Robust trajectory tracking control for a laboratory helicopter

This paper presents a robust nonlinear control strategy to deal with the trajectory tracking control problem for a laboratory helicopter. The helicopter model is considered as a nominal one with uncertainties such as unmodeled nonlinear dynamics, parametric uncertainties, and external disturbances. The proposed control approach incorporates the feedback linearization technique (FLT) and the signal compensation technique. The FLT is first applied to achieve the linearization of the nominal nonlinear model for reducing the conservation of the robust compensator design. A nominal controller based on the linear quadratic regulation method is designed for the linearized nominal system, whereas a robust compensator is introduced to restrain the influences of the uncertainties. It is shown that the trajectory tracking errors of the closed-loop system are ultimately bounded, and the boundaries can be specified by choosing the controller parameters. Simulation and experimental results on the lab helicopter verify the effectiveness of the proposed method.     

On the hidden beauty of the proper orthogonal decomposition

The proper orthogonal decomposition theorem (Loève, 1955) of probability theory has been proposed by Lumley (1967, 1972, 1981) for detection of spatial coherent patterns in turbulent flows. More specifically, the decomposition extracts deterministic functions from second-order statistics of a random field and converges optimally fast in quadratic mean (i.e., in energy). The technique can be made completely deterministic in the sense that it can be applied to spatially and temporally evolving flows. The remarkable property of this deterministic decomposition is not only in its optimal convergence (as emphasized before) but also in its space/time symmetry which permits access to the spatiotemporal dynamics. The flow is decomposed into both spatial and temporal orthogonal modes which are coupled: each space component is associated with a time component partner. The latter is the time evolution of the former and the former is the spatial configuration of the latter. This generalizes the notion of spatial and temporal structures which can be followed through the various instabilities that the flow undergoes as Reynolds number increases. It also provides a nonlinear dynamics tool for spatiotemporal dynamical systems and can be used for bifurcation detection and analysis as well as dimension and degree of complexity estimates.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported by an NSF/PYI award MSS89-57462, and partially by a NATO Grant No. 900265 which are gratefully acknowledged.     

Finite-time tracking control for a class of high-order nonlinear systems and its applications

This study investigates the problem of finite-time tracking control for a class of high-order nonlinear systems. Due to the existence of uncertain time-varying control coefficient and unknown nonlinear perturbations in the nonlinear dynamics, the existing finite-time control results cannot solve the finite-time tracking problem for this kind of nonlinear systems. Based on the technique of adding a power integrator a variable structure control method is proposed. Under the proposed control law, it is shown that the reference signal can be tracked in a finite time. As an application of the proposed theoretic results, the problem of finite-time attitude tracking control for the roll channel of bank-to-turn missile is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Low-complexity robust tracking of high-order nonlinear systems with application to underactuated mechanical dynamics

This paper presents a low-complexity design approach with predefined transient and steady-state tracking performance for global practical tracking of uncertain high-order nonlinear systems. It is assumed that all nonlinearities and their bounding functions are unknown and the reference signal is time varying. A simple output tracking scheme consisting of nonlinearly transformed errors and positive design parameters is presented in the presence of virtual and actual control variables with high powers where the error transformation technique using time-varying performance functions is employed. Contrary to the existing results using known nonlinear bounding functions of model nonlinearities, the proposed tracking scheme can be implemented without using nonlinear bounding functions (i.e., the feedback domination design), any adaptive and function approximation techniques for estimating unknown nonlinearities. It is shown that the tracking performance of the proposed control system is ensured within preassigned bounds, regardless of high-power virtual and actual control variables. The motion tracking problem of an underactuated unstable mechanical system with unknown model parameters and nonlinearities is considered as a practical application, and simulation results are provided to show the effectiveness of the proposed theoretical result.     

Backstepping control for the optoelectronic stabilized platform based on adaptive fuzzy logic system and nonlinear disturbance observer

A composite controller based on a backstepping controller with an adaptive fuzzy logic system and a nonlinear disturbance observer is proposed in this paper to address the disturbance and uncertainty issues in the control of the optoelectronic stabilized platform. The matched and unmatched disturbances and system uncertainty are included in the stabilized platform model. The system's uncertainty and disturbance are approximated and estimated using an adaptive fuzzy logic system and a nonlinear disturbance observer. Moreover, the backstepping control algorithm is utilized to control the system. The simulations are performed in four states to confirm the viability of the proposed control technique. The proportional integral controller, proportional integral-disturbance observer controller, and fuzzy backstepping controller are contrasted with the proposed controller. It has been noted that the proposed controller's instantaneous disturbance's highest value is 5.1°/s. The maximal value of the coupling output for the two gimbals utilizing the proposed controller, however, is 0.0008°/s and 0.0018°/s, respectively. The findings presented here demonstrate that the backstepping controller, which is based on an adaptive fuzzy logic system and a nonlinear disturbance observer, is capable of precise tracking and dynamic tracking of a stabilized platform under disturbance and uncertainty.

     

Simplified global fault accommodation control design of uncertain nonlinear systems with unknown time-varying powers

This paper addresses the problem of global robust fault accommodation tracking for a class of uncertain nonlinear systems with unknown powers and actuator faults. It is assumed that the powers of the concerned system are unknown time-varying functions, all system nonlinearities are unknown, and unknown actuator faults depend on the time-varying power of a control input. A fault accommodation state-feedback controller is explicitly constructed based on the nonlinear error transformation technique using time-varying performance functions. Global tracking with the preselected performance bounds is established in the presence of unknown time-varying powers and unexpected actuator faults. Different from the previous results dealing with the problem of unknown time-varying powers, the proposed tracking strategy does not require the knowledge of the bounds of the time-varying powers and the nonlinear bounding functions of system nonlinearities. An underactuated mechanical system is simulated to validate the effectiveness of the proposed theoretical approach.     

Robust nonlinear control for a model-scaled helicopter with parameter uncertainties

A robust nonlinear controller is designed for the trajectory tracking of a model-scaled helicopter with uncertain parameters (including uncertain inertial parameters, uncertain structural parameters and uncertain aerodynamic parameters). The proposed controller is based upon the backstepping technique, with modifications to accommodate helicopter dynamics. Aerodynamic uncertainties are addressed by dynamic inverters, and derivatives of virtual controls in the backstepping process are calculated through command filters to avoid complex analytical solutions. Errors resulted from dynamic inverters, command filters, and uncertain parameters are then regarded as disturbances, and treated by nonlinear damping terms. With the proposed controller, it can be proved that tracking errors of the closed-loop system are ultimately bounded with tunable ultimate bounds. Performances of the proposed controller are evaluated by simulation results.     

最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间,针对平动点航天器编队重构的均衡耗能最优轨迹规划问题,提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解,并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域;同时,不需要对协态初值准确猜测,避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟,结果表明,本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标,具有一定的应用价值。     

System modes and dynamics of the proposed space station type configurations

The paper studies libration/vibration interaction dynamics of the space station Freedom during its evolutionary phases. To that end, a relatively general nonlinear formulation, applicable to a system of interconnected plate and beam-type structural members forming a tree topology is developed. System modes, obtained through a finite element analysis, are employed in the discretization process and the response study is purposely confined to the orbital plane to emphasize interactions between librational dynamics and flexibility. Finally, an approximate closed-form nonlinear solution of the problem is attempted using the variation of parameters method. Its validity is assessed through comparison with the numerically obtained results over a range of system parameters and initial conditions. Results provide information pertaining to the levels of librational and vibrational response and the associated acceleration tield, which may prove helpful in appropriately locating experiments and monitoring instruments. It may also aid in the planning of the control system. The analytical approach provides surprisingly close correlation with the more elaborate numerical procedure, thus promising better physical appreciation of the complex interactions as well as a considerable saving in the computational cost.     

Finite-time chaos control of unified chaotic systems with uncertain parameters

This paper is concerned with finite-time chaos control of unified chaotic systems with uncertain parameters. Based on the finite-time stability theory in the cascade-connected system, a nonlinear control law is presented to achieve finite-time chaos control. The controller is simple and easy to be constructed. Simulation results for Lorenz, Lü, and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme. Supported by the National Natural Science Foundation of China (Grant No. 60674024).     

Robust finite-time tracking for a square fully actuated class of nonlinear systems

In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

     

Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems

The output-feedback control problem of a class of uncertain SISO nonlinear systems is investigated based on an indirect adaptive fuzzy approach. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. Compared with the existing results in the observer design, the main advantages of the proposed adaptive fuzzy output-feedback control approach are as follows: (1) It does not require to assume that the sign of the control gain coefficient is known and Nussbaum-gain technique is utilized to control the nonlinear systems with both the unknown control direction and the unmeasured states; (2) The observer in this paper is designed for the states rather than the tracking errors, then it is convenient to compute; (3) The controller singularity problem is perfectly avoided. The stability of the closed-loop system is analyzed by using Lyapunov method. A simulation example is given to verify the feasibility of the proposed approach.     

多体系统轨迹跟踪的瞬时最优控制保辛方法

随着近年来机器人在各行业领域的广泛应用,对机器人的动力学与控制性能不断提出新的要求,特别是对设计越来越复杂、操作越来越灵巧的智能机器人,要求其能够对目标轨迹实现高精度跟踪以满足实际工作需求. 因此,针对机器人多体系统对目标轨迹跟踪的任务需求,基于微分代数方程提出瞬时最优控制保辛方法. 首先,采用多体动力学绝对坐标建模方法建立机器人系统的普适动力学方程,即微分代数方程;然后,采用保辛方法将连续时间域内的微分代数方程进行离散化,进而得到以当前位置、速度和拉式乘子为未知量的非线性代数方程组;其次,通过引入对目标轨迹跟踪以及对控制加权的瞬时最优性能指标,根据瞬时最优控制理论获得当前最优控制输入;最后,通过离散时间步的更新完成对目标轨迹的跟踪任务. 为了验证本文方法的有效性,以双摆轨迹跟踪控制为例进行了数值仿真,结果表明:针对机器人轨迹跟踪任务所提出的瞬时最优控制保辛方法能够实现对目标轨迹的高精度跟踪,且瞬时最优控制由受控微分代数方程推导获得,更具一般性,能够适应其他复杂多体系统的轨迹跟踪控制问题.      

Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances

In this paper, the composite nonlinear feedback control method is considered for robust tracking and model following of uncertain linear systems. The control law guarantees that the tracking error decreases asymptotically to zero in the presence of time varying uncertain parameters and disturbances. For performance improvement of the dynamical system, the proposed robust tracking controller consists of linear and nonlinear feedback parts without any switching element. The linear feedback law is designed to allow the closed loop system have a small damping ratio and a quick response while the nonlinear feedback law increases the damping ratio of the system as the system output approaches the output of the reference model. A new collection of different nonlinear functions used in the control law are offered to improve the reference tracking performance of the system. The proposed robust tracking controller improves the transient performance and steady state accuracy simultaneously. Finally, the simulations are provided to verify the theoretical results.     

惯性平台稳定回路基于Backstepping的动态滑模控制(英文)

针对带不匹配不确定非线性干扰的惯性平台稳定回路跟踪控制问题,提出了基于backstepping的动态滑模控制方法。首先,建立了惯性平台稳定回路的等价模型,该模型由一个线性模型加上一个不确定的非线性函数组成。然后,基于backstepping方法设计了带渐近稳定滑模面的动态滑模控制器,解决了模型不匹配的问题,并提高了系统的鲁棒性。进而应用Lyapunov稳定性理论证明了所设计的控制器不仅能保证闭环系统的稳定性,而且可以通过选择适当的控制器参数来调整跟踪误差的收敛率。最后,仿真结果表明,基于backstepping的动态滑模控制方法与PID控制方法相比,提高了系统的跟踪精度,增强了鲁棒性。     

Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.     

Libration suppression of tethered space system with a moving climber in circular orbit

This paper studies the dynamics and libration suppression of a tethered system with a moving climber in circular orbits. The tethered system is modeled by a two-piece dumbbell model that consists of one main satellite, one climber and one end-body connected by two straight, massless and inextensible tethers. A new tension control strategy to suppress the libration of the tethered system due to the moving climber is proposed by reeling in-out tether at the end-body without thrust. The control strategy is implemented with the sliding mode control to suppress the libration angle of the climber to zero by the end of climber’s transfer phase. The numerical results show that the proposed control strategy is very effective in suppressing the libration of the climber in the three-body tethered system with tension control only. Furthermore, cases with limited tension control are examined. It reveals that a longer tether between the climber and the end-body is required to supplement the limited tension in suppressing the libration of the climber.     

Velocity-sensorless proportional–derivative trajectory tracking control with active damping for quadcopters

The proposed observer-based control mechanism solves the trajectory tracking problem in the presence of external disturbances with the reduction in sensor numbers. This systematically considers the quadcopter nonlinear dynamics and parameter and load variations by adopting the standard controller design approach based on a disturbance observer (DOB). The first feature is designing first-order observers for estimating the velocity and angular velocity error, with their parameter independence obtained from the DOB design technique. As the second feature, the resultant velocity observer-based control action including active damping and DOBs secures first-order tracking behavior for the position and attitude (angle) loops through pole zero cancellation, thereby forming a proportional–derivative control structure. Closed-loop analysis results reveal the performance recovery and steady-state error removal properties in the absence of tracking error integrators. The numerical verification confirms the effectiveness of the proposed mechanism using MATLAB/Simulink.

     

Adaptive dynamic surface neural network control for nonstrict-feedback uncertain nonlinear systems with constraints

This paper presents an adaptive dynamic surface neural network control for a class of nonstrict-feedback uncertain nonlinear systems subjected to input saturation, dead zone and output constraint. The problem of input saturation is solved by designing an anti-windup compensator, and the issue of output constraint is addressed by introducing tan-type Barrier Lyapunov function. Furthermore, based on adaptive backstepping technique, a series of novel stabilizing functions are derived. First-order sliding mode differentiator is introduced into backstepping design to obtain the first-order derivative of virtual control. The real control input is obtained using dead-zone inverse method. It is proved that the proposed control scheme can achieve finite time convergence of the output tracking error into a small neighbor of the origin and guarantee all the closed-loop signals are bounded. Simulation results demonstrate the effectiveness of the proposed control scheme.     

Adaptive fault compensation control for a class of nonlinear systems with unknown time-varying delayed faults

An adaptive approximation design for the fault compensation (FC) control is addressed for a class of nonlinear systems with unknown multiple time-delayed nonlinear faults. The magnitude and occurrence time of the multiple faults with unknown time-varying delays are unknown. The function approximation technique using neural networks is employed to adaptively approximate the unknown nonlinear effects and changes in model dynamics due to the time-delayed faults. We design an adaptive memoryless FC control system with a prescribed performance bound to compensate the faults and to guarantee the transient performance of the tracking error from unexpected changes of system dynamics. The adaptive laws for neural networks and the bound of residual approximation errors are derived using the Lyapunov stability theorem, which are used for proving that the tracking error is preserved within the prescribed performance bound regardless of unknown multiple time-delayed nonlinear faults. Simulation examples are presented for illustrating the effectiveness of the proposed control methodology