On Nonlinear Control Perspectives of a Challenging Benchmark

Robust Nonlinear EGR and VGT Control with Integral Action for Diesel Engines

In this paper, we study the congestion control problem in TCP satellite networks, and present a new design for TCP network congestion control based on a nonlinear control and optimization framework. The proposed TCP/AQM control framework consists of two levels: the high-level generates the desired queue size for routers in the network by solving a network utility maximization problem using a distributed optimization scheme; the low-level provides a local nonlinear feedback control for the probability of packet mark/drop based on a typical fluid-flow model for TCP dynamical behaviors. The nonlinear control design is done using a backstepping method and its stability is proven by the Lyapunov direct method. Simulation results are included to show the effectiveness of the proposed new design.

In response to the non-linear and underactuated characteristics of quadrotor UAV suspension transportation system, this paper proposes a novel control strategy aimed at achieving precise position control, attitude control, and anti-swing capabilities. Firstly, a dynamical model required for controller design is established through the Newton-Euler method. In the controller design process, the paper employs the energy method and barrier Lyapunov function to design a double-closed-loop nonlinear controller. This controller is capable of not only accurately controlling the position and attitude angles of the quadrotor UAV suspension transportation system but also effectively suppressing the swing of the payload. Building on this, considering the elastic deformation of the lifting cable, and by analyzing the forces in the Newton-Euler equations, this paper proposes an adaptive control design for the case where the length of the cable connecting the UAV and the payload is unknown. To validate the effectiveness of the proposed control scheme, comparative experiments were conducted in the MATLAB simulation environment, and the results indicate that the method proposed in this paper exhibits superior control performance compared to traditional controllers.

A nonlinear adaptive control strategy is derived from the biological control system that regulates arterial blood pressure. The parallel control system consists of a linear controller and a nonlinear controller that interact via a reciprocal lateral inhibitory mechanism. The linear controller design is based on an empirical linear model, while the nonlinear controller is constructed from locally supported radial basis functions that are updated on-line using a model reference adaptive control technique. The control strategy is evaluated using a simple model of a pH neutralization system.

Electric power system is complex interconnected system that is subjected to rapid change in its structure. Addition of new equipment, operation close to stability limits and variation in load in summer and winter are some factors that make power system unstable and introduce electro-mechanical oscillations in the system.;Electro-mechanical oscillations of small magnitude often persist for long periods of time and restrict the power transfer capacity. These oscillations can further increase with the variation in load and system operating points. To stabilize the power system different control strategies are used to damp the oscillations. In the past, the dynamic stability of power system was modeled using linearized modeling of power system at operating points. Linear eigenvalue controllers damp the oscillation to some extent but are not robust for disturbance and variation in system operating points and therefore can render system unstable.;Non-linear controller design has found extensive application in robotics for stabilizing system. Synergetic Controller based on Synergetic Control Theory, is a non-linear controller that forces the system towards global stability and has extensively been used in power electronics.;In this research, a Single Machine Infinite Bus (SMIB) with HVDC link is considered for comparing the performance of linear and non-linear controllers. The test system has Static Var Compensator (SVC) connected on load bus. Reactive modulation is performed through SVC to damp oscillations in the system. The Synergetic Controller is designed for full transient model and the classical model of the synchronous machine.;The performance of both non-linear controller and linear controller is compared for different disturbance and variation in system parameters. Results show the robustness of non-linear controller which damps the oscillations effectively.

The paper deals with design and simulation of nonlinear adaptive control of a shell and tube heat exchanger. The method is based on factorization of the controller on a nonlinear static part and an adaptive linear dynamic part. The nonlinear static part is derived using inversion and subsequent exponential approximation of simulated or measured steady-state characteristics of the exchanger. The linear dynamic part is then obtained from an external linear model of nonlinear elements of the closed-loop. The parameters of the external linear model are recursively estimated via a corresponding delta model. The control law in the 1DOF and 2DOF control system structures is derived using the polynomial approach. INTRODUCTION Heat exchangers are an essential part of many technologies in energy and chemical industry, polymer manufacturing, petroleum refineries, and many others. By construction, heat exchangers can be classified into exchangers with direct contact, various types of plate exchangers, and, shell and tube heat exchangers (STHEs), see, e.g. (Smith 2005; Hewitt et al. 1994; Incropera et al. 2011). As known, STHEs are most common types of heat exchangers. From the system theory, they belong to a class of nonlinear distributed parameter systems with mathematical models in the form of nonlinear partial differential equations. Modelling and simulation of such processes are described in many publications, e.g. in (Luyben 1989; Corriou 2004; Babu 2004; Ogunnaike and Rao 1994). As known, these processes can be hardly controllable by conventional methods that can lead to control of a poor quality. In this case, some advanced control methods should be used such as adaptive, predictive, optimal or nonlinear control, and some others. Obviously, control design always requires a preliminary steady-state and dynamic analysis of the process by simulation tools. Some methods of numerical mathematics used to build simulation models can be found e.g. in (Nevriva et al. 2009; Cook 2002). The aim of the paper is an application of nonlinear control and subsequent control simulation of a simple type of the shell and tube heat exchanger. The control strategy is based on the idea of factorization of the controller on a nonlinear static part (NSP) and an adaptive linear dynamic part (LDP). Similar approaches can be found e.g. in (Chen et al. 2006; Dostal et al. 2011b). The nonlinear static part is obtained from simulated or measured steady-state characteristic of the STHE, its inversion, exponential approximation, and, subsequently, its differentiation. On behalf of development of the linear part, the NSP including the nonlinear model of the STHE is approximated by a continuous-time external linear model (CT ELM). For the CT ELM parameter estimation, an external delta model with the same structure as the CT model is used. The basics of delta models have been described e.g. in (Mukhopadhyay et al. 1992; Garnier and Wang 2008). Although delta models belong into discrete models, they do not have such disadvantageous properties connected with shortening of a sampling period as discrete zmodels. In addition, parameters of delta models can directly be estimated from sampled signals. Moreover, it can be easily proved that these parameters converge to parameters of CT models for a sufficiently small sampling period (compared to the dynamics of the controlled process), as shown in (Stericker and Sinha 1993; Dostal et al. 2004). The 1DOF and the 2DOF control system structures are considered. In the first case, the control system includes only a feedback controller, in the second case, the controller consist of a feedback and a feedforward part. Such structures were described and applied e.g. in (Dostal et al. 2011a; Grimble 1993). Then, resulting CT controllers are derived using the polynomial approach and the pole placement method (Kucera 1993; Mikles and Fikar 2004). The simulations are performed on a nonlinear model of the STHE. MODEL OF THE STHE Consider an ideal plug-flow shell and tube heat exchanger in the fluid phase and with the counterflow cooling. The fluid flowing in tubes is cooled by a fluid flowing in the shell as shown in Fig. 1. Heat losses and heat conduction along the metal walls of tubes are Proceedings 28th European Conference on Modelling and Simulation ©ECMS Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani (Editors) ISBN: 978-0-9564944-8-1 / ISBN: 978-0-9564944-9-8 (CD) assumed to be negligible, but dynamics of the metal walls of tubes are significant. All densities, heat capacities, and heat transfer coefficients are assumed to be constant. Under above assumptions, the STHE model can be described by three partial differential equations (PDEs) in the form

During recent years there has been considerable interest in using bilinear systems [1, 2] as mathematical models to represent the dynamic behavior of a wide class of engineering, biological and economic systems. Moreover, there are some methods [3] which may approximate nonlinear control systems by bilinear systems. For the first time Zubov has proposed a method of stabilization control synthesis for a set of programmed motions in linear systems [4]. In papers [5, 6] this method has been developed and used to solve the same problem for bilinear systems.In the present paper the following problems are considered. First, synthesis of nonlinear control as feedback under which the bilinear control system has a given set of programmed and asymptotic stable motions. Because this control is not unique, the second problem concerns optimal stabilization. In this paper a method for the design of nonlinear optimal control is suggested. This control is constructed in the form of a convergent series. The theorem on the sufficient conditions to solve this problem is represented.

This paper is concerned with control design for a generalized discrete-time Takagi-Sugeno fuzzy system. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations. It is a great tool to analyze a nonlinear system and to design a stabilizing controller for it. However, there is a case where a controller design for a nonlinear system based on the Takagi-Sugeno fuzzy system becomes difficult due to its representation. A generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems, and gives a different representation from the standard Takagi-Sugeno fuzzy system, which leads to a rather easy controller design. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of nonlinear controllers. Then, the resulting closed-loop system becomes a fuzzy system with linear system structures locally, which makes the control design easier. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

In this paper, the parameterized dynamical model of the diesel engine intake and exhaust system using a data-based method, namely a Gain-Scheduled model is proposed and designed based on the data from a virtual engine test bench under normal load conditions. In the first step, the Multiple Input Multiple Output model structure is defined with five inputs and two outputs. Using the constructed model, it is possible to establish the relations between intake Manifold Pressure, Air Mass Flow, the control signals, and changes of the load. Then, the model is further used to design a Nonlinear Model Predictive Control controller, aimed at optimizing the efficiency of the combustion system in terms of the control reference value tracking with respect to emission reduction. This paper follows a model-based design approach to construct the Nonlinear Model Predictive Control objective function for the engine intake Manifold Pressure and Air Mass Flow nonlinear control problem. The proposed data-based dynamical modeling method is shown to increase the flexibility for the modeling of nonlinear plant at a low cost in computational requirements. The experimental results illustrate that the optimized nonlinear control approach significantly improve the control reference tracking performance and the exhaust emissions against the standard decentralized Single Input Single Output control in the standard production Engine Control Unit.

The control problem of the single machine infinite bus system with TCSC is dealt with. Based on the maximization of the external disturbances on the system model, an adaptive nonlinear controller for large disturbance attenuation and a parameter updating law are designed by using the backstepping method. The parameter uncertainty of the transmission line is considered, as well as the influences of large external disturbances to the system output are mainly discussed. The nonlinear controller does not have the sensitivity to the influences of external disturbances, but also has strong robustness for system parameters variation. The simulation results show that the control effect of the large disturbance attenuation controller more advantages by comparing with the control performance of conventional nonlinear robust controller.

This paper is concerned about the finite-time stabilizability and instabilizability for a class of delayed memristive neural networks (DMNNs). Through the design of a new nonlinear controller, algebraic criteria based on M -matrix are established for the finite-time stabilizability of DMNNs, and the upper bound of the settling time for stabilization is estimated. In addition, finite-time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller. The effectiveness and the superiority of the obtained results are supported by numerical simulations.

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

The nonlinear dynamics of a single-degree-of-freedom pneumatic vibration isolator are studied. Based on a physical model, a nonsymmetric stiffness nonlinearity is derived to describe the stiffness property of the isolator. For a full nonlinear pneumatic isolator model, the response to two different types of disturbances is studied: forces applied to the isolated payload and base vibrations. The dynamic behavior of the isolator in case of a disturbance applied to the payload is studied using the generalized force-mobility function and features coexisting steady-state responses and a superharmonic resonance. Base vibrations transmitted via the isolator are studied on the basis of the generalized transmissibility function again showing rich nonlinear dynamic behavior. The presence of a nonsymmetric nonlinearity also induces high-energy low-frequency response to multiple high-frequency excitation. For both types of excitation, the nonlinear behavior is seriously compromising the performance of the isolator. To avoid any expression of nonlinearity whatsoever and, at the same time, to enhance the performance of the passive isolator, an overall nonlinear control design is proposed. It consists of a linear PID-based controller together with a nonlinear computed torque controller (CTC). For either linear or nonlinear control, the isolator performance is quantified in terms of generalized force mobility and transmissibility. The latter with a special focus on multiple high-frequency excitation.

Using the Approximate Dynamic Programming (ADP) approach, nonlinear optimal control problems can be solved by using a dual neural network architecture called the Adaptive Critic (AC). A Single Network Adaptive Critic (SNAC) architecture has been shown to have much faster convergence than AC. Even though the SNAC offers a systematic optimal control design method for optimal state regulation for a class of nonlinear control systems, it lacks the generality necessary for command tracking as it is practically difficult to anticipate a proper training domain in state space when the command sequence is not known a priori. Dynamic Inversion (DI), on the other hand, is a very popular nonlinear control design method for both output regulation and command tracking that offers a closed form expression for control. However, it lacks the interpretation and advantages of optimal control design. In this paper we propose a systematic technique for selecting the DI gains with the help of a pre-synthesized SNAC network in order that the resulting DI solution closely mimics the SNAC solution for output regulation and can be extended to command tracking problems. Moreover, it retains all the benefits of DI design. The potential of this new methodology of near-optimal dynamic inversion design is demonstrated in this paper by considering a benchmark nonlinear system.

Feedback linearisation is perhaps the most important nonlinear control design strategy developed during the last few decades [5]. The main objective of the approach is to algebraically transform a nonlinear dynamic system into a linear dynamic system by using a static state feedback and a nonlinear coordinate transformation based on a differential geometric analysis of the system. By eliminating nonlinearities in the closed loop system, conventional linear control techniques can be applied. Our presentation of relative degree, normal forms, zero dynamics and feedback linearisation for nonlinear control affine systems given in Section 3.1 follows the notation that is used in the mainstream nonlinear control literature [5, 56]. The method of input-output feedback linearisation for nonlinear MIMO control affine systems, which is central in this book, is presented in Section 3.1.3. Other linearisation techniques, such as exact linearisation and Volterra linearisation, are reviewed in Section 3.2. Finally, two feedback linearisation techniques that are applicable to systems that are not control affine are briefly presented in Section 3.3.KeywordsRelative DegreeFeedback LinearisationCharacteristic MatrixZero DynamicDynamic Neural NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.