Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control

The output feedback control of the popular magnetic ball levitation system is addressed from a suitable combination of several complementary viewpoints. We use: first, recent developments on exact feedforward linearisation controllers for nonlinear flat systems to substantially reduce the linear feedback controller efforts through pre-compensation. Second, an on-line ball velocity estimation strategy is proposed by using a model-based integral reconstructor, which is a linear combination of iterated integrals of the input and the output of the system, thus avoiding the use of traditional observers or noisy derivative estimations. Finally, we use a generalised proportional integral (GPI) controller which compensates the errors in the integral reconstructor and further bestows the enhanced robustness on the closed-loop system via output tracking error iterated integration feedback. This methodology only requires the measurements of the position of the levitated ball and of the control input voltage. The proposed feedback regulation scheme is shown to locally guarantee an asymptotically exponentially stable behaviour of the controlled ball position and, definitely, allows for the possibilities of safely carrying out the rest-to-rest trajectory tracking tasks on the ball position. The proposed output feedback controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilisation and trajectory tracking tasks.     

A global robust iterative learning position control for current-fed permanent magnet step motors

The tracking control problem via state feedback for uncertain current-fed permanent magnet step motors with non-sinusoidal flux distribution and uncertain position-dependent load torque is addressed: a periodic reference signal (of known period) for the rotor position is required to be tracked. A robust iterative learning control algorithm is designed which, for any motor initial condition and without requiring any resetting procedure, guarantees, despite system uncertainties: exponential convergence of the rotor position tracking error to a residual ball (centered at the origin) whose radius can be made arbitrarily small by properly setting the learning gain; asymptotic convergence of the rotor position tracking error to zero. A sufficient condition for the asymptotic estimation of the uncertain reference input achieving, for compatible initial conditions, perfect tracking is derived. Robustness with respect to a finite memory implementation of the control algorithm based on the piecewise linear approximation theory is shown to be guaranteed; satisfactory performances of a discrete-time implementation of the control algorithm are obtained in realistic simulations for the full-order voltage-fed motor.     

An Active Disturbance Rejection Approach to Leader‐Follower Controlled Formation

This article describes the design of a linearizing, observer‐based, robust dynamic feedback control scheme for output reference trajectory tracking tasks in a leader‐follower non‐holonomic car formation problem. The approach is based on the cars' kinematic models. A radical simplification in the form of a global ultra‐model is proposed on the follower's exact open loop position tracking error dynamics obtained via flatness considerations. This results in a system described by an additively disturbed set of two, second order integrators with non‐linear velocity dependent control input gain matrix. The unknown additive disturbances are modeled as absolutely uniformly bounded time signals which may be locally approximated by arbitrary elements of a sufficiently high degree family of Taylor polynomials. Linear high‐gain Luenberger observers of the generalized proportional integral (GPI) type may be readily designed. These observers include the self updating internal model of the unknown disturbance input vector components in the form of generic, instantaneous, time‐polynomial models. The proposed (GPI) observers, which are the dual counterpart of GPI controllers [17], achieve a simultaneous disturbance estimation and tracking error phase variables estimation. This on‐line gathered information is used to advantage on the follower's feedback controller thus allowing for a simple, yet efficient, disturbance and control input gain cancelation effort. The results are applied to have the follower track a time‐delayed version of the actual leader's trajectory. Experimental results are presented which illustrate the robustness and viability of the proposed approach.     

作业型遥控水下运载器的多变量backstepping鲁棒控制

针对作业型遥控水下运载器（ROV）存在复杂外干扰、参数不确定性以及强非线性耦合的特性,提出了作业型ROV的多变量backstepping控制方法．使用Lyapunov稳定性分析方法,证明了当存在系统参数不确定性和未知常值外干扰的情况时,系统的局部渐近稳定性．以及跟踪误差的局部渐近收敛性．针对作业型ROV在动力定位时的特点,得到了系统动力定位时的四自由度简化模型．仿真结果表明,所提出的多变量backstepping鲁棒控制器具有比常规PID控制器更好的控制品质和鲁棒性能．     

Composite adaptive dynamic surface control using online recorded data

This paper presents an online recorded data‐based design of composite adaptive dynamic surface control for a class of uncertain parameter strict‐feedback nonlinear systems, where both tracking errors and prediction errors are applied to update parametric estimates. Differing from the traditional composite adaptation that utilizes identification models and linear filters to generate filtered modeling errors as prediction errors, the proposed composite adaptation integrates closed‐loop tracking error equations in a moving time window to generate modified modeling errors as prediction errors. The time‐interval integral operation takes full advantage of online recorded data to improve parameter convergence such that the application of both identification models and linear filters is not necessary. Semiglobal practical asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The major contribution of this study is that composite adaptation based on online recorded data is achieved at the presence of mismatched uncertainties. Simulation results have been provided to verify the effectiveness and superiority of this approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive sensorless robust control of AC drives based on sliding mode control theory

This paper focuses in the design of a new adaptive sensorless robust control to improve the trajectory tracking performance of induction motors. The proposed design employs the so‐called vector (or field oriented) control theory for the induction motor drives, being the designed control law based on an integral sliding‐mode algorithm that overcomes the system uncertainties. This sliding‐mode control law incorporates an adaptive switching gain in order to avoid the need of calculating an upper limit for the system uncertainties. The proposed design also includes a new method in order to estimate the rotor speed. In this method, the rotor speed estimation error is presented as a first‐order simple function based on the difference between the real stator currents and the estimated stator currents. The stability analysis of the proposed controller under parameter uncertainties and load disturbances is provided using the Lyapunov stability theory. The simulated results show, on the one hand that the proposed controller with the proposed rotor speed estimator provides high‐performance dynamic characteristics, and on the other hand that this scheme is robust with respect to plant parameter variations and external load disturbances. Finally, experimental results show the performance of the proposed control scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

Improving transient performance of adaptive control via a modified reference model and novel adaptation

This paper presents a new model reference adaptive control (MRAC) framework for a class of nonlinear systems to address the improvement of transient performance. The main idea is to introduce a nonlinear compensator to reshape the closed‐loop system transient, and to suggest a new adaptive law with guaranteed convergence. The compensator captures the unknown system dynamics and modifies the given nominal reference model and the control action. This modified controlled system can approach the response of the ideal reference model. The transient is easily tuned by a new design parameter of this compensator. The nominal adaptive law is augmented by new leakage terms containing the parameter estimation errors. This allows for fast, smooth and exponential convergence of both the tracking error and parameter estimation, which again improves overall reference model following. We also show that the required excitation condition for the estimation convergence is equivalent to the classical persistent excitation (PE) condition. In this respect, this paper provides an intuitive and numerically feasible approach to online validate the PE condition. The salient feature of the suggested methodology is that the rapid suppression of uncertainties in the controlled system can be achieved without using a large, high‐gain induced, learning rate in the adaptive laws. Extensive simulations are given to show the effectiveness and the improved response of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

Frequency‐shifting‐based algebraic approach to stable on‐line parameter identification and state estimation of multirotor UAV

In this paper, a frequency‐shifting‐based (FSB) algebraic approach to stable on‐line parameter identification and state estimation is proposed. The proposed simultaneous parameter identification and state estimation algebraic approach are applied to multirotor adaptive‐like tracking control assuming that only position measurement is available. The proposed algebraic approach provides very fast convergence towards true values of system parameters and states, without transients that depend on initial conditions and without peaking phenomenon which is characteristics of high‐gain observers. The efficiency of the proposed algorithm is illustrated by a simulation example.     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式...     

Adaptive Active Fault Tolerant Control for Discrete‐Time Systems with Uncertainties

An active fault‐tolerant control scheme for discrete‐time systems is proposed to solve a difficult problem of fault‐tolerant controller design in the presence of partial loss of actuator effectiveness faults and structural parameter uncertainties assumed to be matched, using adaptive control techniques to help a faster and more accurate compensation of failure and uncertainty. An automated fault estimation scheme is developed together with an adaptive model parameter identification to obtain system parameter estimates. With these estimates fed back to the system, a model reference adaptive controller is constructed to achieve a desired tracking performance. Since parameters are obtained and updated online, the control system has an automatic failure compensation capability so as to recognize or reconfigure the control law in real time in response to failure indications. The stability and convergence follow from discrete‐time Lyapunov arguments. Simulation results from the linearized lateral dynamics model of the Boeing 747 airplane are presented to show the efficiency of proposed methods.     

串联机器人的双模糊自适应滑模控制

提出了一种串联机器人的改进控制算法。采用一自适应模糊控制器,根据滑模到达条件对滑模切换增益进行估算,消除滑模控制中输出力矩的抖振现象,增强其对不确定性因素的适应能力。采用另一自适应模糊控制器对指数趋近律系数进行修正,改善由于大范围初始位姿产生的偏差而引起的大力矩和速度跳变问题。该方法无需确定被控对象的具体数学模型,具有强鲁棒性和高跟踪精度。基于Lyapunov方法进行了稳定性证明,保证控制系统的稳定性与收敛性。实验结果表明,该方法应用于串联机器人,跟踪效果良好并产生了平滑的力矩输出和速度输出。     

Output feedback second order sliding mode control for spacecraft attitude and translation motion

This paper studies an output feedback control problem for spacecraft position and attitude control when uncertainties related to system parameters and external disturbances are present. Firstly, a new finite-time control law is designed using second order sliding mode concepts. In the presence of external disturbances and inertia uncertainties, the new control law provides finite-time convergence and high tracking precision. Secondly, a new sliding-mode-based filter is developed to estimate the first time derivatives of attitude and position in finite time. Instead of the translational and angular velocity variables, the estimated derivative values are used for the controller design. The proposed controller with this filter is an output feedback controller since translational and angular velocity measurements are not required. The closed-loop system under this controller is non-homogeneous and the stability is proven by using concepts of a strong Lyapunov function and Lyapunov stability theory. The trajectories of the closed-loop system can be controlled to converge to a ball centered at the origin that can be made as small as desired. Numerical simulations of position and attitude control of spacecraft are given to demonstrate the performance of the proposed controller and filter.     

Robust adaptive fault-tolerant control for a class of uncertain nonlinear systems with multiple time delays

This study is concerned with the problem of robust adaptive fuzzy fault-tolerant control for a class of uncertain nonlinear systems with mismatching parameter uncertainties, external disturbances, multiple state time delays perturbations and actuator failures, which include loss of effectiveness, outage and stuck modes. A novel direct adaptive fuzzy tracking control scheme is developed to achieve the fault-tolerant control objective. First, by introducing a positive nonlinear control gain function, the effects of state time delays and actuator failures are effectively compensated. Then, a suitable fuzzy logic system (FLS), which is used to approximate the corresponding nonlinear function, is constructed to eliminate the influences on mismatched parameter uncertainty and external disturbance. Moreover, it is shown that all the closed-loop system signals are uniformly bounded and that the tracking error converges to a small neighborhood of the origin via Lyapunov–Krasovskii stability analysis. Finally, the proposed adaptive fuzzy fault-tolerant tracking design approach is illustrated on a two stage chemical reactor system with delayed recycle streams.     

控制增益未知的多变量极值搜索系统神经网络自适应协同控制

针对一类控制增益未知的多变量极值搜索系统,提出了一种神经网络自适应协同控制方法.该方法利用协同控制实现状态变量之间的协同收敛,并确保对系统内部参数扰动和外界干扰具有不变性;以极值搜索控制方法得到的搜寻变量作为输入量,设计多层神经网络逼近状态变量的极值变化率和未知的变量与函数;采用Nussbaum函数解决系统控制增益未知的问题;同时运用自适应参数抵消神经网络逼近误差的影响.稳定性分析证明了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指数收敛至原点的一个有界邻域.理论分析与仿真结果验证了该方法的有效性.     

A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments

The recently proposed saturated adaptive robust controller is integrated with desired trajectory compensation to achieve global stability with much improved tracking performance. The algorithm is tested on a linear motor drive system which has limited control effort and is subject to parametric uncertainties, unmodeled nonlinearities, and external disturbances. Global stability is achieved by employing back-stepping design with bounded (virtual) control input in each step. A guaranteed transient performance and final tracking accuracy is achieved by incorporating the well-developed adaptive robust controller with effective parameter identifier. Signal noise that affects the adaptation function is alleviated by replacing the noisy velocity signal with the cleaner position feedback. Furthermore, asymptotic output tracking can be achieved when only parametric uncertainties are present.     

A fast non-singular terminal sliding mode control based on perturbation estimation for piezoelectric actuators systems

Piezoelectric actuators (PEAs) are the key devices in micro/nano positioning system. However, the PEA performance is significantly degraded by the inherent non-linear behaviour. This behaviour is a consequence of the hysteresis properties contained within PEAs. Therefore, in micro/nano positioning applications, a robust control system has to be adopted for such actuators. This paper proposes a systematic control method that utilises a fast non-singular terminal sliding mode (FNTSM) based on online perturbation estimation technique for PEAs. Unlike other sliding mode methods, the FNTSM control method is characterised by chatter free. Besides, a zero error convergence can be guaranteed in finite time in the presence of disturbance and system uncertainties (i.e., hysteresis and gain changes). The design of the FNTSM control based on perturbation estimation (FNTSMPE) is presented. A model-free robust exact differentiator is used to estimate the states of the feedback system from merely measurable position signal. Theoretical analysis and the experimental results of FNTSMPE control reveal that high-precision and robust performance is achieved in comparison with ordinary FNTSM control.     

Adaptive Backstepping Tracking Control of a 6-DOF Unmanned Helicopter

This paper presents an adaptive backstepping control design for a class of unmanned helicopters with parametric uncertainties. The control objective is to let the helicopter track some pre-defined position and yaw trajectories. In order to facilitate the control design, we divide the helicopter's dynamic model into three subsystems. The proposed controller combines the backstepping method with online parameter update laws to achieve the control objective. The global asymptotical stability (GAS) of the closed-loop system is proved by a Lyapunov based stability analysis. Numerical simulations demonstrate that the controller can achieve good tracking performance in the presence of parametric uncertainties.      

基于复合自适应律的直线电机自适应鲁棒控制

自适应鲁棒控制(ARC)能克服参数不确定性与扰动对系统的影响, 具有良好的输出跟踪性能. 然而常规ARC的参数估计值难以逼近真值. 为实现高性能的控制与准确的参数估计, 本文提出了基于复合自适应律的自适应鲁棒控制(CAARC). 该方法同时采用了输出误差与参数估计误差的相关信息构造自适应律, 具有比常规ARC更好的参数估计效果. 本文在理论上证明了CAARC的闭环稳定性与参数估计误差的收敛性, 并通过分析表明CAARC具有比常规ARC更好的输出跟踪性能, 最后通过仿真验证了该方法的有效性.     

Intelligent mixed H2/H∞ adaptive tracking control system design using self-organizing recurrent fuzzy-wavelet-neural-network for uncertain two-axis motion control system

In this paper, an intelligent adaptive tracking control system (IATCS) based on the mixed H₂/H_∞ approach under uncertain plant parameters and external disturbances for achieving high precision performance of a two-axis motion control system is proposed. The two-axis motion control system is an X–Y table driven by two permanent-magnet linear synchronous motors (PMLSMs) servo drives. The proposed control scheme incorporates a mixed H₂/H_∞ controller, a self-organizing recurrent fuzzy-wavelet-neural-network controller (SORFWNNC) and a robust controller. The combinations of these control methods would insure the stability, robustness, optimality, overcome the uncertainties, and performance properties of the two-axis motion control system. The SORFWNNC is used as the main tracking controller to adaptively estimate an unknown nonlinear dynamic function that includes the lumped parameter uncertainties, external disturbances, cross-coupled interference and frictional force. Moreover, the structure and the parameter learning phases of the SORFWNNC are performed concurrently and online. Furthermore, a robust controller is designed to deal with the uncertainties, including the approximation error, optimal parameter vectors and higher order terms in Taylor series. Besides, the mixed H₂/H_∞ controller is designed such that the quadratic cost function is minimized and the worst case effect of the unknown nonlinear dynamic function on the tracking error must be attenuated below a desired attenuation level. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance. The sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking problem in terms of a pair of coupled algebraic equations instead of coupled nonlinear differential equations. The coupled algebraic equations can be solved analytically. The online adaptive control laws are derived based on Lyapunov theorem and the mixed H₂/H_∞ tracking performance so that the stability of the proposed IATCS can be guaranteed. Furthermore, the control algorithms are implemented in a DSP-based control computer. From the experimental results, the motions at X-axis and Y-axis are controlled separately, and the dynamic behaviors of the proposed IATCS can achieve favorable tracking performance and are robust to parameter uncertainties.     

Nonlinear tracking control for sensorless permanent magnet synchronous motors with uncertainties

The recent advanced solution in Marino, Tomei, and Verrelli (2013) to the tracking control problem for sensorless IMs with parameter uncertainties is translated on the basis of letter swap connections between the models of (nonsalient-pole surface) permanent magnet synchronous motors (PMSMs) and induction ones (IMs). The (stability proof-based) nonlinear adaptive position/speed tracking control for sensorless PMSMs (with simultaneous estimation of uncertain constant load torque and stator resistance), which is accordingly obtained by exploring and decoding the design paths in Marino et al. (2013) and which surprisingly represents a simple generalization of the controller in Tomei and Verrelli (2011), constitutes an innovative solution to the related open problem. Illustrative experimental results are included.