Nonlinear Adaptive Control Design for Quadrotor UAV Transportation System

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.

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.

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.

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

Dynamical systems are often nonlinear in nature. It motives people to explore various theoretical nonlinear analysis and control design tools, of which constructive nonlinear design methods are the most celebrated ones. However, applying a constructive tool faces up a big hurdle that the tool deals only with a certain dynamical structure, often not possessed by the natural dynamics. Nonlinear constructive control designs heavily relies on the identification of a particular structure via coordinate transformation and control transformation. To be realistic, these theoretical tools are not general to all of the nonlinear systems. Here, a challenging benchmark example–a four degrees of freedom inverted pendulum under the influence of a planar force–is considered that is nonlinear, multiple input and multiple output, underactuated and unstable. The benchmark is also of practical interests because it is an abstract of several applications. Three challenging control objectives are envisaged for the first time in the literature in order to how to apply various cuttingedge theoretical nonlinear control tools. In fact, the key step of all of the nonlinear designs is to identify spectral structures– certain “normal” forms. From this aspect, a sequence of preliminary designs will accompany the existing tools to construct nonlinear controllers, which is quite different from the linear control designs.

This paper presents the design of a novel nonlinear position controller for an interior permanent-magnet synchronous motor (IPMSM) servo drive. The motor model equations provide the basis for the proposed controller, which is designed with the adaptive backstepping technique. Various system uncertainties, particularly mechanical-parameter uncertainties, are incorporated in the design of the controller. Using Lyapunov's stability theory, it is verified that the control variables are asymptotically stable. The complete drive system is then simulated with MATLAB/Simulink software. Performance of the proposed adaptive-backstepping-based nonlinear position controller (ABNPC) is investigated under different dynamic operating conditions such as step changes in command positions, step changes in load, and parameter variations. The results indicate that the proposed ABNPC-based IPMSM drive could be a candidate for real-time industrial servo motor drive applications.

The combination of symbolic computation and numerical calculation will undoubtedly increase the power of control systems design. Although several control design toolboxes exist, many based on the simulation software MATLAB, they are primarily geared for matrix operations. General nonlinear controller design certainly needs the combination of both symbolic and numerical computations. People may argue that one can use the MATLAB symbolic toolbox which is essentially a small subset of Maple-V. However, this symbolic toolbox can only be used to solve small scale nonlinear control design problems. It is not suitable for general nonlinear computer aided control systems design without further C code for interface, as one cannot dynamically allocate memory for an indexed function of time t of arbitrary dimension, for example. This interface will use no less effort than using Mathlink as an interface between Mathematica and MATLAB. Dynamic sliding mode control using state feedback for minimum phase MIMO systems and for MIMO uncertain systems has been developed. These methods have been implemented with Mathematica and MATLAB using Mathlink as an interface. These packages have been used for nonlinear control design.

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.

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.

Direct feedback control design for nonlinear systems

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.

Robustness of an adaptive backstepping controller without modification

This paper addresses the position tracking control problem of an underactuated hovercraft vehicle. A nonlinear Lyapunov-based tracking controller is developed and proved to exponentially stabilize the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be a specially chosen (e.g., a trimming trajectory). In fact, it can be any sufficiently smooth bounded curve parameterized by time. The nonlinear controller has been experimentally validated on the Caltech Multi-Vehicle Wireless Testbed (MVWT), a platform for the development and implementation of novel single-and multiple-vehicle control designs. Experimental results are given for tracking of prescribed trajectories and for target following.

Feedback linearization (FBL) and sliding mode control (SMC) are two widely used control schemes for nonlinear systems, however, they can not be designed with explicit input constraints. In this paper, a general nonlinear optimal control design is provided which accommodates input constraints using a linear algebraic equivalence of the nonlinear controller (FBL/SMC). First, the linear algebraic equivalence of the nonlinear controller design is shown and then a nonlinear optimal controller is designed based on that equivalence. Quadratic programming and constrained linear least squares methods are used to solve the proposed control algorithm. The algorithm is applied to an ill-conditioned thermal process to illustrate the design process.