Ruyi Yuan

A Class of Adaptive Extended State Observers for Nonlinear Disturbed Systems

This paper proposes a novel class of adaptive extended state observers (AESOs) that significantly expand the applications of extended state observers (ESOs) to nonlinear disturbed systems. An AESO is designed as a linear time-varying form that, as a result, combines both the advantages of theoretical completeness in a conventional linear ESO (LESO) and good practical performance in a conventional nonlinear ESO (NESO). To tune the time-varying observer gains, AESO error dynamics is first transformed into a canonical (phase-variable) form. Then, time-varying PD-eigenvalues are assigned for the canonical system based on differential algebraic spectral theory. Theorems for stability and estimate error bounds of the AESO are given in the presence of unknown disturbances. These theorems also offer some important guidelines for assigning the PD-eigenvalues. To demonstrate the effectiveness of this new observer, two representative applications, including a numerical single-input-single-output example and a practical multiple-input-multiple-output hypersonic vehicle application, are exemplified, and comparison simulations are conducted among AESO, LESO, and NESO. Future work is pointed out in the end.

Robust adaptive neural network control for a class of uncertain nonlinear systems with actuator amplitude and rate saturations

An adaptive controller which is designed with a priori consideration of actuator saturation effects and guarantees H^~ tracking performance for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems with extern disturbances and actuator saturations is presented in this paper. Adaptive radial basis function (RBF) neural networks are used in this controller to approximate the unknown nonlinearities. An auxiliary system is constructed to compensate the effects of actuator saturations. Furthermore, in order to deal with approximation errors for unknown nonlinearities and extern disturbances, a supervisory control is designed, which guarantees that the closed loop system achieves a prescribed disturbance attenuation level so that H^~ tracking performance is achieved. Steady and transient tracking performance are analyzed and the tracking error is adjustable by explicit choice of design parameters. Computer simulations are presented to illustrate the efficiency of the proposed controller.

Selective Harmonic Elimination With Groebner Bases and Symmetric Polynomials

Selective harmonic elimination (SHE) technology has been widely used in many medium- and high-power converters which operates at very low switching frequency; however, it is still a challenging work to solve the switching angles from a group of nonlinear transcendental equations, especially for the multilevel converters. Based on the Groebner bases and symmetric polynomial theory, an algebraic method is proposed for SHE. The SHE equations are transformed to an equivalent canonical system which consists of a univariate high-order equations and a group of univariate linear equations, thus the solving procedure is simplified dramatically. In order to solve the final solutions from the definition of the elementary symmetric polynomials, a univariate polynomial equation is constructed according to the intermediate solutions and two criteria are given to check whether the results are true or not. Unlike the commonly used numerical and random searching methods, this method has no requirement on choosing initial values and can find all the solutions. Compared with the existing algebraic methods, such as the resultant elimination method, the calculation efficiency is improved, and the maximum solvable switching angles is nine. Experiments on three-phase two-level and 13-level inverters verify the correctness of the switching angles solved by the proposed method.

Adaptive trajectory tracking control system design for hypersonic vehicles with parametric uncertainty

A new nonlinear adaptive control scheme based on the immersion and invariance theory is presented to achieve robust velocity and altitude tracking for hypersonic vehicles with parametric uncertainty. The longitudinal dynamics of the hypersonic vehicle are first decomposed into velocity, altitude/flight-path angle, and angle of attack/pitch rate subsystems. Then a non-certainty-equivalent controller based on immersion and invariance, consisting of a control module and a parameter estimator, is designed for each subsystem with all the aerodynamic parameters unknown. The main feature of this method lies in the construction of the estimator, which is a sum of a partial estimate generated from the update law and an additional nonlinear term. The new term is capable of assigning appointed stable dynamics to the parameter estimate error. Stability analysis is presented using Lyapunov theory and shows asymptotical convergence of the tracking error to zero. Representative simulations are performed. Rapid and accurate command tracking is demonstrated in these numerical simulations, which illustrate the effectiveness and robustness of the proposed approach.

A Groebner Bases Theory-Based Method for Selective Harmonic Elimination

An algebraic method is proposed for selective harmonic elimination PWM (SHEPWM). By computing its Groebner bases under the pure lexicographic monomial order, the nonlinear high-order SHE equations are converted to an equivalent triangular form, and then a recursive algorithm is used to solve the triangular equations one by one. Based on the proposed method, a user-friendly software package has been developed and some computation results are given. Unlike the commonly used numerical and intelligent methods, this method does not need to choose the initial values and can find all the solutions. Also, this method can give a definite answer to the question of whether the SHE equations have solutions or not, and the accuracy of the solved switching angles are much higher than that of the reference method. Compared with the existing algebraic methods, such as the resultant elimination method, the calculation efficiency is improved. Experimental verification is also shown in this paper.

Unified Selective Harmonic Elimination for Multilevel Converters

For multilevel converters, as their selective harmonic elimination (SHE) equations are highly related to the switching patterns, it is almost impossible to give a complete study for all the switching patterns under the traditional SHE framework. In this paper, a unified SHE approach is proposed, in which the various SHE equations for different switching patterns are merged into one group of unified SHE equations and the inequality constraints on the switching angles are eliminated at all. This unified SHE equations can be solved by any methods, which have been used in solving the traditional SHE problems. By using the theory of Groebner bases and symmetric polynomials, all the possible switching patterns and the corresponding switching angles can be solved simultaneously. The study on the case for four switching angles discovers some unusual switching patterns that have the lowest total harmonic distortion for low-modulation indices. Also, the case for nine switching angles with modulation index m=0.72 is studied; in total, there exist 43 groups of switching angles, which belong to 33 different switching patterns. Experiments on a 13-level cascaded-H bridge converter verify the correctness of this unified multilevel SHE approach.

Immersion and Invariance-Based Output Feedback Control of Air-Breathing Hypersonic Vehicles

A new output feedback control design for robust velocity and altitude tracking of an air-breathing hypersonic vehicle (AHSV) is presented in this paper. The control scheme is performed on the assumption that only partial states of AHSV are measurable. The key idea is to employ the immersion and invariance approach to design globally asymptotically stable observers for the unmeasurable states. For controller design, the whole control architecture is constructed using dynamic surface control, based on the decomposition of the longitudinal dynamics of AHSV into velocity and altitude subsystems. Stability analysis is presented using the Lyapunov theory. Representative simulations are carried out on the high-fidelity model, which illustrate the effectiveness and robustness of the proposed scheme.

Direct adaptive type-2 fuzzy neural network control for a generic hypersonic flight vehicle

A direct adaptive interval type-2 fuzzy neural network (IT2-FNN) controller is designed for the first time in hypersonic flight control. The generic hypersonic flight vehicle is a multi-input multi-output system whose longitudinal model is high-order, highly nonlinear, tight coupling and most of all includes big uncertainties. Interval type-2 fuzzy sets with Gaussian membership functions are used in antecedent and consequent parts of fuzzy rules. The IT2-FNN directly outputs elevator deflection and throttle setting which make the GHFV track the altitude command signal and meanwhile maintain its velocity. The parameter adaptive law of IT2-FNN is derived using backpropagation method. The deviation of the control signal from the nominal dynamic inversion control signal is used as the reference output signal of IT2-FNN. The tracking errors of velocity and altitude are used as inputs of IT2-FNN. Tracking differentiator is designed to form an arranged transition process (ATP) of the command signal as well as ATP’s high-order derivatives. Nonlinear state observer is designed to get the approximations of velocity, altitude as well as their high-order derivatives. Simulation results validate the effectiveness and robustness of the proposed controller especially under big uncertainties.

Adaptive controller design for uncertain nonlinear systems with input magnitude and rate limitations

An adaptive controller for a class of multiple input-multiple-output (MIMO) uncertain nonlinear systems with extern disturbance and control input limitations is presented in this paper. The controller is designed with a priori consideration of input limitation effects, hence it can generate control signals satisfying input limitations. This controller uses adaptive radial basis function (RBF) neural networks to approximate the unknown nonlinearities. To compensate the effects of input limitations, an auxiliary system is constructed and used in neural network parameter update laws. Furthermore, in order to deal with approximation errors for unknown nonlinearities and extern disturbances, a supervisory control is designed, which guarantees that the closed loop system achieves a desired level H∞ tracking performance. The closed loop system performance is analyzed by Lyapunov method. Steady state and transient tracking performance index are established and can be adjusted by design parameters. Computer simulations are presented to illustrate the efficiency and tracking performance of the proposed controller.

Design of robust backstepping controller for unmanned aerial vehicle using analytical redundancy and extended state observer

In current flight control system (FCS) practice for unmanned aerial vehicles(UAVs), flight safety becomes more and more important in extreme weather or in the face of sensor and control effector failures. Flight safety is guaranteed traditionally by specifying functionally redundant control hardware. Compared with extra burden increased by hardware redundancy on UAV, design of analytical redundancy becomes attractive in recent years. This paper proposes a new hybrid design scheme of analytical redundance FCS, which is composed of analytical redundance, core flight control algorithm and uncertainties compensator. Analytical redundancy for attitude angle rates adopts reduced order nonlinear state observer method. The core backstepping flight controller realizes linearization and decoupling of the highly nonlinear and tightly coupled UAV model. For cancelling out uncertainties such as unmodeled dynamics and external disturbances, an extended state observer(ESO) compensator is designed to enhance the robustness of FCS. Pseudoinverse method is applied to establish the mapping between moments and multiple control surfaces. Numerical simulation shows that UAV equipped with the hybrid control scheme has good maneuverability, strong self-learning ability of compensating the unmodeled dynamics and enough robust stability against constraints of actuators.