Robust precision attitude tracking of an uncertain rigid spacecraft based on regulation theory

This paper explores regulation theory for the design of robust precision attitude tracking of an uncertain rigid spacecraft with external disturbances. Focusing on the attitude system in terms of unit quaternions with an unknown inertia matrix and unmodeled input disturbances, we first introduce specific nonlinear logic such that the resultant error‐quaternion system has an input‐to‐state stability property. Then, we establish an attitude deviation system with an output feedback normal form that has a strict vector relative degree of unity. This enables us to achieve robust output regulation based on an internal model. In particular, we can construct a high‐gain stabilizer for the relevant augmented system. As a major consequence, our study achieves not only precision attitude tracking with exponential convergence but also the input‐to‐state stability disturbance attenuation for the closed‐loop system. Finally, we show extensive simulation and experimental results to illustrate the approach.     

基于鲁棒自适应反步的可重复使用飞行器再入姿态控制

考虑惯性矩阵不确定和力矩扰动的影响, 设计再入可重复使用飞行器的鲁棒自适应反步姿态控制器. 首先, 设计虚拟控制时, 通过自适应实现对不确定项的未知边界的估计; 其次, 设计实际控制输入时, 为消除反步法的“计算爆炸”问题, 将虚拟控制导数作为不确定项, 引入鲁棒项消除不确定与力矩扰动的影响; 再次, 基于Lyapunov 理论证明了跟踪误差收敛到任意小邻域; 最后, 基于X-33 的六自由度模型仿真验证了所设计的控制策略的有效性.     

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.     

Practical time-varying formation tracking for high-order nonlinear multi-agent systems based on the distributed extended state observer

Practical time-varying formation tracking analysis and design problems for high-order nonlinear multi-agent systems are investigated, where the time-varying formation tracking error is controlled within an arbitrarily small bound. The states of followers form a predefined time-varying formation while tracking the state of the leader with unknown control input. Besides, the dynamics of each agent has heterogeneous nonlinearity and disturbance. First, a distributed extended state observer is constructed to estimate the follower's nonlinearity and disturbance, and the leader's unknown control input simultaneously. A protocol based on the distributed extended state observer is proposed. Second, sufficient conditions for the multi-agent systems to achieve the practical time-varying formation tracking under the protocol are presented by using the Lyapunov stability theory. Third, an approach is derived to design the proposed protocol by solving a linear matrix inequality. Finally, numerical simulation results are given to illustrate the effectiveness of the theoretical results.     

Intelligent Excitation for Adaptive Control With Unknown Parameters in Reference Input

Model reference adaptive control problem is considered for a class of reference inputs dependent upon the unknown parameters of the system. Due to the uncertainty in the reference input, the tracking objective cannot be achieved without parameter convergence. The common approach of injecting persistent excitation (PE) in the reference input leads to tracking of the excited reference input as opposed to the true one. A new technique, named intelligent excitation, is presented for introducing an excitation signal in the reference input and regulating its amplitude, dependent upon the convergence of the output tracking and parameter errors. Intelligent excitation ensures parameter convergence, similar to conventional PE; it vanishes as the errors converge to zero and reinitiates with every change in the unknown parameters. As a result, the regulated output tracks the desired reference input and not the excited one.     

未知时变惯量航天器自适应姿态跟踪容错控制

针对存在未知时变惯量不确定性、执行机构衰退故障和外部干扰力矩的非刚体航天器系统,研究了航天器自适应姿态跟踪容错控制问题,结合非线性鲁棒控制方法、自适应方法、容错控制理论和参数估计方法,提出了一种鲁棒自适应姿态跟踪容错控制器。所设计的控制器克服了执行器故障、惯量不确定性以及外界干扰对系统稳定性的影响,保证了航天器姿态及角速度能够跟踪上时变的期望状态,实现了跟踪误差系统最终一致有界稳定。最后通过数字仿真验证了所提方法的有效性,并且与已有方法进行了对比,说明了所提方法的优越性。     

Adaptive fuzzy fault-tolerant attitude control of spacecraft

This paper investigates the attitude control of spacecraft in the presence of unknown mass moment of inertia matrix, external disturbances, actuator failures, and control input constraints. A robust adaptive controller is proposed with the utilization of fuzzy logic and backstepping techniques. The unit quaternion is employed to describe the attitude of spacecraft for global representation without singularities. The system uncertainty is estimated by introducing a fuzzy logic system. The adaptive mechanism has only two parameters to be adapted on-line because the adaptive law of the proposed controller is derived from the norm of the weight matrix. The stability of the closed-loop system is guaranteed by Lyapunov direct approach. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of parametric uncertainties, external disturbances, actuator failures, and control input constraints.     

Adaptive speed/position control of induction motor based on SPR approach

A sensorless speed/position tracking control scheme for induction motors is proposed subject to unknown load torque via adaptive strictly positive real (SPR) approach design. A special nonlinear coordinate transform is first provided to reform the dynamical model of the induction motor. The information on rotor fluxes can thus be derived from the dynamical model to decide on the proportion of input voltage in the d-q frame under the constraint of the maximum power transfer property of induction motors. Based on the SPR approach, the speed and position control objectives can be achieved. The proposed control scheme is to provide the speed/position control of induction motors while lacking the knowledge of some mechanical system parameters, such as the motor inertia, motor damping coefficient, and the unknown payload. The adaptive control technique is thus involved in the field oriented control scheme to deal with the unknown parameters. The thorough proof is derived to guarantee the stability of the speed and position of control systems of induction motors. Besides, numerical simulation and experimental results are also provided to validate the effectiveness of the proposed control scheme.     

具有输入饱和的不确定非线性系统自适应渐近跟踪控制

将一类具有输入饱和的严格反馈单输入单输出非线性系统作为研究对象,解决其自适应渐近跟踪控制问题.与已有结果不同,所考虑的虚拟控制参数可以是未知且增益函数的上界信息也是未知的,这给控制器的设计带来了挑战.通过结合光滑函数及有界估计方法,设计一种新颖的自适应渐近跟踪控制策略;其次,通过引入Nassbaum函数解决由输入饱和不确定参数以及未知虚拟控制参数带来的影响;此外,通过利用未知增益的下界信息巧妙地构造一个特殊的李雅普诺夫函数并结合不等式技巧,可以消除对控制增益函数上界信息的需要,并保证系统的全局稳定性和跟踪性能;最后,通过实例仿真及对比仿真表明所提出自适应渐近跟踪控制算法的有效性.     

无需角速度的含通信时延卫星编队飞行自适应姿态协同跟踪控制

针对编队卫星姿态协同跟踪控制中存在相异星间通信时变时间延迟的问题,提出了采用一阶滤波器来设计含通信时延的输出反馈控制器, 并通过引入参数在线自适应辨识技术,以实现利用卫星姿态误差信息来实现对卫星的转动惯量进行在线估计.对于系统稳定性的分析, 通过构造一新型Lyapunov函数,证明该控制器不仅能够有效地克服通信时间延迟对编队系统协同性的影响,同时可论证无需角速度信息反馈的闭环系统的有界稳定性.最后,将提出的算法应用于只需要角速度信息反馈的卫星编队飞行的协同控制,仿真结果表明该方法的可行性与有效性,具有实际的应用前景.     

航天器姿态跟踪系统的自适应滑模控制

针对存在不确定惯量矩阵和外干扰的刚体航天器姿态跟踪系统,提出了一种自适应滑模控制方法。首先建立了姿态跟踪误差动力学方程,并对刚体航天器跟踪误差动力学定义了滑模,设计了自适应滑模控制律,该控制律的优点在于可以估计系统不确定块,消除了传统滑模控制中对不确定界的要求。Lyapunov分析表明了提出的自适应滑模控制器确保闭环系统取得渐近稳定性。仿真结果验证了提出的控制策略的有效性。     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

一类约束条件下的跟踪保性能控制

本文研究了一类时变非线性系统在输入有位置约束条件下的跟踪保性能控制问题.首先对非线性对象选择合适的特征运行状况,采用瞬时线性化技术得到多个线性化控制模型,将之看作是一个线性不确定系统,提出应用基于线性矩阵不等式的跟踪保性能控制设计控制器,然后经过推导得到了满足控制约束的充分条件,以定理的形式给出了约束条件下跟踪保性能控制器存在的充分条件.最后给出了仿真算例,仿真结果表明了所提方法的有效性和可行性.     

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

挠性卫星姿态跟踪自适应L2增益控制

针对在轨挠性卫星姿态跟踪时存在参数不确定、外部干扰以及控制输入受限等问题,提出了一种自适应L2增益控制方法.首先利用神经网络来逼近系统中的未知非线性动态特性,设计自适应控制律来处理系统中的不确定参数:其次设计了一鲁棒控制器使得干扰力矩对系统性能输出具有L2增益,从而实现对干扰的抑制控制.最后通过引入附加的输入误差系统,...     

Inertia‐free saturated output feedback attitude stabilization for uncertain spacecraft

In this article, the problem of robust output feedback attitude stabilization control for a class of uncertain spacecraft is investigated, which contains external disturbances, model parameter uncertainty, unknown and uncertain inertia, controller's gain perturbations, measurement errors, and input saturation. The aim of this work is to design a dynamic output feedback controller such that the closed‐loop attitude system is stabilized, while the H_∞ norm of the transfer function from the lumped disturbance and measurement error to output is ensured to be less than a pre‐specified disturbance attenuation level, and the actual control input is confined into a certain range simultaneously. Based on the Lyapunov theory, the existence conditions of such controller are derived in terms of linear matrix inequalities. It is worth mentioning that the controller's additive and multiplicative perturbations are accounted for respectively. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed control design method.     

Nonlinear PI control of uncertain systems: an alternative to parameter adaptation

A novel approach to stabilization and trajectory tracking for nonlinear systems with unknown parameters and uncertain disturbances is developed. We take a drastic departure from the classical adaptive control approach consisting of a parameterized feedback law and an identifier, which tries to minimize a tracking (or prediction) error. Instead, we propose a simple nonlinear PI structure that generates a stable error equation with a perturbation function that exhibits at least one root. Trajectories are forced to converge to this root by suitably adjusting the nonlinear PI gains. We consider the two basic problems of: (i) matched uncertainties, when the uncertain terms are in the image of the input matrix, and (ii) unknown control directions, when the control signal is multiplied by a gain of unknown sign. We show that, without knowing the system parameters, and with only basic information on the uncertainties we can achieve global asymptotic stability and global tracking, without injecting high gains into the loop. Interestingly, we prove that we can take as our nonlinear PI structure an activation function reminiscent of that used in neural networks. Although most of the results are derived assuming full state measurement, we also present an observer-based solution for a chain of integrators with unknown control direction. The procedure is shown to provide simple solutions to the classical problems of neural network function approximation, as well as eccentricity control and friction compensation of mechanical systems.     

Stable Sampled-data Adaptive Control of Robot Arms Using Neural Networks

Stable neural network-based sampled-data indirect and direct adaptivecontrol approaches, which are the integration of a neural network (NN)approach and the adaptive implementation of the discrete variable structurecontrol, are developed in this paper for the trajectory tracking control ofa robot arm with unknown nonlinear dynamics. The robot arm is assumed tohave an upper and lower bound of its inertia matrix norm and its states areavailable for measurement. The discrete variable structure control servestwo purposes, i.e., one is to force the system states to be within the stateregion in which neural networks are used when the system goes out of neuralcontrol; and the other is to improve the tracking performance within the NNapproximation region. Main theory results for designing stable neuralnetwork-based sampled data indirect and direct adaptive controllers aregiven, and the extension of the proposed control approaches to the compositeadaptive control of a flexible-link robot is discussed. Finally, theeffectiveness of the proposed control approaches is illustrated throughsimulation studies.