空速/高度精确解耦跟踪控制研究及仿真

飞行器空速／高度的精确解耦跟踪,控制本质上是非最小相位输出精确解耦跟踪控制问题,由于存在内动态不稳定性,经典逆系统方法无法使用。将稳定逆办法与滑模控制相结合来解决存在的问题。首先针对稳定逆非因果性带来的问题,给出了一种稳定逆因果近似解的求法,经计算证明了近似结果误差的渐近收敛特性;然后利用稳定逆困果近似解将输出跟踪问题转化为不确定系统的鲁棒镇定问题,并对滑模控制和干扰观测器设计了相应的反馈镇定控制器。经过仿真表明综合稳定逆因果近似解和滑模控制的方案既发挥了逆系统方法的动态解耦能力,又利用了滑模控制的鲁棒性实现飞行器空速／高度精确解耦跟踪控制,也可以很好的兼顾控制器的鲁棒性和抗干扰性。     

Control of nonlinear systems with output tracking error constraints and its application to magnetic bearings

A constructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficiently smooth reference trajectory asymptotically. Under a suitable condition on the initial output tracking error, the proposed controllers guarantee the output tracking error within a symmetric or an asymmetric pre-specified limit range, and boundedness of all signals of the closed-loop system. A transformation is introduced to take care of the output tracking error constraint. Smooth and/or p-times differentiable step functions are proposed and incorporated in the output tracking error transformation to overcome difficulties due to the asymmetric limit range on the output tracking error. As a result, there are no switchings in the proposed controllers despite the asymmetric limit range. The proposed control design is then applied to design a tracking controller for active magnetic bearings as an illustrating application.     

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.     

一类增长率依赖输出的非线性系统的输出反馈输出跟踪控制

研究一类增长率依赖输出非线性系统的输出反馈输出跟踪控制问题.利用系统结构特点,构造出系统实现输出跟踪时内部状态的渐近轨迹.通过建立状态与渐近轨迹偏差的动态方程,将输出跟踪问题转化为偏差系统的镇定问题,然后通过设计偏差系统的输出反馈镇定控制器给出输出反馈输出跟踪控制器.最后以仿真实例验证本文结论.     

Global approximate output tracking for nonlinear systems

Addresses the global output tracking problem for nonlinear systems with singular points. For nonlinear systems which satisfy a suitable observability condition, the authors identify a class of smooth output trajectories which the system can track using continuous open-loop controls. This class includes all output trajectories generated by smooth state feedback. They then study the problem of approximate output tracking using discontinuous time-varying feedback controllers. Given a smooth output trajectory for which exact tracking is possible, the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations. Finally, it is shown that their results can be applied to the control of a chain system, and some numerical results are presented to illustrate the performance of their controller     

H ∞ output tracking control for discrete‐time switched systems via output feedback

This paper studies the problem of H _∞ output tracking control for a class of discrete‐time switched systems. Neither the measurability of the system state nor the solvability of the output tracking control problem for each individual subsystem is required. We design controllers for subsystems and a switching law to solve the H _∞ output tracking problem for the switched system. The designed controllers use only the measured output feedback, and the switching law is based on the measured output tracking error. In addition, the quadratic function corresponding to each subsystem is not required to be positive definite. A numerical example is provided to demonstrate the feasibility and validity of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

Output tracking of stochastic nonlinear systems with unstable linearization

This paper studies the output tracking problem for a class of stochastic nonlinear systems whose linearization parts may have unstable modes via output‐feedback control. This is in contrast with most of the existing results where only state‐feedback control is considered. On the basis of the homogeneous domination technique, an output tracking controller is designed. It is shown that the expectation of tracking error can be made arbitrarily small while all the states of the closed‐loop system remain to be bounded in probability. Finally, a simulation example is given to illustrate the effectiveness of the tracking controller.     

Additive‐state‐decomposition‐based tracking control framework for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances

This paper aims to propose an additive‐state‐decomposition‐based tracking control framework, based on which the output feedback tracking problem is solved for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances. This framework is to ‘additively’ decompose the output feedback tracking problem into two more tractable problems, namely an output feedback tracking problem for a linear time invariant system and a state feedback stabilization problem for a nonlinear system. Then, one can design a controller for each problem respectively using existing methods, and these two designed controllers are combined together to achieve the original control goal. The main contribution of the paper lies on the introduction of an additive state decomposition scheme and its implementation to mitigate the design difficulty of the output feedback tracking control problem for nonminimum phase nonlinear systems. To demonstrate the effectiveness, an illustrative example is given. Copyright © 2013 John Wiley & Sons, Ltd.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Hermite Polynomials for Iterative Output Replanning for Flat Systems Affected by Additive Noise

The paper considers the output tracking problem for nonlinear systems whose performance output is also a flat output of the system itself. A desired output signal is sought on the actual performance output by using a feedforward inverse input that is periodically updated with discrete‐time feedback of the sampled state of the system. The proposed method is based on an iterative output replanning that uses the desired output trajectory and the sampled state to replan an output trajectory whose inverse input helps in reducing the tracking error. This iterative replanning exploits the Hermite interpolating polynomials to achieve an overall arbitrarily smooth input and a tracking error that can be made arbitrarily small if the state sampling period is sufficiently small and mild assumptions are considered. Some simulation results are presented for the cases of a unicycle and a one‐trailer system affected by additive noise.     

Practical output tracking of nonlinear systems with uncontrollableunstable linearization

The paper focuses on the problem of having the output of nonlinear systems track a prescribed C¹ reference signal. It is proved that, under mild assumptions, global practical output tracking is achievable by smooth state feedback, although asymptotic output tracking is usually not possible (even locally) because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane. Smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed, based on a modified 'adding a power integrator' approach. This feedback design method also leads to solutions to challenging benchmark control problems, including practical output tracking of an underactuated unstable two degrees of freedom mechanical system     

Conditions of exact tracking by the linear system output of the standard model of a reduced order

A problem is considered for an exact tracking by the output of a linear stationary system presented in the space of states of the standard model of a reduced order in comparison with the dimension of the system state vector. A minimum possible order of the standard model is defined, at which it is possible to perform the exact tracking of it by the output, conditions are defined of the exact tracking by the output of the standard model of a reduced order, and also a set of the control laws that ensure the exact tracking and the internal stability of the system. The solution relies on the method of canonization of matrices. A methodical example is given.     

非线性相似组合系统的鲁棒输出跟踪控制*

研究一类具有相似结构的非线性不确定组合系统的分散输出跟踪控制问题,利用的相似结构,提出一种设计具有相似结构的分散滑模控制器的方法,所设计的控制器,对于所有允许的不确定性,均使系统输出渐近跟踪所给定的参考输出。     

Output tracking control of switched nonlinear systems with multiple time-varying delays

In this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.     

一类线性不确定组合系统的输出反馈分散输出跟踪控制

讨论了线性不确定组合系统的鲁棒分散输出渐近跟踪问题.基于Lyapunov方程正 定解的存在性,给出了输出反馈跟踪控制器的设计方法.对于系统中所有允许的不确定性,所 设计的控制器均使系统的输出渐近跟踪所给定的参考信号,同时系统的状态保持有界.     

A new nonlinear output tracking controller via output-feedback

In this paper, the output tracking control is investigated for a class of nonlinear systems when only output is available for feedback. Based on the multivariable analog of circle criterion, an observer is first introduced. Then, the observer-based output tracking controller is constructively designed by using the integral backstepping approach together with completing square. It is shown that, under relatively mild conditions, all the closed-loop signals are uniformly bounded. Meanwhile the system output asymptotically tracks the desired output. A simulation example is given to illustrate the effectiveness of the theoretical results.     

An adaptive actuator failure compensation controller using outputfeedback

An adaptive control scheme using output feedback for output tracking is developed for systems with unknown actuator failures. Such actuator failures are characterized by some unknown inputs stuck at some unknown fixed values at unknown time instants. An effective output feedback controller structure is proposed for actuator failure compensation. When implemented with true matching parameters, the controller achieves desired plant-model output matching. When implemented with adaptive parameter estimates, the controller achieves asymptotic output tracking. A stable adaptive law is derived for parameter adaptation in the presence of parameter uncertainties. Closed-loop signal boundedness and asymptotic output tracking, despite the uncertainties in actuator failures and plant parameters, are ensured analytically and verified by simulation results     

轮式移动机器人的位置量测输出反馈轨迹跟踪控制

针对机器人的姿态角难以精确测量的困难,本文研究基于位置测量的轮式移动机器人的轨迹跟踪问题.首先提出一种利用机器人的位置信息估计其姿态角的降维状态观测器,当机器人的线速度严格大于零时,可保证姿态角观测误差的指数收敛.然后给出一种新的状态反馈轨迹跟踪控制律,当参考轨迹满足一定的激励条件时,可以保证机器人的线速度严格大于零且跟踪误差全局渐近收敛.进一步结合姿态角观测器和状态反馈控制律,得到一种输出反馈轨迹跟踪控制算法.理论分析表明,当参考轨迹满足一定的激励条件时,所提出的输出反馈控制算法可以保证跟踪误差的全局渐近收敛.最后对所提出的姿态角观测器、状态反馈和输出反馈轨迹跟踪控制算法进行了仿真验证,证实了算法的有效性,并且当存在位置测量误差时,所提出的输出反馈轨迹跟踪控制算法仍可以保证机器人对参考轨迹的实际跟踪.