Robustness of an adaptive backstepping controller without modification

Design of an adaptive controller for complex dynamic systems is a big challenge faced by the researchers. In this paper, we propose a novel method for the design of an error- based robust adaptive controller to make the system response reasonably fast with no overshoot. Here the control action is designed by introducing the notion of ‘error-based adaptive controller’ (EB-AC). In the design of this feedback adaptive controller, parameters of the controller are designed as a function of the system error. For example, the position feedback parameter K p (e, t), which controls the bandwidth of the system as well as the dynamic response, is a function of the system error e(t). In the design of the position feedback parameter K p (e, t), for large error K p (e, t) is kept large, thus increasing the bandwidth of the system which yields a fast response, whereas for decreasing errors, K p (e, t) is continuously decreased to a small value. Thus, during the dynamic response of the system, the bandwidth of the system is continuously controlled by the system error e(t). Similarly, the velocity feedback parameter K v (e, t) which controls the damping of the system is kept very small for large errors, and continuously increased to a large value for decreasing value of error. Hence, in the design of the proposed adaptive controller, the position feedback K p (e, t) and the velocity feedback K v (e, t) are formulated as a function of the system error, and this approach for formulating the adaptive controller yields a very fast response with no overshoot. In this paper, we present an error-based robust adaptive control design methodology for a linear system.

<span>This paper is aimed at addressing the design of an effective adaptive nonlinear control of a photovoltaic (PV) water pumping system powering a submersible induction motor and a centrifugal water pump. Four objectives are achieved using an adaptive Backstepping controller. First, it is applied to ensure maximum power point tracking, and uses the latter as a reference in regulation of the rotor speed to convert the maximum electrical power into maximum mechanical power. Second, the adaptive controller is synthesized to control motor rotor flux and restrict the magnetic circuit to its linear interval. Third, it is used to online estimate the rotor time-constant and the load torque disturbance estimation. Finally, this controller is employed to limit the stator currents to protect induction motor windings. Mathematical modelling of the main elements of the system is presented. A sliding mode rotor flux estimator is employed in the output feedback control of the whole system. DC-AC converter is controlled by pulse width modulation. The feasibility, the robustness and the effectiveness of the proposed adaptive nonlinear controller are evaluated through simulations in MATLAB/Simulink environment.</span>

<div class="htmlview paragraph">In this paper, a robust adaptive optimal tracking control design for the air-path system of diesel engines with uncertain parameters and external driver commands is proposed.</div> <div class="htmlview paragraph">First, an optimal controller based on the analytic solution of a performance index is derived. It achieves tracking of suitable references (corresponding to low emissions and fuel consumption) for both the air-fuel ratio and the fraction of the recirculated exhaust gas. Then, a fuzzy estimation algorithm is used to identify the plant parameters and consequently to adapt the controller online.</div> <div class="htmlview paragraph">The simulated diesel engine is a medium duty Caterpillar 3126B with six cylinders, equipped with a variable geometry turbocharger and an exhaust gas recirculation valve. The proposed controller design is based on the reduced third order mean value model and implemented as a closed-form nonlinear model predictive control law on the full order model. The resulting controllers, with and without adaptation, are assessed through simulations with a SIL architecture using dSpace simulator. The adaptive controller, in particular, exhibits good control performance, with zero tracking offset with also ensuring global stability and tracking of output references.</div>

A novel single fuzzy approximation based adaptive control for a class of uncertain strict-feedback discrete-time nonlinear systems

This paper considers augmentation of an existing inertial damping mechanism by neural network-based adaptive control, for controlling a micromanipulator that is serially attached to a macromanipulator. The approach is demonstrated using an experimental test bed in which the micromanipulator is mounted at the tip of a cantilevered beam that resembles a macromanipulator with its joint locked. The inertial damping control combines acceleration feedback with position control for the micromanipulator so as to simultaneously suppress vibrations caused by the flexible beam while achieving precise tip positioning. Neural network-based adaptive elements are employed to augment the inertial damping controller when the existing control system becomes deficient due to modeling errors and uncertain operating conditions. There were several design challenges that had to be faced from an adaptive control perspective. One challenge was the presence of a nonminimum phase zero in an output feedback adaptive control design setting in which the regulated output variable has zero relative degree. Other challenges included flexibility in the actuation devices, lack of control degrees of freedom, and high dimensionality of the system dynamics. In this paper we describe how we overcame these difficulties by modifying a previous augmenting adaptive approach to make it suitable for this application. Experimental results are provided to illustrate the effectiveness of the augmenting approach to adaptive output feedback control design.

Concerns nonlinear model predictive control, and particularly the nonlinear optimization problem. Usually the control sequence can be determined by using some effective numerical iteration approaches, especially for multistep predictive control. This work focuses on the multistep adaptive NMPC controller design using neural-net. The main ideas are (A) initialisation of the multistep control laws by using one-step ahead predictive control law; (B) linearization of the neural-net predictor at every operating point; and (C) tuning of the neural-net predictor through online learning using teacher signals generated by closed-loop system input-output data. As an illustrative example of our approach, an explicit control laws are derived for the control horizon Nu=2 case.

There is a growing interest in the modeling and control of model helicopters using nonlinear dynamic models and nonlinear control. A helicopter is an underactuated system with fewer independent control actuators than degrees of freedom to be controlled, making the control difficult. Further, most of the models and control are derived for separate flight conditions such as take-off or hovering because of the complexity involved. This simplification in fact seems to make the problem more difficult since the simplified model might not have the properties associated with the original physical system. Analytical techniques based on Lyapunov theory are then used to design the controller and the design can become extremely complex. In this paper, we present a new nonlinear and adaptive controller design. The design methodology basically involves making the combined dynamics of the helicopter and the controller to resemble the dynamics of a nonlinear time varying electrical circuit having the required properties, using a process similar to reverse engineering. This conceptually simple procedure leads to a new general class of complex nonlinear and adaptive controller algorithms without the use of or the necessity for complex analytical tools, and hence can be understood and applied easily. Even though the solution provided here is for a particular flight condition, this approach can easily be extended to multiflight conditions.

This chapter is focused on the design and analysis of adaptive controllers for dynamical systems operating in the presence of nonparametric unknown nonlinear functions and bounded time-varying disturbances. In order to counter these types of uncertainties, we will employ direct adaptive model reference controllers equipped with online function approximation architectures, such as artificial neural networks (NNs). We begin with an introductory review of theoretical results related to function approximation by NNs, (Sects. 12.1, 12.2, and 12.3). As for any other function representation constructs, NN-based approximations are valid only on bounded sets. So, a suitable control design must account for a set of state limiting constraints imposed by the chosen function approximation method. For our proposed adaptive control design (Sect.12.4), we will utilize online tunable artificial NNs to represent unstructured uncertainties in the system dynamics of interest. In addition, we will add a state limiting design modification to keep the system trajectories within predefined NN-induced state limiting constraints. We end this chapter with a comprehensive step-by-step design example of an automatic landing system for a medium-size transport aircraft.

Robust Adaptive Control

This paper investigates adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems in strict feedback form. The considered nonlinear systems contain unknown nonaffine nonlinear faults and unmeasured states. Fuzzy logic systems are used to approximate cost function and unknown nonlinear functions, respectively. It is assumed that the states of the systems to be controlled are unmeasurable, thus an adaptive state observer is developed. To solve the nonaffine nonlinear fault control design problem, filtered signals are introduced into the adaptive backstepping control design procedures, and in the framework of adaptive critic technique and fault-tolerant control technique, a novel adaptive fuzzy fault-tolerant optimal control scheme is developed. The stability of the closed-loop system is proved by using Lyapunov stability theory. The simulation results verify the effectiveness of the proposed control strategy.

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

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.

This study focuses a trajectory control problem of a quadrotor, created by combining the dynamics of a spherical pendulum with the dynamics of a quadrotor. A spherical pendulum is a physical system comprising a mass suspended by a string or rod that has the freedom to swing in any direction. During the operation of a quadrotor, the payload connected to it behaves similar to the dynamics of a spherical pendulum. Consequently, it is essential to design a trajectory control problem by considering both quadrotor and spherical pendulum dynamics together, as this constitutes a significant aspect. Due to the varying masses of the payload that are attached to the quadrotor during each take off, the adaptability of the total mass in model-based control design poses a significant challenge. In addition, it is crucial to consider mass adaptation when the payload attached to the quadrotor is released during flight. The proposed Lyapunov based adaptive backstepping controller algorithm can predict the total mass of the quadrotor without prior knowledge of the actual payload. The ability to estimate varying payload masses is crucial for enhancing the quadrotor’s operational flexibility and reliability, particularly in real-world applications where payloads may change dynamically. This innovation paves the way for more versatile, real-world deployment of quadrotor systems in scenarios requiring precise and adaptive control.

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

Backstepping is a systematic method for nonlinear control design, which can be applied to a broad class of systems. The name “backstepping” refers to the recursive nature of the design procedure. First, only a small subsystem is considered, for which a “virtual” control law is constructed based on a Lyapunov function (Krstic et al., Nonlinear and Adaptive Control Design, Wiley Interscience, New York, 1995; Slotine and Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, 1991) for the subsystem. Then, the design is extended in several steps until a control law for the full system has been constructed. Along with the control law, a Lyapunov function is successively constructed. An important feature of backstepping is that useful nonlinearities, which act stabilizing, can be retained. This is in contrast to feedback linearization control where nonlinearities are cancelled using nonlinear feedback. Retaining nonlinearities instead of cancelling them requires less precise models and may also require less control effort. Backstepping can be applied to nonlinear systems which are in strict feedback form or pure feedback form. In this paper controller design for ascent phase of reusable launch vehicle in pitch plane using backstepping is presented.