Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> We survey nonlinear control system techniques ranging from ad hoc or process-specific strategies to predictive control approaches based on nonlinear programming. The capabilities of these techniques to handle the common problems associated with chemical processes, such as time delays, constraints, and model uncertainty are discussed. A significant number of goals for future research in nonlinear control of chemical processes are detailed <s> BIB001 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Preface. 1. Introduction. 2. Basic Concepts of Nonlinear Control Theory. 3. Design Principles of Single-Input Single-Output Nonlinear Control Systems. 4. Design Principles of Multi-Input Multi-Output Nonlinear Control Systems. 5. Basic Mathematical Descriptions for Electric Power Systems. 6. Nonlinear Excitation Control of Large Synchronous Generators. 7. Nonlinear Steam Valving Control. 8. Nonlinear Control of HVDC Systems. 9. Nonlinear Control of Static Var Systems. 10. Nonlinear Robust Control of Power Systems. Index. <s> BIB002 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Power electronics circuits are rich in non-linear dynamics. Their operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of non-linear behaviours. Over the past two decades, a lot of research activities have focused on identifying bifurcations and chaos, and explaining them using the theory of non-linear dynamics. As power electronics engineers gain more knowledge and deeper understanding of non-linear dynamics in power electronics, they begin to look for possible applications. As a result, research of applications of non-linear dynamics in power electronics has become a hot topic. Recently, some applications of non-linear dynamics in power electronics systems and related theory have been identified. This paper tries to provide an overview of these successful applications. <s> BIB003 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract Using singular perturbation techniques, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+ T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed. <s> BIB004 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> The discrete and random occurrence of chemical reactions far from thermodynamic equilibrium, and low copy numbers of chemical species, in systems biology necessitate stochastic approaches. This review is an effort to give the reader a flavor of the most important stochastic approaches relevant to systems biology. Notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy-to-follow presentation of a stochastic framework for modeling subcellular biochemical systems. In particular, we make an effort to show how the notion of propensity, the chemical master equation (CME), and the stochastic simulation algorithm arise as consequences of the Markov property. Most stochastic modeling reviews focus on stochastic simulation approaches—the exact stochastic simulation algorithm and its various improvements and approximations. We complement this with an outline of an analytical approximation. The most common formulation of stochastic models for biochemical networks is the CME. Although stochastic simulations are a practical way to realize the CME, analytical approximations offer more insight into the influence of randomness on system's behavior. Toward that end, we cover the chemical Langevin equation and the related Fokker–Planck equation and the two-moment approximation (2MA). Throughout the text, two pedagogical examples are used to key illustrate ideas. With extensive references to the literature, our goal is to clarify key concepts and thereby prepare the reader for more advanced texts. Copyright © 2009 John Wiley & Sons, Inc. ::: ::: ::: ::: For further resources related to this article, please visit the WIREs website. <s> BIB005 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK. <s> BIB006 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Passivity-based control is widely used in electronic circuit systems because it can utilize their internal structures to facilitate the controller design. In this paper, we first propose a dissipative Hamiltonian realization of power systems and discuss the disadvantages of the traditional passivity-based excitation controller. Then, a novel excitation controller is put forward to reassign the interconnection and dissipative matrix, and the corresponding Hamiltonian function. Simulation results verify that the proposed controller can effectively improve the transient stability of the power system. <s> BIB007 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> A novel direct-driven and portable exoskeleton robotic system for the hand is proposed. The system design is based on the multi-parametric optimisation procedure, which considers isotropy, dexterity and exertion of perpendicular forces on the finger phalanges. Actuators for the proposed device were selected based on results of experiments with users having different hand sizes. These experiments measured various parameters including average and maximum force exertion levels of a human hand. The experimental results were used to realise the mechanical design and to develop a prototype. The device can exert force levels (of 45 N) beyond any existing hand exoskeleton. Preliminary trials carried out on the fabricated prototype dictate efficacy and potential of the proposed system. <s> BIB008 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract This research presents a novel hand exoskeleton rehabilitation device to facilitate tendon therapy exercises. The exoskeleton is designed to assist fingers flexion and extension motions in a natural manner. The proposed multi-Degree Of Freedom (DOF) system consists of a direct-driven, optimized and underactuated serial linkage mechanism having capability to exert extremely high force levels perpendicularly on the finger phalanges. Kinematic and dynamic models of the proposed device have been derived. The device design is based on the results of multi-objective optimization algorithm and series of experiments conducted to study capabilities of the human hand. To permit a user-friendly interaction with the device, the control is based on minimum jerk trajectory generation. Using this control system, the transient response and steady state behavior of the proposed device are analyzed after designing and fabricating a two-fingered prototype. The pilot study shows that the proposed rehabilitation system is capable of flexing and extending the fingers with accurate trajectories. <s> BIB009 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Offering an up-to-date account of systems theories and its applications, this book provides a different way of resolving problems and addressing challenges in a swift and practical way, without losing overview and not having a grip on the details. From this perspective, it offers a different way of thinking in order to incorporate different perspectives and to consider multiple aspects of any given problem. Drawing examples from a wide range of disciplines, it also presents worked cases to illustrate the principles. The multidisciplinary perspective and the formal approach to modelling of systems and processes of ‘Applied Systems Theory’ makes it suitable for managers, engineers, students, researchers, academics and professionals from a wide range of disciplines; they can use this ‘toolbox’ for describing, analysing and designing biological, engineering and organisational systems as well as getting a better understanding of societal problems. <s> BIB010 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Model-based predictive control (MPC) for power converters and drives is a control technique that has gained attention in the research community. The main reason for this is that although MPC presents high computational burden, it can easily handle multivariable case and system constraints and nonlinearities in a very intuitive way. Taking advantage of that, MPC has been successfully used for different applications such as an active front end (AFE), power converters connected to resistor inductor RL loads, uninterruptible power supplies, and high-performance drives for induction machines, among others. This article provides a review of the application of MPC in the power electronics area. <s> BIB011 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Robotic manipulators have reshaped industrial processes. The scientific community has witnessed an ever increasing trend in robots deployed to accomplish various tasks in industry. The complex nature and constrained requirements of robots may demand non-trivial control approaches. This paper deals with the design, simulation and hardware realization of two sophisticated control strategies: computed torque control (CTC) and variable structure control (VSC) on a pseudo-industrial manipulator with six degrees of freedom (DOF). Based on the derived kinematic and dynamic models of the robot, control laws have been formulated, which are then subjected to various test inputs in a simulation to characterize the tracking performance. The simulation results were then validated by implementing control laws on a custom-developed pseudo-industrial autonomous articulated robotic educational platform (AUTAREP). The experimental results show the effectiveness of the control strategies to track a desired trajectory. <s> BIB012 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> A wearable hand exoskeleton (EXO) device that permits exertion of bidirectional forces on finger phalanges throughout the human finger workspace is proposed. The novelty of the proposed device lies in its direct-driven, portable and optimised mechanism with the ability to adjust variable hand sizes in addition to other distinguishing features. The adjustable link lengths and structure of the device have emerged from kinematic-based optimisation criterion, which targets the natural finger workspace. The selection of actuators for the EXO is backed by the results of experiments conducted using appropriate sensory instrumentation to measure the force exertion levels of a human hand. A four-fingered prototype of the EXO is designed and fabricated. The device is then subjected to various test inputs to characterise the tracking performance. Preliminary results demonstrate that the proposed device can flex and extend the fingers following accurate trajectories. <s> BIB013 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection. <s> BIB014 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> To meet increasing demand for higher reliability in power electronics converters applicable in electric vehicles, fault detection (FD) is an important part of the control algorithm. In this study, a model-based open transistor fault diagnsosis method is presented for a voltage-source inverter (VSI) supplying a five-phase permanent magnet motor drive. To realise this goal, a model-based observer is designed to estimate model parameters. After that, the estimated parameters are used to design a sliding mode observer in order to estimate the phase current in an ideal model. Subsequently, the proposed FD technique measures the similarity between the estimated current and real current using cross-correlation factor. This factor is used for the first time in this study to define a FD index in VSI. The presented FD scheme is simple and fast; also, it is able to detect multiple open switch or open phase faults in contrast to conventional methods. On the other side, in order to track reference current of the motor, the estimated parameters are used to design a proportional resonant controller. The FD technique is used to operate a multiphase fault-tolerant brushless direct current (BLDC) motor drive. Experimental results on a five-phase BLDC motor with in-wheel outer rotor applicable in electrical vehicles are conducted to validate the theory. <s> BIB015 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract Vehicle state estimation during anti-lock braking is considered. A novel nonlinear observer based on a vehicle dynamics model and a simplified Pacejka tire model is introduced in order to provide estimates of longitudinal and lateral vehicle velocities and the tire-road friction coefficient for vehicle safety control systems, specifically anti-lock braking control. The approach differs from previous work on vehicle state estimation in two main respects. The first is the introduction of a switched nonlinear observer in order to deal with the fact that in some driving situations the information provided by the sensor is not sufficient to carry out state estimation (i.e., not all states are observable). This is shown through an observability analysis. The second contribution is the introduction of tire-road friction estimation depending on vehicle longitudinal motion. Stability properties of the observer are analyzed using a Lyapunov function based method. Practical applicability of the proposed nonlinear observer is shown by means of experimental results. <s> BIB016 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> The performance of a robotic arm includes accuracy, repeatability and reliability to accomplish a task. These parameters, in turn, are function of associated control law. Multi-Degree Of Freedom (DOF) robotic arms, because of their inherent highly non-linear dynamics, demand sophisticated control laws. Trivial control strategies fail to cope with disturbances and uncertainties that are common in today’s plants. This paper presents the design, simulation and physical implementation of a non-linear control technique Variable Structure Control (VSC) for a 6 DOF arm. Based on the derived dynamic model of the arm and designed control law, simulations have been conducted in MATLAB/Simulink. The controller parameters have been tuned for optimal response. Various desired trajectories characterize the tracking performance of the control law. The simulation results have been then validated by implementing the law on a custom-developed novel AUTonomous Articulated Robotic Educational Platform (AUTAREP). Coupling effects between various joints of the robot have also been investigated. Results of this research find potential in industrial control of robotic manipulators to perform complex tasks. DOI: http://dx.doi.org/10.5755/j01.eee.22.1.14094 <s> BIB017 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract. Human safety becomes critical when robot enters the human environment. Compliant control can be used to address some safety issues in human-robot physical interaction. This paper proposes an integral sliding mode controller (ISMC) based compliance control scheme for the Bristol Robotics Laboratory's humanoid BERT II robot arm. Apart from introducing a model reference compliance controller, the ISMC scheme is aimed to deal with the robot arm dynamic model's inaccuracies and un-modelled nonlinearities. The control scheme consists of a feedback linearization (FL) and an ISMC part. In addition, a posture controller has been incorporated to employ the redundant DOF and generate human like motion. The desired level of compliance can be tuned by selecting the stiffness and damping parameters in the sliding mode variable (compliance reference model). The results show that the compliant control is feasible at different levels for BERT II in simulation and experiment. The positioning control has been satisfactorily achieved and nonlinearities and un-modelled dynamics have been successfully overcome. <s> BIB018 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> This book investigates a biologically inspired method of robot arm control, developed with the objective of synthesising human-like motion dynamically, using nonlinear, robust and adaptive control techniques in practical robot systems. The control method caters to a rising interest in humanoid robots and the need for appropriate control schemes to match these systems. Unlike the classic kinematic schemes used in industrial manipulators, the dynamic approachesproposed here promote human-like motion with better exploitation of the robots physical structure. This also benefits human-robot interaction. The control schemes proposed in this book are inspired by a wealth of human-motion literature that indicates the drivers of motion to be dynamic, model-based and optimal. Such considerations lend themselves nicely to achievement via nonlinear control techniques without the necessity for extensive and complex biological models. The operational-space method of robot control forms the basis of many of the techniques investigated in this book. The method includes attractive features such as the decoupling of motion into task and posture components. Various developments are made in each of these elements. Simple cost functions inspired by biomechanical effort and discomfort generate realistic posture motion. Sliding-mode techniques overcome robustness shortcomings for practical implementation. Arm compliance is achieved via a method of model-free adaptive control that also deals with actuator saturation via anti-windup compensation. A neural-network-centered learning-by-observation scheme generates new task motions, based on motion-capture data recorded from human volunteers. In other parts of the book, motion capture is used to test theories of human movement. All developed controllers are applied to the reaching motion of a humanoid robot arm and are demonstrated to be practically realisable. This book is designed to be of interest to those wishing to achieve dynamics-based human-like robot-arm motion in academic research, advanced study or certain industrial environments. The book provides motivations, extensive reviews, research results and detailed explanations. It is not only suited to practising control engineers, but also applicable for general roboticists who wish to develop control systems expertise in this area. <s> BIB019 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract In this paper, the modelling, dynamic optimization and nonlinear control of an industrial emulsion polymerization reactor producing poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase according to the model described in our previous work ( Gil et al., 2014 ). The case study corresponds to an industrial reactor operated at a chemical company in Bogota (Colombia). An industrial scale reactor (11 m 3 of capacity) is simulated. Three different dynamic optimization problems are solved from the more simplistic (only one control variable: reactor temperature) to the more complex (three control variables: reactor temperature, initiator flow rate and monomer flow rate) in order to minimize the reaction time. The results show that it is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy defined constraints. The optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used as optimal set points for reactor control. A nonlinear geometric controller based on input/output linearization is implemented for temperature control. <s> BIB020 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract Wind turbine uses a pitch angle controller to reduce the power captured above the rated wind speed and release the mechanical stress of the drive train. This paper investigates a nonlinear PI (N-PI) based pitch angle controller, by designing an extended-order state and perturbation observer to estimate and compensate unknown time-varying nonlinearities and disturbances. The proposed N-PI does not require the accurate model and uses only one set of PI parameters to provide a global optimal performance under wind speed changes. Simulation verification is based on a simplified two-mass wind turbine model and a detailed aero-elastic wind turbine simulator (FAST), respectively. Simulation results show that the N-PI controller can provide better dynamic performances of power regulation, load stress reduction and actuator usage, comparing with the conventional PI and gain-scheduled PI controller, and better robustness against of model uncertainties than feedback linearization control. <s> BIB021 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> A nonlinear discrete-time model along with an optimal stabilizing controller using a unified power quality conditioner (UPQC) is proposed for weak/islanded grids in this paper. An advanced stabilizing controller greatly benefits islanded medium-sized grid and microgrid due to their relatively small stored energy levels, which adversely affect their stability, as opposed to larger grids. In addition, a discrete-time grid model and controller are preferred for digital implementation. Here, the discrete-time Hamilton–Jacobi–Isaacs optimal control method is employed to design an optimal grid stabilizer. While UPQC is conventionally utilized for power quality improvement in distribution systems in the presence of renewable energy, here, the stabilizing control is added and applied to the UPQC series voltage in order to mitigate the grid’s oscillations besides UPQC’s power conditioning tasks. Consequently, the UPQC can be employed to stabilize a grid-tie inverter (GTI) or a synchronous generator (SG) with minimum control effort. When controlling the GTI associated with renewable energy sources, a reduced UPQC structure is proposed that only employs the series compensator. Next, a successive approximation method along with neural networks is utilized to approximate a cost function of the grid dynamical states, the UPQC control parameters, and disturbance, in a two-player zero-sum game with the players being UPQC control and grid disturbances. Subsequently, the cost function is used to obtain the nonlinear optimal controller that is applied to the UPQC. Simulation results show effective damping behavior of the proposed nonlinear controller in controlling both GTI and SG in weak and islanded grids. <s> BIB022 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> This paper presents a sliding mode robust control based active-power modulation (SMAPM) for voltage source converter based multi-terminal HVDC (VSC-MTDC) systems, which could enhance the stability of the onshore power system subjected to disturbances by fast changing transmitted power of onshore VSCs. The development of the SMAPM includes three steps. First, the onshore disturbed ac system could be divided into two areas with generators sharing different swing modes. The center of the inertia (COI) reference frame is utilized to be the representative of the area's behavior. Secondly, an index called sensitive index is proposed to quantify the sensitivity of generator angular speed to the active-power change of an onshore VSC. A strategy is developed to determine the modulation direction and intensity of each onshore converter. Thirdly, the final control law is derived based on sliding mode variable structure control method. Simulation verifications are run in a four-machine ac system and a modified New England 39-bus system. <s> BIB023 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract Penetration of wind and solar power are increasing in power systems. Intermittent characteristics of renewable sources and random load variation result in system voltage and frequency fluctuation. A load frequency control (LFC) strategy based on sliding mode control (SMC) theory and disturbance observer is proposed for the single area power system. In order to reduce the frequency deviation caused by the unmatched parameter uncertainties such as the renewable source and different load disturbance, the sliding mode load frequency controller is constructed by selecting the appropriate proportional and integral switching surface and the reaching law condition. Furthermore, the sliding mode load frequency controller is reconstructed based on the designed disturbance observer (DOB) to improve the dynamic performance and suppress the chattering. The proposed method is compared with the conventional sliding mode LFC and the robust adaptive LFC (RALFC) by using the matlab software, the simulation results show that the designed LFC has faster response speed and better robust performance. <s> BIB024 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> This paper aims to focus on the smooth output of DC-DC buck converters in wireless power transfer systems under input perturbations and load disturbances using the high-order sliding mode controller (HOSM) and HOSM with super-twisting differentiator (HOSM + STD). The proposed control approach needs only measurement of converter output voltage. Theoretical analysis and design procedures, as well as the super-twisting differentiator of the proposed controller are presented in detail with the prescribed convergence law of high-order sliding modes. Comparisons of both simulation and experimental results among conventional proportional-integral (PI) control, traditional sliding mode control (SMC), HOSM and HOSM + STD under various test conditions such as steady state, input voltage perturbations and output load disturbances, are presented and discussed. The results demonstrate and validate the effectiveness and robustness of the proposed control method. <s> BIB025 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> In this paper, a nonlinear controller with a current-limiting property is proposed to guarantee accurate dc output voltage regulation and unity power factor operation for single-phase pulse-width-modulating rectifiers without the need of a phase-locked-loop (PLL). The proposed current-limiting controller is fully independent of the system parameters and can guarantee asymptotic stability and convergence to a unique solution for the closed-loop system using nonlinear control theory. Without requiring the instantaneous measurement of the grid voltage, a PLL, an external limiter, or a saturation unit, the proposed strategy guarantees that the input current of the rectifier will always remain below a given value. An analytic framework for selecting the controller parameters is also presented to provide a complete controller design procedure and it is also proved that the current-limiting property is maintained even when the grid voltage drops. Extensive experimental results are presented to verify the proposed controller when the load changes, the reference dc output voltage changes, and the grid voltage drops. <s> BIB026 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Switched-capacitor (SC) converters are a type of variable structure systems. In the past, most of the SC converters were initially introduced for the low power applications and monolithic integration. Recently, SC converters have been used in high power area with the open-loop control and some other simple linear voltage feedback controls. However, the simplicity of such approaches sacrifice performance with the slow dynamic response, narrow operation region and large voltage ripple. Some new nonlinear control methods have been proposed, however, such control methods are only useful for applications involving low power SC converter. This paper proposed a new nonlinear constant on time variable frequency control (COTVF) based on the capacitor ampere-second balance principle. The proposed variable frequency control method successfully addresses the regulation issue in high power SC converters. The control concept is straightforward yet with excellent performance. In combination with the high power 2X two-switch boosting switched-capacitor (TBSC) converter, simulation results demonstrate that the proposed control method highly improve the dynamic response speed with good line and load regulation in wide operation range. <s> BIB027 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract This paper studies the control of fixed-wing unmanned aerial vehicles (UAVs) in the presence of stochastic winds. A nonlinear controller is designed based on a full nonlinear mathematical model that includes the stochastic wind effects. The air velocity is controlled exclusively using the position of the throttle, and the rest of the dynamics are controlled with the aileron, elevator, and rudder deflections. The nonlinear control design is based on a smooth approximation of a sliding mode controller. An extended Kalman filter (EKF) is proposed for the state estimation and filtering. A case study is presented: landing control of a UAV on a ship deck in the presence of wind based exclusively on LADAR measurements. The effectiveness of the nonlinear control algorithm is illustrated through a simulation example. <s> BIB028 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract The water level control problem of steam generators has been a main cause of unexpected shutdowns of nuclear power plants which must be considered for plant safety and availability. The control problem is challenging, especially at low power levels due to shrink and swell phenomena and flow measurement errors. Moreover, the dynamics of steam generator vary as the power level changes. Therefore, it is necessary to improve the water level control system of SG. In this paper, at the first a nonlinear model based on the fundamental conservation equations for mass, energy and momentum is presented for the nuclear steam generator which is validated with other computer programs and experimental results and then, an adaptive dynamic sliding mode control method is applied for the level control problem of U-tube steam generators based on the presented nonlinear model. The proposed method exhibits the desired dynamic properties during the entire output tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness and stability. Simulation results confirm the improvement in transient response obtained by using the proposed controller. <s> BIB029 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract The present contribution proposes a new strategy for temperature control of a bench-scaled batch reactor equipped with a mono-fluid heating/cooling system. A cascade-like nonlinear parametric predictive control structure combined with a predictive functional control concept is presented. First principle models of the thermal flux related to heat transfer in the pilot plant were developed. To demonstrate the performance of the control methodology, experimental results are presented. The developed controllers were first tested in a simulated environment and then in the field. The controller demonstrates a remarkable capacity to deal with process nonlinearities and to drive the plant more closely along a desired temperature reference trajectory. The success of the proposed controller technique as a process control paradigm for temperature has been demonstrated, and the implemented controller algorithm can be adapted easily to other heat transfer processes in industrial applications. <s> BIB030 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract Model predictive control (MPC) is highly suitable for building heating and cooling control because it exploits disturbance predictions, obeys constraints, and enables optimal building operation in terms of user comfort and energy efficiency. This work presents a highly efficient nonlinear modular MPC concept. It optimally controls both, heating and cooling activities in a low-energy office building simultaneously. Relevant system nonlinearities are considered through a nonlinear prediction model, an LTI MPC optimization step, and an efficient mixed-integer mapping to setpoint temperatures in the building. The involved optimization problems are efficiently solvable and enable realtime control, and the controller structure allows for retrofitting and can directly be incorporated into the existing building control infrastructure. A clear formulation of thermal user comfort and energy efficiency allows straightforward tuning. Excellent control performance and robustness are observed in detailed co-simulation studies, significantly outperforming a classical rule-based reference control law. Possible approaches to analyze robust stability of the controlled system are discussed and related to results of robust TS-fuzzy system analysis. <s> BIB031 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Abstract This paper proposes a price-based demand response program by the nonlinear control method. The demand response program is formulated as a nonlinear power management system with price feedback. We give the conditions of the price parameters for both the global asymptotic stability of the system and the social welfare optimality of the equilibrium point. Furthermore, the system is shown to be input-to-state (ISS) stable when there are additive disturbances on the power measurements and the price, and the discrete-time implementation of the power management system is given. Simulation results demonstrate the balance between supply and demand and the stability of the system with and without disturbances. <s> BIB032 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Recent Advances <s> Continuous adjustment of Propofol in manual delivery of anesthesia for conducting a surgical procedure overburdens the workload of an anesthetist who is working in a multi-tasking scenario. Going beyond manual administration and Target Controlled Infusion, closed-loop control of Propofol infusion has the potential to offer several benefits in terms of handling perturbations and reducing the effect of inter-patient variability. This paper proposes a closed-loop automated drug administration approach to control Depth Of Hypnosis in anesthesia. In contrast with most of the existing research on anesthesia control which makes use of linear control strategies or their improved variants, the novelty of the present research lies in applying robust control strategy i.e. Sliding Mode Control to accurately control drug infusion. Based on the derived patient's model, the designed controller uses measurements from EEG to regulate DOH on Bispectral Index by controlling infusion rate of Propofol. The performance of the controller is investigated and characterized with real dataset of 8 patients undergoing surgery. Results of this in silico study indicate that for all the patients, with 0% overshoot observed, the steady state error lies in between ±5. Clinically, this implies that in all the cases, without any overdose, the controller maintains the desired DOH level for smooth conduction of surgical procedures. <s> BIB033
In the last two decades, the advancements in nonlinear control systems have been in two folds; advances in theoretical approaches and more importantly applicationdriven developments. In theory, major breakthrough has been seen in the areas of sliding control, feedback linearization and nonlinear adaptive strategies. Recently, nonlinear control systems have gained high popularity primarily due to the extensive application of theoretical concepts to solve real world problems in various domains like electrical, mechanical, medical, avionics, space etc. Moreover, the advances in computer hardware and information technology have greatly resolved the computational constraints on analysis and design of nonlinear control systems. Now we see numerous applications of nonlinear control systems ranging from 'drive by wire' cars to 'fly by wire' aircraft flight control systems, to robotic, medical, industrial and space systems. Robotic manipulators have reshaped the industrial automation and are now an integral part of most of the modern plants. Although linear control strategies like PID  have been the main workhorse in industry since decades, however, the trend to employ nonlinear approaches is gradually increasing  . A typical example of implementation of a nonlinear approach i.e. SMC on a customdeveloped pseudo-industrial platform BIB017 is presented in BIB012 . The control objective was to ensure tracking of desired trajectory (q d ). This was achieved by defining a sliding manifold (S =ė+Ce) based on error signal (e = q d − q). The control law giving required input joint torque (τ) is expressed in (9) while the corresponding blockdigram is illustrated in Fig. 4 . (9) where M (q) denotes the inertia matrix, V (q,q) is the matrix comprising of Centrifugal and Corollis forces and G(q) represents the gravity effect. The matrices K = diag {k 1 k 2 k 3 k 4 } and C = diag {c 1 c 2 c 3 c 4 } are sliding surface constant and switching gain constant respectively. The system dynamics can be altered by varying K and C. A more advanced variant of SMC, Integral Sliding Mode Control (ISMC) eliminates reaching phase and improves performance in terms of position error. It also significantly reduces the chattering phenomena. Based on ISMC law, Khan and Jalani proposed and experimentally validated a scheme for a humanoid robot arm control. They have also demonstrated compliance control via this scheme employing joint torque sensors BIB018 . The scheme is illustrated in Fig. 5 . Recently, the book by Speirs et al. BIB019 presents bio-inspired nonlinear control for generating human-like posture, mimicking human motion and model reference adaptive compliance approaches. They have addressed the associated actuator saturation issues by introducing anti-windup compensators. In medical domain, recent applications of nonlinear control includes anesthesia administration and control of devices for rehabilitation and prosthetics BIB008 BIB009 BIB013 . A nonlinear control approach to regulate Depth Of hypnosis (DOH) in Propofol anesthesia is reported in BIB033 . The pa- BIB018 tient's hypnosis level is measured by EEG-based sensors e.g. Bispectral Index (BIS). Based on the derived patient's model, SMC minimizes steady state error to maintain hypnosis level within allowable range so as to conduct surgical procedures. Fig. 6 presents simulation results of eight patients after the infusion of drug for surgery. DOH level of 100 represents awake state while the level of 40-60 refers to moderate hypnotic state and is considered as safe range to execute surgery. As shown in the figure, all the patients achieved the desired level of hypnosis. The last decade has seen the emergence of the systems biology approach to understand biological systems in a holistic manner BIB005 . Rather than enumerating individual components (molecules, proteins) the systems biology approach focuses on the interactions between subsystems in order to understand the emergent dynamic behavior of the living system. Both the structural and functional organizations are important for characterizing the so-called symbiotic state of the biological system under study BIB010 . The structural organization involves network topologies including gene regulatory networks and biochemical reaction networks, and physical layers including molecules within organelles, organelles within cells, cells within tissues, tissues with organs and so forth. The functional organization involves cell functions including cell growth, cell division, cell differentiation (specialization) and cell death (apoptosis). The essence of systems biology is an understanding of the nonlinear dynamics of the biological system, which in turn requires the developments of computational models. Construction and analysis of such models of different subsystems (modules) of a system allow us to identify feedback loops in the system. Computer simulations could be used to test a drug or therapy before expensive clinical trials. In control-theoretic terms, a disease could be represented by some region of the state space of a living system. Viewed as a control system, the reference or desired state of the system could represent the healthy state. The drug or therapy could be represented by a controller in the loop. An application of nonlinear control can be found in BIB004 where the authors apply feedback linearization and optimal control strategies to a nonlinear state-space model of HIV infection. Other applications of optimal control of biological systems can be found in BIB006 . The curious reader might wonder why nonlinearity is ubiquitous in biological systems. This question can be answered fully in a brief account like this text but a justification will be provided by a few examples. Under appropriate assumptions, the mass action kinetics and mass action-like kinetics. Mass action-like kinetics are obeyed by intracellular biochemical reactions, cell-cell interactions and inter-species interactions including the epidemiological and predator-prey interactions. The state variables in mass action-like kinetics multiply which gives rise to nonlinear terms in the differential equations BIB005 . For instance, the rate of a chemical interaction between two species, commonly written as depends on the probability of encounter (collision) per unit time of the reactant (interacting) species. Computing such a probability involves multiplication of the abundances of the reactant species. Other sources of nonlinearity include the feedback mechanisms in which a product of a reaction cascade could enhance or inhibit the reactants. Simplifications resulting from specific assumptions (e.g. quasi-steady state) including the Michaelis-Menten kinetics and Hill kinetics are in the form of fractions, and hence nonlinear terms in the model. The rich variety of such rateequation models has been outlined in Fig. 7 . In chemical industry, the control of basic variables like pressure, levels, temperatures, flows and some quality variables is usually achieved by PID based law enhanced with advanced structures such as feedforward control, cascade control, ratio control, dead-time compensators etc. Common process characteristics in a chemical industry include BIB001 ; unmeasured state variables and disturbances, multivariable interactions between variables, high order and distributed processes, uncertain and timevarying parameters and dead-time on inputs and measure- BIB033 ments. Complex problems arising due to constraints, delays, lags and model uncertainty can better be resolved using nonlinear control approaches. Owing to these reasons, Model Predictive Control (MPC), explicitly based on nonlinear dynamic representation of the chemical process, was developed. MPC is based on mathematical optimization and is now de-facto standard in nonlinear control of process industries. Other related concepts include Dynamic Programming (DP) and iterative learning control for batch processes. A new trend BIB014 is to realize MPC law based on Support Vector Machine (SVM) and Genetic Algorithm (GA) for trajectory tracking and disturbance rejection. Nonlinear control techniques are gradually replacing their linear counterparts in refineries and petrochemical plants to handle chemicals and polymers BIB020 . A detailed review presenting challenges and progress of control systems in chemical industry is reported in  . Most of the power systems involve varying operating conditions and/or uncertainties, some of which may not be anticipated a priori BIB002 . Power systems e.g. Flexible AC Transmission Systems (FACTS) demand controllers that have to tuned online, thus making the trivial decentralised control laws inadequate. The major contributions of nonlinear control in power systems is to; regulate frequency and voltage, adequately damp the oscillations and preserve synchronisation in the presence of disturbances. Relevant techniques with eminent recent advances include; Nonlinear PI BIB021 , Optimal Control BIB022 , MPC  , Passivity-based control BIB007 , SMC BIB023 and Observer-based SMC BIB024 . In power electronics, commonly encountered circuits exhibit nonlinear dynamics primarily due to the consequences of cyclic switching BIB003 . Existence of chaos, bifurcations and limit cycles in the circuits highlights the governing role of nonlinear control. In this context, MPC and SMC are common in power electronics owing to its ability to handle system constraints, multi-variable case and nonlinearities. Applications of MPC with prominent works in power electronics has been systematically reviewed in BIB011 . Scientific literature reports several successful implementations of control laws for applications like Uninterruptible Power Supplies (UPS), Active Front End (AFE), drives for induction machines and power converters connected to RL loads. Noticeable recent advancements include; SMC  and its variants BIB025  , Observer-based control BIB015 and reinforcement learning based nonlinear control  . Further control approaches based on physical principles e.g. current-limitation capability BIB026 and capacitor ampere-second balance BIB027 have also been proposed. Other recent applications of nonlinear control systems are reported for vehicle state estimation BIB016 and for control of Unmanned Aerial Vehicles (UAV) BIB028 , Autonomous Underwater Vehicle (AUV)  , Nuclear steam generator BIB029 , reactor BIB030 , building's heating and cooling BIB031 , power pricing and management BIB032 and so on. Another trend which is gaining popularity since last two decades is to introduce adaptability and optimality in traditional nonlinear control strategies.