Backstepping Scheme Research Articles

Prescribed Performance Quantized Tracking Control for a Class of Delayed Switched Nonlinear Systems With Actuator Hysteresis Using a Filter-Connected Switched Hysteretic Quantizer

This article proposes a prescribed adaptive backstepping scheme with new filter-connected switched hysteretic quantizer (FCSHQ) for switched nonlinear systems with nonstrict-feedback structure and time-delay. The system model is subjected to unknown functions, unknown delays, and unknown Bouc-Wen hysteresis nonlinearity. The coexistence of quantized input and actuator hysteresis may deteriorate the shape of hysteresis loop and, consequently, fail to guarantee the stability. To deal with this issue, a new FCSHQ is introduced to smooth the input hysteresis. This adaptive filter also provides us a degree of freedom at choosing the desired communication rate. The repetitive differentiations of virtual control laws and existing a lot of learning parameters in the neural network (NN)-based controller may result in an algebraic loop problem and high computational time, especially in a nonstrict-feedback form. This challenge is eased by the key advantage of NNs' property where the upper bound of the weight vector is employed. Then, by an appropriate Lyapunov-Krasovskii functional, a common Lyapunov function is presented for all subsystems. It is shown that the proposed controller ensures the predefined output tracking accuracies and boundedness of the closed-loop signals under any arbitrary switching. Finally, the proposed control scheme is verified on a practical example where simulation results demonstrate the effectiveness of the proposed scheme.

Aerial Slung-Load Position Tracking Under Unknown Wind Forces

We propose a dynamic controller for position tracking of a point-mass load attached to an omnidirectional aerial vehicle by means of a cable. Both the load and the aerial vehicle are subject to unknown wind forces. We model the dynamics of the slung-load system and put it into canonical form, i.e., a form which is independent of the system's physical parameters. Following a backstepping strategy, we design a dynamic control law for the canonical system that contains four estimators, since each of the two wind disturbances has two separate effects: an effect on the linear acceleration and another on the angular acceleration. Loosely speaking, the difference between the wind forces is an input-additive disturbance, while the wind force on the load is not, which makes removing the wind force on the load nontrivial. We identify conditions on the desired position trajectory and on the wind on the load, which guarantee that a well-defined equilibrium trajectory exists. The designed controller guarantees simultaneously that the latter trajectory is asymptotically tracked and the cable remains taut, provided that the system is initialized in a suitable set. Simulations illustrate our results.

Adaptive event-triggered fuzzy tracking control of nonlinear systems with dead-zones and unmeasurable states

In this paper, the adaptive event-triggered tracking control of uncertain nonlinear systems with dead-zone inputs is developed based on fuzzy approximation technique. Firstly, a robust fuzzy state observer is constructed to effectively estimate all the unmeasurable states. Next, an adaptive output feedback controller with parameter updated law only containing one on-line adjusted variable is designed via the backstepping scheme. Concomitantly, a novel event-triggered condition related to the upper and lower bounds of dead-zone parameters and the decreasing function of tracking errors is given to substantially alleviate the computation load of the communication process. Moreover, the desired closed-loop stability of the resulting systems can be achieved by exploiting Lyapunov function analysis. Finally, simulation results verify the effectiveness of the proposed method.

A Composite Nonlinear Controller for Power Systems with STATCOM under External Disturbances

This paper concentrates on the design of a composite nonlinear stabilizing state feedback control for power systems with static synchronous compensator (STATCOM) with the help of a combination of backstepping strategy and a nonlinear disturbance approach. The disturbance observer is used to estimate unavoidably external disturbances. Thus, the obtained control law can be used to successfully stabilize the system stability and reject undesired external disturbances. In order to demonstrate the effectiveness of the developed process design, numerical simulation results are provided to indicate that the presented composite controller can improve dynamic performances, rapidly suppress system oscillations of the overall closed-loop dynamics, and despite having inevitably external disturbances, performs better than a conventional backstepping control technique.

Sliding Mode Self-Sensing Control of Synchronous Machine Using Super Twisting Interconnected Observers

The aim of this study is to propose a self-sensing control of internal permanent-magnet synchronous machines (IPMSMs) based on new high order sliding mode approaches. The high order sliding mode control will be combined with the backstepping strategy to achieve global or semi global attraction and ensure finite time convergence. The proposed control strategy should be able to reject the unmatched perturbations and reject the external perturbation. On the other hand, the super-twisting algorithm will be combined with the interconnected observer methodology to propose the multi-input–multi-output observer. This observer will be used to estimate the rotor position, the rotor speed and the stator resistance. The proposed controller and observer ensure the finite-time convergence to the desired reference and measured state, respectively. The obtained results confirm the effectiveness of the suggested method in the presence of parametric uncertainties and unmeasured load torque at various speed ranges.

Adaptive Bipartite Tracking Control of Nonlinear Multiagent Systems With Input Quantization.

This article studies the bipartite tracking control problem of distributed nonlinear multiagent systems with input quantization, external disturbances, and actuator faults. We use the radial basis function (RBF) neural networks (NNs) to model unknown nonlinearities. Due to the fact that the upper bounds of disturbances and the number of actuator faults are unknown, an intermediate control law is designed based on a backstepping strategy, where a compensation term is introduced to eliminate external disturbances and actuator faults. Meanwhile, a novel smooth function is incorporated into the real distributed controller to reduce the effect of quantization on the virtual controller. The proposed distributed controller not only realizes the bipartite tracking control but also ensures that all signals are bounded in the closed-loop systems and the outputs of all followers converge to a neighborhood of the leader output. Finally, simulation results demonstrate the effectiveness of the proposed control algorithm.

Improved finite-time command filtered backstepping fault-tolerant control for flexible hypersonic vehicle

The tracking control of a flexible hypersonic vehicle with system perturbation and actuator fault is investigated in this paper. A control-oriented model is constructed, which is composed of velocity loop and altitude loop. A double-layer fast adaptive-gain super-twisting disturbance observer (ASTDO) is designed to provide finite-time estimation of the lumped terms of external disturbances and actuator faults. The ASTDO has the property of the non-overestimation of adaptive gains and chattering reduction with higher precision. Based on the estimation of ASTDO, a novel finite-time command filtered backstepping (FCFB) scheme is proposed for the high-order altitude loop. The merit lies in the modified compensating signals and new virtual commands to compensate the command filter errors. The remarkable features of the developed algorithm include the finite-time convergence with higher accuracy and the chattering suppression. Finally, comparative simulation results are given to demonstrate the superiority of the proposed method.

Control of magnetic levitation system using recurrent neural network-based adaptive optimal backstepping strategy

In this paper, a novel approach is proposed for adjusting the position of a magnetic levitation system using projection recurrent neural network-based adaptive backstepping control (PRNN-ABC). The principles of designing magnetic levitation systems have widespread applications in the industry, including in the production of magnetic bearings and in maglev trains. Levitating a ball in space is carried out via the surrounding attracting or repelling magnetic forces. In such systems, the permissible range of the actuator is significant, especially in practical applications. In the proposed scheme, the procedure of designing the backstepping control laws based on the nonlinear state-space model is carried out first. Then, a constrained optimization problem is formed by defining a performance index and taking into account the control limits. To formulate the recurrent neural network (RNN), the optimization problem is first converted into a constrained quadratic programming (QP). Then, the dynamic model of the RNN is derived based on the Karush-Kuhn-Tucker (KKT) optimization conditions and the variational inequality theory. The convergence analysis of the neural network and the stability analysis of the closed-loop system are performed using the Lyapunov stability theory. The performance of the closed-loop system is assessed with respect to tracking error and control feasibility.

Adaptive Finite-Time Containment Control of Uncertain Multiple Manipulator Systems.

This article is concerned with the containment control of multiple manipulators with uncertain parameters. A novel distributed adaptive backstepping strategy is given in the finite-time control framework. The finite-time command filters (FTCFs) used in the strategy can avoid the explosion of complexity problem for conventional backstepping. To further improve the control performance, the filtering errors caused by the used FTCFs are removed by using the error compensation mechanism (ECM). The proposed virtual control signal, the control torque, and the adaptive updating law can guarantee the set tracking errors converge to an adjustable neighborhood of the origin in finite time in the presence of uncertain parameters. Because the virtual control signal and ECM only use the local information, the established method is completely distributed. Two simulation examples are given to show the effectiveness of the proposed scheme.

Tracking Control of an unknown switched nonlinear system based on adaptive backstepping with nonlinear disturbance observer

In this paper, an adaptive control schemes to solve the output tracking control problem of a class of nonlinear switched systems in presence of the disturbance is proposed. First, an nonlinear disturbance observer (NDO) is designed and the backstepping scheme is constructed based on the standard Lyapunov function method for tracking purpose. With the propose scheme, the existence of a standard Lyapunov function for all subsystems with unknown parameters infers the global uniform asymptotic stability of this more generic switched system The switching parameters used in the switching system are defined differently for each subsystem. Analyzing the system's stability proved that the closed-loop signal boundedness under arbitrary switching is well ensured. It is shown that the proposed adaptive anti-disturbance control scheme based on a nonlinear disturbance observer is a suitable control approach for a class of nonlinear switched systems.

Command filtering-based adaptive fuzzy control for permanent magnet synchronous motors with full-state constraints

Focusing on the problem of position tracking control for permanent magnet synchronous motors (PMSMs) with full-state constraints, this article proposes an adaptive fuzzy control scheme based on command filtering error compensation mechanism. Firstly, the unknown nonlinear functions of PMSM drive systems are approximated by utilizing the fuzzy logic systems (FLSs). Then, the command filtering technique is employed to deal with the “explosion of complexity” problem arising from conventional backstepping scheme, and the filtering errors are reduced by the error compensation mechanism. In addition, the barrier Lyapunov functions (BLFs) are constructed to guarantee that the state variables are restricted in compact bounding sets. Finally, simulation results show the effectiveness of the proposed scheme.

Fixed-TimeBackstepping Control of Quadrotor Trajectory Tracking Based On Neural Network

This paper aims at the trajectory tracking of a quadrotor. A novel fixed-time backstepping control design scheme is proposed for the quadrotor based on adaptive neural control approach. The suggested adaptive controller ensures that the quadrotor well tracks the desired trajectory in finite time in spite of appearance of model uncertainties. Finally, simulation results are given to verify the effectiveness of the proposed control strategy.

Adaptive Quantized Control of Output Feedback Nonlinear Systems With Input Unmodeled Dynamics Based on Backstepping and Small-Gain Method

In this article, an adaptive quantized neural backstepping strategy is investigated for a class of nonlinear systems with input unmodeled dynamics and output constraints based on the small-gain method. A challenge lies in the considered input-quantized actuator possessing both unknown control gain and input unmodeled dynamics, and the application of the small-gain theorem when the system possesses input unmodeled dynamics and the output constraints. By the coordinate transformation of the state variables, the input unmodeled dynamics subsystem is transformed into a suitable form for applying the small-gain theorem. By a logarithmic one to one mapping, the time-varying output constraints are tackled. With these methods, the stability proof based on the small-gain theorem is completed. It is shown that all the signals are bounded, and the output signal is constrained within the preset range.

Adaptive Backstepping Nonsingular Fast Terminal Sliding Mode Control for Hydro-Turbine Governor Design

To investigate a typical large-scale nonlinear hydropower system (HS) with a stochastic water flow, a novel nonlinear adaptive control scheme, which is created by the combination of a backstepping strategy, nonsingular fast terminal sliding mode surface and command filter, is proposed for the hydro-turbine governor design of a HS to not only improve the transient stability of the HS but also increase the energy conversion efficiency and improve the reliability and availability of the electricity supply. In contrast to previous research based on ideal hydro-turbine models with accurate parameters, an adaptive backstepping nonsingular fast terminal sliding mode control (ABNFTSMC) with command filtered (CF) is proposed in which virtual control inputs and error compensations are applied to overcome distribution characteristics resulting from energy losses, while guaranteeing finite-time convergence. In addition, to avoid the requirement of analytic differentiation in Lyapunov stability, a command filter method is used to generate certain compensating signals and their derivatives. In this paper, the Nazi Gorge hydropower station in China is used as our verification model of a hydropower plant with monitored data, where energy losses and random water flow disturbances are considered. Simulation results illustrate that the proposed control strategy for a hydro-turbine governor can significantly increase the stability, reliability, and system performance of a HS even in the presence of uncertainties.

Back-stepping sliding mode control Design for glucose regulation in type 1 diabetic patients

This article presents a robust scheme for regulating blood glucose in the patients suffering from type I diabetes based on BMM. A pump is used to inject glucose/insulin under the patient’s skin to control its concentration. Previous studies have presented a variety of such controllers. But, they mainly suffered from long settling time. This study employs back-stepping sliding control to reduce the settling time. Since the controller presented in this study employs sliding mode control, it is robust against external disturbances. Since the back-stepping scheme is used in this design, it guarantees that the state variables of the system converge to the desired value. The results obtained from simulation verify performance of the presented scheme.

Sensorless Control Technique of Open-End Winding Five Phase Induction Motor under Partial Stator Winding Short-Circuit

Open-end winding induction machines are gaining more attention in the last years due to their attractive advantages in the industrial applications, where high reliability is required. However, despite their inherit robustness, they are subjected to various electrical or mechanical faults that can ultimately reduce the motor efficiency and later leads to full failure. This paper proposes a method of modeling the five phase induction machine with open end stator winding taking into consideration the short-circuit fault between turns. The fault modeling is based on the theory of electromagnetic coupling of electrical circuits. In addition, a sliding mode observer is used to estimate the speed rotor. The idea of proposed backstepping strategy is used in this paper to allow to the studied machine to continue its operating state under short circuit fault between turns. The proposed sensorless control strategy is evaluated in terms of the healthy and faulty performances through the simulation results presented in this paper. The obtained results prove that the proposed sensorless control technique allows to the open-end winding five phase induction machine to continue its operation mode under the specified fault of partial short-circuit of the stator winding. This can be a very practical situation in the industrial applications, especially in the case where the maintenance is not easy and the operation of the industrial process should not be interrupted suddenly.

A novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure-feedback form

In this paper, a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure-feedback systems. Different from the existing results that are based on traditional back-stepping schemes as well as approximation technique of fuzzy logic systems (FLSs) for stochastic nonlinear systems, this new approach assumes that the norm of optimal approximation parameter vector of FLSs is bounded by unknown parameter. At each design step of this new approach, fewer bounded adaptive parameters need to be adjusted. Thus, this new approach can alleviate the online computation burden and improve the robust control performance. Meanwhile, combining Lyapunov theorem analysis, it is proven that all the signals in the closed-loop system are uniformly ultimately bounded (UUB) and the tracking error can converge to a small neighborhood of zero. The good performance of this approach is well demonstrated in a simulation example.

Adaptive Backstepping Fractional Fuzzy Sliding Mode Control of Active Power Filter

An adaptive fractional-order fuzzy control method for a three-phase active power filter (APF) using a backstepping and sliding mode controller is developed for the purpose of compensating harmonic current and stabilizing the DC voltage quickly. The dynamic model of APF is changed to an analogical cascade system for the convenience of the backstepping strategy. Then a fractional-order sliding mode surface is designed and a fuzzy controller is proposed to approximate the unknown term in the controller, where parameters can be adjusted online. The simulation experiments are conducted and investigated using MATLAB/SIMULINK software package to verify the advantage of the proposed controller. Furthermore, the comparison study between the fractional-order controller and integer-order one is also conducted in order to demonstrate the better performance of the proposed controller in total harmonic distortion (THD), a significant index to evaluate the current quality in the smart grid.

Barrier Lyapunov function based adaptive finite-time control for hypersonic flight vehicles with state constraints

This paper investigates the finite-time tracking control problem of the hypersonic flight vehicle (HFV) with state constraints. Firstly, a control-oriented model is introduced to enable the application of adaptive backstepping scheme. To meet strict requirements in terms of working conditions of HFV, barrier Lyapunov function is adopted to constrain the tracking errors, while piecewise saturation function is constructed to restrict the virtual signals. To guarantee the finite-time convergent property of HFV dynamics, an adaptive scheme in accordance with finite-time stability theory is designed. Meanwhile, a sliding mode differentiator is employed to estimate the derivatives of the virtual control laws. Novel auxiliary systems are then designed to consider the side effects of the possible saturation and to maintain the finite-time convergent property. In the final stage, the effectiveness and performance of the proposed method is demonstrated by numerical simulations.

Adaptive Backstepping Sliding Mode Control for Equilibrium Position Tracking of an Electrohydraulic Elastic Manipulator

The electrohydraulic elastic manipulator (EEM) includes an electrohydraulic servo system and a variable stiffness mechanism. It is a complex system with nonlinear elements, such as friction, parametric uncertainties, and modeling error as well as coupling torques in the elastic joint. This paper focuses on developing an equilibrium position controller for the EEM with the presence of the matched and unmatched uncertainties. The proposed controller is based on a backstepping scheme optimized using an adaptive sliding mode technique and an adaptive nonlinear PI structure. To estimate parameters of known functions in the system dynamics, the parametric learning laws are employed, while adaptive switching gain laws are used to adjust robust gains of discontinuous control terms. The robust switching gains increase or decrease as state control variables move away or close to the surfaces, respectively. Working together, these kinds of adaptation laws can effectively deal with the problem of matched and unmatched uncertainties. Next, the Lyapunov approach is used to prove the robustness and stability of the whole system. The proposed method is practically implemented and compared with other controllers to demonstrate the effectiveness of the proposed method with the variant stiffness and the uncertainties.