameter values, are carried out to investigate the effectiveness of the proposed control measures.

A novel fuzzy framework for nonlinear system control

Nonlinear PID and gain scheduling controls have attracted much research interests in recent years. These control strategies can accommodate some nonlinear characteristics by allowing the gains varied or rescheduled as a function of system states. In this paper, a novel fuzzy framework is developed to transfer this type of nonlinear controller to its fuzzy domain representation. It is proved that the resulting fuzzy controller is functionally exactly identical to the original control system. One of the benefits of the suggested approach is that it provides a well-defined prototype for the design of fuzzy control system. The resulting linguistic representation can facilitate investigation in linguistic terms into how the controller operates, whereas expert knowledge can be effectively implemented to improve control performance. The viability of the proposed mapping technique is demonstrated by using simulations corresponding to a flexible-link robot.

Multi-loop nonlinear predictive control scheme for a simplistic hybrid energy system

Abstract A simplistic hybrid energy system is composed of the wind turbine, electrolyzer, and PEM fuel cell stack. In view of the high current demand and fast load changes, the hybrid dynamic simulation shows that the fuel cell may be in risk of oxygen starvation and overheating problems. Regarding the safe operation as well as long lifetime of the fuel cell, the effective control manner is expected to regulate both the stack temperature and oxygen excess ratio in the cathode at the desired level. Under the multi-loop nonlinear predictive control framework, the controlled output variables are specified independently by manipulating air (oxygen) and water flowrates, respectively. The dynamic modeling and control implementation are realized in the Matlab–Simulink™ environment.

Microcantilever-Based Force Tracking With Applications to High-Resolution Imaging and Nanomanipulation

This paper presents the development and implementation of a robust nonlinear control framework for piezoresistive nanomechanical-cantilever (NMC)-based force tracking with applications to high-resolution imaging and nanomanipulation. Among many nanoscale force sensing platforms, NMC is an attractive approach to measure and apply forces at this scale when compared with other previously reported configurations utilizing complicated MEMS devices or inconvenient-to-handle nanowires and nanotubes. More specifically, a piezoresistive layer is utilized here to measure nanoscale forces at the NMC's tip instead of bulky laser-based feedback that is commonly used in atomic force microscopy. Excluding the laser from the sensing loop offers a compact, inexpensive, and portable yet precise nanoscale force sensing platform. In order to track a predefined force trajectory at the NMC's tip, there is a need to model the piezoresistive NMC and design appropriate controller to move its base to provide the desired force. In previous publications of the authors, a new distributed-parameter modeling framework has been proposed to precisely predict the force acting on the microcantilever's tip. In contrast to this approach and in an effort to ease the follow-up controller development, the NMC-based force sensor is modeled here as a lumped-parameter system. However, replacing the NMC with a linear mass-spring-damper trio creates a variety of uncertainties and unmodeled dynamics that need to be addressed for a precise force sensor's readout. Moreover, the very slow response of NMC's piezoresistive layer to force variations at the NMC's tip makes the tracking problem even more challenging. For this, a modified robust controller, built around sliding mode control strategy and augmented with a perturbation estimation module, is proposed to overcome these roadblocks. Extensive numerical simulations and experimental results are presented to demonstrate the stability and performance characteristics of the designed controller. It is shown that utilizing the proposed controller instead of the commonly used proportional-integral-derivative controller can significantly enhance the controller's stability and performance characteristics and, ultimately, the imaging resolution and manipulation accuracy needed at this scale.

Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example

A general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.

Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints

AbstractA direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed‐loop tracking error dynamics in the face of amplitude and rate saturation constraints, the control signal to a given reference (governor or supervisor) system is modified to effectively robustify the error dynamics to the saturation constraints. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.

Intelligent state estimation for fault tolerant nonlinear predictive control

There is growing realization that on-line model maintenance is the key to realizing long term benefits of a predictive control scheme. In this work, a novel intelligent nonlinear state estimation strategy is proposed, which keeps diagnosing the root cause(s) of the plant model mismatch by isolating the subset of active faults (abrupt changes in parameters/disturbances, biases in sensors/actuators, actuator/sensor failures) and auto-corrects the model on-line so as to accommodate the isolated faults/failures. To carry out the task of fault diagnosis in multivariate nonlinear time varying systems, we propose a nonlinear version of the generalized likelihood ratio (GLR) based fault diagnosis and identification (FDI) scheme (NL-GLR). An active fault tolerant NMPC (FTNMPC) scheme is developed that makes use of the fault/failure location and magnitude estimates generated by NL-GLR to correct the state estimator and prediction model used in NMPC formulation. This facilitates application of the fault tolerant scheme to nonlinear and time varying processes including batch and semi-batch processes. The advantages of the proposed intelligent state estimation and FTNMPC schemes are demonstrated by conducting simulation studies on a benchmark CSTR system, which exhibits input multiplicity and change in the sign of steady state gain, and a fed batch bioreactor, which exhibits strongly nonlinear dynamics. By simulating a regulatory control problem associated with an unstable nonlinear system given by Chen and Allgower [H. Chen, F. Allgower, A quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica 34(10) (1998) 1205–1217], we also demonstrate that the proposed intelligent state estimation strategy can be used to maintain asymptotic closed loop stability in the face of abrupt changes in model parameters. Analysis of the simulation results reveals that the proposed approach provides a comprehensive method for treating both faults (biases/drifts in sensors/actuators/model parameters) and failures (sensor/ actuator failures) under the unified framework of fault tolerant nonlinear predictive control.

Nonlinear model based control of two-product reactive distillation column

Nonlinear feedback control scheme for reactive distillation column has been proposed. The proposed control scheme is derived in the framework of Nonlinear Internal Model Control. The product compositions and liquid and vapor flow rates in sections of the reactive distillation column are estimated from selected tray temperature measurements by an observer. The control scheme is applied to an example reactive distillation column in which two products are produced in a single column and the reversible reaction A+B=C+D occurs. The relative volatilities are favorable for reactive distillation so that the reactants are intermediate boilers between the light product C and the heavy product D. Ideal physical properties, kinetics, and vapor-liquid equilibrium are also assumed. It is shown that the proposed control scheme keeps tight product composition control.

Optimal control and infectiology: Application to an HIV/AIDS model

An existing infectious model describing the interaction of HIV virus and the immune system of the human body is utilized to determine the optimal methodology for administering anti-viral medication therapies to fight HIV infection. This work investigates the fundamental role of chemotherapy treatment in controlling the virus reproduction. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. We obtain an optimality system that we seek to solve numerically by a competitive Gauss–Seidel like implicit difference method.

A MIXED CONTINUOUS-BATCH PROCESS: IMPLEMENTATION OF HYBRID PREDICTIVE CONTROLLERS

This paper deals with a mixed continuous-batch process, a pilot plant of our Lab, where both continuous decisions and scheduling take place. The interest of this contribution comes not only from the fact that it is a challenging control problem, but because problems with a similar structure are present in many industrial process. The paper describes the process, the instrumentation (classical analogical/discrete devices, Field Bus devices) and the global architecture of the pilot plant control (Distributed Control System DCS, Supervisory Control and Data Acquisition SCADA, OPC communication, etc.). From a control point of view, it presents a brief description of control problem formulation in the framework of non-linear model predictive control, and a generic methodology to design this kind of predictive controllers. Finally it is presented the results of some real experiments.

High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.

A Lyapunov-based adaptive control framework for discrete-time non-linear systems with exogenous disturbances

A direct adaptive non-linear control framework for discrete-time multivariable non-linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non-linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. In the case of bounded energy ℓ 2 disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input–output map. Finally, three illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Backstepping-based cascade control scheme for batch distillation columns

Nonstationary dynamics, finite-time operation, large thermodynamical uncertainty and delayed composition measurements make the control of batch distillation processes a challenging and interesting problem. In this paper, a cascade control design to regulate the overhead composition of a batch distillation column is presented. The controller is designed within the framework of robust nonlinear control with modeling error compensation techniques in conjunction with a backstepping approach. The result is a cascade controller with a master loop that, driven by the composition regulation error, produces a time-varying set point for the temperature in a certain tray; and with a secondary controller that manipulates the internal reflux ratio to track the time-varying set point determined by the master composition loop. How to extend the controller design to have multiple slave temperature controllers, to improve the regulation of the overhead composition in a batch distillation column, is also presented. The proposed control approach is illustrated by numerical simulations on a full dynamical model.

A note on the identification and control of batch distillation columns

A method for the identification and control of a batch distillation process is presented in this note. The proposed model consists of a first-order integrating process in composition with a high-frequency gain. The feedback controller is designed in the framework of robust nonlinear control with modeling error compensation techniques for the control of distillate composition via manipulations of the reflux ratio. The proposed identification and control procedures are illustrated via numerical simulations.

A note on stability, robustness and performance of output feedback nonlinear model predictive control

In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties.

Model-Reference Fuzzy Adaptive Control as a Framework for Nonlinear System Control

The paper presents a general methodology of adaptive control based on fuzzy model to deal with unknown plants. The problem of parameter estimation is solved using a direct approach, i.e. the controller parameters are adapted without explicitly estimating plant parameters. Thus, very simple adaptive and control laws are obtained using Lyapunov stability criterion. The generality of the approach is substantiated by Stone-Weierstrass theorem, which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control, this implies the adaptive law with fuzzified adaptive control parameters. The proposed control algorithm may be viewed as an extension of classical adaptive control for linear plants, but compared to the latter it provides higher adaptation ability and consequently better performance if the plant is nonlinear. The global stability of the control system is assured and the tracking error converges to the residual set that depends on fuzzification properties. The main advantage of the approach is simplicity that suits control engineers since wide range of industrial processes can be controlled by the proposed method. In the paper, the control of heat exchanger is performed.

Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes

3R23. Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes. - PD Christofides (Dept of Chem Eng, UCLA, Los Angeles CA 90095-1592). Birkhauser Boston, Cambridge MA. 2001. 248 pp. ISBN 0-8176-4156-4. $69.95.Reviewed by J Chow (Adv Tech Center, Org L9-24, Lockheed Martin, 3251 Hanover St, Palo Alto CA 94304-1191).The author has written a book that seeks to present practical, general nonlinear, and robust control methods for hyperbolic and parabolic PDE systems, and to illustrate their application to transport-reaction processes that are found in the chemical industry. There is also an attempt to compare their effectiveness with respect to traditional control methods for PDE systems. This book is written for process control engineers, researchers, and students at the graduate level.The field of chemical engineering contains many different examples of hyperbolic and parabolic PDE systems. As the author rightly states in his preface, “The interest in control of nonlinear partial differential equation (PDE) systems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations.” As a result, there is a requirement to provide the chemical process community with an overview of the most recent advances in nonlinear PDE control theory. In this book, general and practical methods for synthesizing nonlinear controllers for hyperbolic and parabolic PDE systems are systematically developed, and then extended to include robustness. Geometric and Lyapunov-based control techniques are used to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve a stable closed-loop system in the face of model uncertainty. All the PDE systems considered in this text are assumed to have unique solutions that are sufficiently smooth. Readers are assumed to have a basic knowledge about PDE systems and control theories. The first two chapters focus first on quasi-linear, first-order hyperbolic PDE systems, and then on the same type of hyperbolic PDE systems, but those which include time-varying uncertain variables and unmodeled dynamics. These control methods are based on geometric control concepts and are applied to nonisothermal plug-flow reactor examples. The next two chapters focus on developing general methods for quasi-linear parabolic PDE systems using Galerkin’s method and approximate inertial manifolds, both with and without time-varying uncertain variables. Examples of the methodology’s successful application to the control of temperature profiles for catalytic rods and nonisothermal reactors are presented for illustration. The following chapter deals with the nonlinear and robust control of parabolic PDE systems with moving boundaries, ie, time-dependent spatial domains. General methods for synthesizing nonlinear and robust time-varying output feedback controllers are presented, again using a combination of Galerkin’s method and the approximate inertial manifold. The final chapter presents case studies in which the control methods derived in earlier chapters for parabolic PDE systems are applied. In particular, the control of a rapid thermal chemical vapor deposition process and a Czochralski crystal growth process are illustrated and simulated. The book ends with an extensive set of mathematical proofs to support the results developed in the preceding chapters. It also has an extensive bibliography and is sprinkled throughout with clear figures and examples. Nonlinear and Robust Control of PDE Systems is a well-written book that succeeds in its objectives and is possibly the first one to do so. The control theories and synthesis methodologies are described in exhaustive mathematical detail. This book can also be recommended to researchers and engineers in other fields who are faced with the task of developing nonlinear feedback and robust controllers for hyperbolic and parabolic PDE systems. They will find this book to be very useful because it provides the reader with the general framework for nonlinear feedback control based on detailed mathematical models.

Automotive engine speed control: A robust nonlinear control framework

A controller design procedure based on sliding-mode techniques is presented for speed control in an automotive engine. Only the engine speed and manifold pressure measurements are available to the control law. It is assumed that the load-torque disturbance on the engine is not known, while uncertainties in the system parameters are also taken into consideration. The engine acceleration is estimated through a high-gain observer. A comprehensive nonlinear simulation model is used to assess the performance of the closed-loop system. It is shown that the sliding-mode controller can achieve the full range of setpoint speeds. In addition, the closed-loop system is robust with respect to both initial speed and changes in the load torque.