Adaptive Backstepping Control of Six‐Phase PMSM Using Functional Link Radial Basis Function Network Uncertainty Observer

An adaptive backstepping control (ABSC) using a functional link radial basis function network (FLRBFN) uncertainty observer is proposed in this study to construct a high‐performance six‐phase permanent magnet synchronous motor (PMSM) position servo drive system. The dynamic model of a field‐oriented six‐phase PMSM position servo drive is described first. Then, a backstepping control (BSC) system is designed for the tracking of the position reference. Since the lumped uncertainty of the six‐phase PMSM position servo drive system is difficult to obtain in advance, it is very difficult to design an effective BSC for practical applications. Therefore, an ABSC system is designed using an adaptive law to estimate the required lumped uncertainty in the BSC system. To further increase the robustness of the six‐phase PMSM position servo drive, an FLRBFN uncertainty observer is proposed to estimate the lumped uncertainty of the position servo drive. In addition, an online learning algorithm is derived using Lyapunov stability theorem to learn the parameters of the FLRBFN online. Finally, the proposed position control system is implemented in a 32‐bit floating‐point DSP, TMS320F28335. The effectiveness and robustness of the proposed intelligent ABSC system are verified by some experimental results.     

Three‐dimensional impact angle‐constrained adaptive guidance law considering autopilot lag and input saturation

This work investigates three‐dimensional accurate guidance problem in the presence of impact angle constraint, input saturation, autopilot lag, and external disturbance, and presents a robust adaptive guidance method for maneuvering targets. More specifically, based on integral Lyapunov control algorithm, a robust guidance law, which can drive both terminal line‐of‐sight angle error and its rate to a small region around zero, while resisting the terrible influence caused by external disturbance, is proposed in this work. To deal with input saturation, guidance command is separated into two parts: real input and saturation error, and an adaptive control technique is employed to compensate the influence resulting from external disturbance and saturation error. Moreover, regarding autopilot lag as a first‐order dynamics, a backstepping designed controller with an adaptive term is proposed. Numerical simulations are carried out and their results demonstrate the proposed properties.     

Real‐Time Results for High Order Neural Identification and Block Control Transformation Form Using High Order Sliding Modes

In this paper, real‐time results for a novel continuous‐time adaptive tracking controller algorithm for nonlinear multiple input multiple output systems are presented. The control algorithm includes the combination of a recurrent high order neural network with block control transformation using a high order sliding modes technique as control law. A neural network is used to identify the dynamic plant behavior where a filtered error algorithm is used to train the neural identifier. A decentralized high order sliding mode, named the twisting algorithm, is used to design chattering‐reduced independent controllers to solve the trajectory tracking problem for a robot arm with three degrees of freedom. Stability analyses are given via a Lyapunov approach.     

A time differences of arrival‐based homing strategy for autonomous underwater vehicles

A new sensor‐based homing integrated guidance and control law is presented to drive an underactuated autonomous underwater vehicle (AUV) toward a fixed target, in 3‐D, using the information provided by an ultra‐short baseline (USBL) positioning system. The guidance and control law is first derived at a kinematic level, expressed on the space of the time differences of arrival (TDOAs), as directly measured by the USBL sensor, and assuming the plane wave approximation. Afterwards, the control law is extended for the dynamics of an underactuated AUV resorting to backstepping techniques. The proposed Lyapunov‐based control law yields almost global asymptotic stability (AGAS) in the absence of external disturbances and is further extended, keeping the same properties, to the case where known ocean currents affect the motion of the vehicle. Simulations are presented and discussed that illustrate the performance and behavior of the overall closed‐loop system in the presence of realistic sensor measurements and actuator saturation. Copyright © 2009 John Wiley & Sons, Ltd.     

Design of Adaptive Block Backstepping Controllers with Perturbations Estimation for Nonlinear State‐Delayed Systems in Semi‐Strict Feedback Form

This paper is an extended study of an existing block backstepping control scheme designed for a class of perturbed multi‐input systems with multiple time‐varying delays to solve regulation problems, where the time‐varying delays must be linear with state variables. A new control scheme is proposed in this research where all the unknown multiple time‐varying delay terms in the dynamic equations can be nonlinear state functions in non‐strict feedback form, and the upper bounds of the time‐delays as well as their derivatives need not to be known in advance. Another improvement is to further alleviate the problem of “explosion of complexity,” i.e., to reduce the number of time derivatives of virtual inputs that the designers have to compute in the design of controllers. This is done by utilizing an existent derivative estimation algorithm to estimate the perturbations in the designing of proposed controllers. Adaptive mechanisms are also embedded in the controllers so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are demonstrated to verify the merits and feasibility of the proposed control scheme.     

基于反演设计的块控型极值搜索系统一体化控制方法研究

针对极值搜索控制系统 (Extremum seeking control systems, ESCSs)设计中, 极值搜索算法与控制器采取单独设计时易导致系统难以发挥其最佳性能, 而现有的一体化设计方法却存在需要根据被控对象和具体的极值搜索算法进行不同形式的一体化建模的问题, 以块控型的极值搜索控制系统为研究对象, 提出了一套通用的极值搜索控制系统的一体化控制方法. 首先针对块控型极值搜索控制系统, 采用反馈线性化设计思想, 构建出系统的伪虚拟控制量; 然后以极值搜索算法得到的搜索变量作为其输入量, 设计多层神经网络 (Multilayer neural networks, MNNs)逼近由近似模型与实际模型之间的差异而导致的误差项、状态变量的极值和极值的变化率, 同时运用自适应参数和鲁棒项函数抵消神经网络逼近误差的影响; 最后利用反演控制方法求取出系统的虚拟控制量和实际控制量. 此一体化控制方法确保系统的状态跟踪误差、输出量与其极值之间的误差、 极值搜索变量的跟踪误差以及神经网络各参数的估计误差均有界且指数收敛至系统原点的一个有限邻域内, 且理论分析和仿真结果都验证了此方法的有效性.     

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.     

Flight control of a rotary wing UAV using backstepping

This paper presents a novel application of backstepping controller for autonomous landing of a rotary wing UAV (RUAV). This application, which holds good for the full flight envelope control, is an extension of a backstepping algorithm for general rigid body velocity control. The nonlinear RUAV model used in this paper includes the flapping and servo dynamics. The backstepping‐based controller takes advantage of the ‘decoupling’ of the translation and rotation dynamics of the rigid body, resulting in a two‐step procedure to obtain the RUAV control inputs. The first step is to compute desired thrusts and flapping angles to achieve the commanded position and the second step is to compute control inputs, which achieve the desired thrusts and flapping angles. This paper presents a detailed analysis of the inclusion of a flapping angle correction term in control. The performance of the proposed algorithm is tested using a high‐fidelity RUAV simulation model. The RUAV simulation model is based on miniature rotorcraft parameters. The closed‐loop response of the rotorcraft indicates that the desired position is achieved after a short transient. The Eagle RUAV control inputs, obtained using high‐fidelity simulation results, clearly demonstrate that this algorithm can be implemented on practical RUAVs. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust partial integrated guidance and control approaches for maneuvering targets

A novel observer‐controller framework algorithm based on barrier Lyapunov function and second‐order sliding mode control is presented, which can drive the first‐ and second‐order states of the typical second‐order dynamics subject to unknowns and uncertainties simultaneously converge to zero in finite time. The obtained results are applied in the designs of two partial integrated guidance and control laws for an aerodynamic control interceptor against maneuvering targets: one is for zeroing line‐of‐sight angular rate and the other is for hit‐to‐kill. Owing to the inherent properties of different bandwidth and time delay between control commands and missile dynamics, partial guidance and control is separated with two loops. The outer loop achieves the target maneuvers and generates the control command, and the inner loop is used to track it. Moreover, to overcome the excessive differentiation problem of conventional backstepping design, two integral Lyapunov functions are introduced, which avoid the differentiation of the virtual control laws. Finally, detailed stability discussion and simulation results of the proposed partial guidance and control approaches demonstrate these properties.     

Output‐based disturbance rejection control for 1‐D anti‐stable Schrödinger equation with boundary input matched unknown disturbance

In this paper, we are concerned with the output feedback control design for a system (plant) described by a boundary controlled anti‐stable one‐dimensional Schrödinger equation. Our output measure signals are the displacements at both side. An untraditional infinite‐dimensional disturbance estimator is developed to estimate the disturbance. Based on the estimator, we propose a state observer that is exponentially convergent to the original system and then design a stabilizing control law consisting of two parts: The first part is to compensate the disturbance by using its approximated value and the second part is to stabilize the observer system by applying the classical backstepping approach. The resulting closed‐loop system is shown to be exponentially stable with guaranteeing that all internal systems are uniformly bounded. An effective output‐based disturbance rejection control algorithm is concluded. An application, namely, a cascade of ODE–wave systems, is investigated by the developed control algorithm. Numerical experiments are carried out to illustrate the effectiveness of the proposed control law. Copyright © 2017 John Wiley & Sons, Ltd.     

Formation control for multiquadrotor aircraft: Connectivity preserving and collision avoidance

In this article, we investigate the formation control problem of multiquadrotor aircraft system subject to connectivity preservation and collision avoidance. First, based on the backstepping design method, a novel formation control algorithm is developed to enable multiquadrotor aircraft to move along the desired trajectory while becoming the predefined formation pattern. Meanwhile, the connectivity of the communication network is maintained and the collision among multiquadrotor is avoided. Second, for each quadrotor's desired attitude obtained by the formation controller, an improved finite‐time attitude tracking law is designed to guarantee that the desired attitude can be tracked by the real attitude in a fast finite time. Finally, a numerical example is given to demonstrate the effectiveness of the proposed algorithms.     

Finite‐time stabilization of stochastic nonlinear systems with SiISS inverse dynamics

This paper investigates the finite‐time control problem for a class of stochastic nonlinear systems with stochastic integral input‐to‐state stablility (SiISS) inverse dynamics. Motivated by finite‐time stochastic input‐to‐state stability and the concept of SiISS using Lyapunov functions, a novel finite‐time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite‐time SiISS small‐gain arguments, using the backstepping technique and stochastic finite‐time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state‐feedback controller that can ensure the solution of the closed‐loop system to be finite‐time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive sliding mode dynamic controller with integrator in the loop for nonholonomic wheeled mobile robot trajectory tracking

In this paper, novel adaptive sliding mode dynamic controller with integrator in the loop is proposed for nonholonomic wheeled mobile robot (WMR). The modified kinematics controller is used to generate kinematics velocities of WMR which are subsequently used as the input to adaptive dynamic controller. Actuator dynamics are also derived to generate actuator voltage of WMR through torque and velocity vectors. Stability of both kinematics and dynamic controller is presented using Lyapunov stability analysis. The proposed scheme is verified and validated using computer simulations for tracking the desired trajectory of WMR. The performance of proposed scheme is compared with standard backstepping kinematics controller and classical sliding mode control. In addition, the performance is further compared with standard backstepping kinematics controller with adaptive sliding mode controller without integrator. It is shown that the proposed scheme exhibits zero steady state error, fast error convergence and robustness in the presence of continuous disturbances and uncertainties.     

Backstepping wavelet neural network control for indirect field-oriented induction motor drive

This study address a newly designed decoupling system and a backstepping wavelet neural network (WNN) control system for achieving high-precision position-tracking performance of an indirect field-oriented induction motor (IM) drive. First, a decoupling mechanism with an online inverse time-constant estimation algorithm is derived on the basis of model reference adaptive system theory to preserve the decoupling control characteristic of an indirect field-oriented IM drive. Moreover, based on the backstepping design methodology, a desired feedback control law is developed for ensuring the favorable control performance. However, the uncertainties, such as mechanical parameter uncertainty, external load disturbance, unstructured uncertainty due to nonideal field orientation in transient state, and unmodeled dynamics in practical applications, are difficult to know in advance. Thus, the stability of the desired feedback control may be destroyed. Due to the powerful approximation ability of WNN, a backstepping WNN control scheme is designed in this study to control the rotor position of an indirect field-oriented IM drive for periodic motion. This control scheme contains two parts: one is a WNN control that is utilized to mimic the desired feedback control law, and the other is a robust control that is designed to recover the residual part of approximation for ensuring the stable control characteristic. In addition, numerical simulation and experimental results due to periodic commands are provided to verify the effectiveness of the proposed control strategy.     

轮式移动机器人的数据驱动轨迹跟踪滑模约束控制

针对有输入饱和约束的轮式移动机器人(WMR)的轨迹跟踪问题,提出一种抗饱和无模型自适应积分终端滑模控制方案.该方案基于紧格式动态线性化技术,构建WMR系统的在线数据驱动模型.在积分终端滑模控制器设计过程中,引入动态抗饱和补偿器,以解决WMR系统轨迹跟踪过程中执行器饱和问题.控制器设计仅利用控制系统的输入输出数据,与WMR系统模型信息无关.因此,针对不同类型的WMR系统,该方案均可实现.最后,通过仿真实验将所提出的方法与PID方法的控制效果进行对比,仿真结果表明,所提出的控制算法的跟踪误差更小且响应速度更快.     

Real‐time model predictive control based on dual gradient projection: Theory and fixed‐point FPGA implementation

This paper proposes a method to design robust model predictive control (MPC) laws for discrete‐time linear systems with hard mixed constraints on states and inputs, in case of only an inexact solution of the associated quadratic program is available, because of real‐time requirements. By using a recently proposed dual gradient‐projection algorithm, it is proved that the discrepancy of the optimal control law as compared with the obtained one is bounded even if the solver is implemented in fixed‐point arithmetic. By defining an alternative MPC problem with tightened constraints, a feasible solution is obtained for the original MPC problem, which guarantees recursive feasibility and asymptotic stability of the closed‐loop system with respect to a set including the origin, also considering the presence of external disturbances. The proposed MPC law is implemented on a field‐programmable gate array in order to show the practical applicability of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Reconstruction of 3D contour with an active laser‐vision robotic system

This paper presents a 3D contour reconstruction approach employing a wheeled mobile robot equipped with an active laser‐vision system. With observation from an onboard CCD camera, a laser line projector fixed‐mounted below the camera is used for detecting the bottom shape of an object while an actively‐controlled upper laser line projector is utilized for 3D contour reconstruction. The mobile robot is driven to move around the object by a visual servoing and localization technique while the 3D contour of the object is being reconstructed based on the 2D image of the projected laser line. Asymptotical convergence of the closed‐loop system has been established. The proposed algorithm also has been used experimentally with a Dr Robot X80sv mobile robot upgraded with the low‐cost active laser‐vision system, thereby demonstrating effective real‐time performance. This seemingly novel laser‐vision robotic system can be applied further in unknown environments for obstacle avoidance and guidance control tasks. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Robust Backstepping Sensorless Control for Interior Permanent Magnet Synchronous Motor Using a Super‐Twisting Based Torque Observer

In order to achieve high‐performance speed regulation for sensorless interior permanent magnet synchronous motors (IPMSMS), a robust backstepping sensorless control is presented in this paper. Firstly, instead of a real mechanical sensor, a robust terminal sliding mode observer is used to provide the rotor position. Then, a new super‐twisting algorithm (STA) based observer is designed to obtain estimates of load torque and speed. The proposed observer ensures finite‐time convergence, maintains robust to uncertainties, and eliminates the common assumption of constant or piece‐wise constant load torque. Finally, a sensorless scheme is designed to realize speed control despite parameter uncertainties, by combining the robust backstepping control with sliding mode actions and the presented sliding mode observers. The stability of the observer and controller are verified by using Lyapunov's second method to determine the design gains. Simulation results show the effectiveness of the proposed approach.