非最小相位系统跟踪控制综述

非最小相位系统是指包含不稳定零动态的系统.经典的跟踪控制理论,特别是非线性系统跟踪控制理论,是以最小相位系统为基础建立的,不能直接用于非最小相位系统.研究非最小相位系统跟踪控制理论,是对经典控制理论的扩展和补充,具有重要的意义.本文对目前非最小相位系统跟踪控制领域取得的成果进行综述.首先梳理各种非最小相位系统跟踪控制方法的基本思想,并按照近似跟踪和精确跟踪进行归类,建立非最小相位系统跟踪控制的基本框架.然后围绕该框架对各种方法进行详细介绍.接着讨论非最小相位系统的跟踪性能限制.最后总结现有研究存在的一些问题及对今后的发展方向进行展望.本文的目的在于使控制工作者对非最小相位系统的跟踪控制有一个较为清晰的认识.     

输出重定义下的非线性非最小相位系统迭代学习控制

讨论非线性非最小相位系统实现完全跟踪的迭代学习控制方法, 适于在有限作业区间上重复运行的受控系统. 在控制器设计时, 通过输出重定义以使非最小相位系统的零动态变成渐近稳定特性. 分别采用部分限幅和完全限幅两种学习算法设计控制器, 理论分析表明两种算法能够保证学习系统中所有变量的有界性和跟踪误差在整个作业区间上渐近收敛于零. 数值仿真验证了两种迭代学习控制系统的跟踪性能.     

一类非最小相位非线性系统的自适应控制

针对一类非最小相位的非线性系统,通过引入一个近似系统,提出了一种简单的间接自 适应控制方法,并分析了采用该方法后系统输出的跟踪性能,给出了输出跟踪误差的上限.该 方法可克服现有的非线性自适应控制方法只能控制最小相位的非线性系统并且容易产生过 度控制的缺点.     

垂直/短距起降飞机的轨迹跟踪控制器设计

针对垂直/短距起降飞行器在悬停状态下滚转力矩与横侧向推力存在强耦合、系统具有非最小相位特性的问题,本文设计了轨迹跟踪控制器.首先利用坐标变换和输入输出线性化将系统分解成最小相位子系统和非最小相位子系统.对非最小相位子系统,采用稳态系统中心的方法求解理想内部动态,并跟踪系统理想内模设计了LQR控制器,使得内部动态有界;对最小相位子系统设计了高增益控制器使得外部动态渐进稳定.仿真结果表明本文设计的控制器对给定轨迹和飞行器机动轨迹都有较好的跟踪效果,验证了控制器的有效性.     

通用神经网络非线性系统模型参考自适应控制*

针对任意复杂的具有最小相位,滞后环节和非最小相位特性的离散非线性系统,提出一种通用的直接神经网络模型参考自适应控制。采用具有在线学习功能的最近邻聚类算法训练RBF神经网络控制器,同时引入优化策略对聚类半径进行自动调整,并利用构造伪系统的方法构成一种对非最小相位同样有效的神经网络模型参考自适应控制器。仿真研究证明,该控制策略不仅能使多种非线性对象跟踪多种参考信号,而且抗干扰能力和鲁棒性也很好。     

基于Boost电路的预测PI控制

非最小相位是指具有右半平面零、极点或滞后的线性对象,在DC-DC变换器中,Boost变换器以电容电压作为输出量进行反馈控制时,是一个非最小相位系统。由于目前大多数Boost电路的控制方法选用的是传统PID控制,这种方法具有结构简单、可靠性高等特点,但是系统的动态特性、抗干扰性能却有待进一步提高。由于预测PI控制算法具有抗滞后和抗非最小相位特性的能力,将其应用到Boost电路中进行理论研究并进行实时仿真。仿真结果表明,预测PI控制算法具有良好的动态特性且抗干扰性强,能够体现良好的控制效果。     

基于非线性PID的非最小相位系统控制

提出一种新型非线性PID控制器简单结构,利用非线性PID控制器的非线性特性,抑制非最小相位系统的右半平面零点所造成的负调问题,克服非最小相位系统的超调、负调和调整时间之间的矛盾.数值仿真结果表明,由非线性PID控制器构成的非最小相位系统具有良好的动静态性能、高的控制精度和较强的鲁棒性.数值结果说明方法有效,算法简单,易于实时实现.     

一类输入饱和非仿射非线性系统的非线性动态逆控制

输入饱和是实际系统中经常遇到的问题,很多已有的控制方法要求被控系统具有仿射结构.本文针对一类具有输入饱和的非仿射纯反馈非线性系统提出了一种基于奇异值摄动理论的非线性动态逆控制方法.首先构建一个快变子系统,在慢时间尺度下将非仿射非线性系统转换为具有仿射结构的线性系统,从而应用已有的控制算法实现控制目的.为了消除输入饱和带来的影响,建立一个中间子系统对理想控制量与输入饱和限制下控制量的差进行估计和补偿.所提出的控制方法不依赖于被控系统固有的时标分离特性,并能证明闭环系统指数跟踪参考轨迹.该方法具有良好的扩展性,可以根据实际需求与多种控制算法相结合.与动态面控制器和传统近似动态逆控制器的对比仿真结果验证了本文控制方法的有效性.     

非线性增益递归滑模动态面自适应NN控制

针对一类严反馈非线性不确定系统的跟踪控制问题,提出一种非线性增益递归滑模动态面 (Dynamic surface control, DSC)自适应控制方法. 通过设计一个新的非线性增益函数,并构造递归滑模动态面的控制策略和新的Lyapunov函数,同时利用神经网络在线逼近系统不确定项, 该方法有效解决了具有输入饱和约束条件下系统控制精度与动态品质间的矛盾,增强了控制器对其自身参数摄动的非脆弱性. 理论证明了闭环系统所有状态是半全局一致最终有界的,且跟踪误差可收敛至任意小.     

非最小相位控制系统的智能设计

本文在归纳总结控制工程中大量非最小相位被控制对象特性的基础上,研究了其控制系 统的智能设计问题,提出了一种非最小相位控制系统的智能设计方法,并以此设计了柔性结构 姿态控制系统,证实了本文的设计方法能同时满足系统的稳定性,鲁棒性,静态动态性能,以及 控制器的简单性和控制器本身的稳定性等方面的要求,在同等条件下比较,优于其它设计方 法.     

Output tracking for nonlinear non-minimum phase systems with output delay and application to an F-16 jet fighter

In this article, output tracking for a class of nonlinear non-minimum phase systems with output delay is considered. By applying the first-order Padé approximation technique to deal with the time-delay function, the original control problem is reduced to the output-tracking problem of a new non-minimum phase system without delay. The bounded tracking profiles of the unstable internal dynamics in the new system are generated by using the nonlinear inversion-based method, and a complete sliding mode control scheme is proposed to stabilise the output-tracking error as well as the internal dynamics. Moreover, the proposed control scheme is applied to solve the flight-path angle tracking problem of an F-16 jet fighter.     

Output-feedback Dynamic Surface Control for a Class of Nonlinear Non-minimum Phase Systems

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems. To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control (DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed outputfeedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.      

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.     

Weakly and strongly non-minimum phase systems: properties and limitations

In this paper, a new classification of non-minimum phase systems based on stabilisability of the internal dynamics is introduced. According to this classification, the non-minimum phase systems are categorised as follows: (1) weakly non-minimum systems, for which a finite value of minimum norm of the regulation error can be obtained, and (2) strongly non-minimum phase systems for which this minimum norm of the regulation becomes infinite due to the presence of both transient and steady-state errors while for the weakly non-minimum phase systems there is no steady-state regulation error. It is worth mentioning that based on this new classification a level of non-minimum phase-ness can be further defined for any given desired trajectory. Furthermore, some numerical simulations are carried out to show consistency with theoretical analysis.     

A dynamic feedback control strategy for control loops with time-varying delay

Dynamic systems of nth order with time-varying delay in the control loop are examined in this paper. The infinite-dimensional pure delay problem is approximated using a jth-order Padé approximation. Although the approximation provides a well-matched finite-dimensional configuration, it poses a new challenge in terms of unstable internal dynamics for the resulted non-minimum phase system. Such a non-minimum phase characteristic limits the closed-loop system bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the unstable internal dynamics of the system is captured and a new dynamic compensator is proposed to stabilise it in a systematic framework. A dynamic controller is developed, which provides the overall system stability against unmatched perturbation and meets the desired tracking error dynamics. The proposed approach is then applied to fuelling control in gasoline engines addressing the varying transport delay of the oxygen-sensor measurement in the exhaust. The developed methodology is finally validated on a Ford F-150 SI lean-burn engine model with large time-varying delay in the control loop.     

Iterative learning control with advanced output data for nonlinear non-minimum phase systems

This paper investigates iterative learning control of nonlinear discrete time non-minimum phase systems in tracking problems. The main objective of this paper is to find an input-to-output mapping in order to stabilize the non-minimum phase systems and to obtain an input update law for handling uncertain systems. In conventional approaches on the tracking of non-minimum phase systems, zero dynamics is stabilized from the system equations and the input is calculated from the state information. For the learning of uncertain systems, conventional approaches depend on the output-to-state and state-to-input mappings. In the proposed method, the inverse system is stabilized using the input-to-output mapping for nonlinear non-minimum phase systems. A new input update law is proposed based on the relative degree and the number of non-minimum phase zeros. This makes the overall proposed learning system have a simple structure as in the classical ILC.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.     

非最小相位控制系统的智能设计方法

提出了两种非最小相位控制系统的智能设计方法，并以此设计了控制系统，证实了设计方法能同时满足系统的稳定性、鲁棒性、静态动态性能，以及控制器的简单性和控制器本身的稳定性等方面的要求。     

结构未建模系统的变结构自适应控制器设计

本文对一类结构未建模的动态不确定系统，采用变结构控制与自适应控制相结合的方法，给出了一种鲁棒控制器设计方案。所提方案适用于系统已建模部分为非最小相位的系统，并能保证系统输入输出全局有界稳定。     

Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

ABSTRACT

In this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.