【作者】 张旭；

【导师】 黄显林；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2018， 博士

【摘要】 本文所研究的前向控制技术是在系统浸入与不变流形理论的理论框架下提出来的,是针对一类具有严格反馈形式的高阶非线性系统设计出来的构造性控制方法。前向控制策略通过构造映射,将低阶目标系统浸入到被控对象中,使得被控对象与目标系统有一致的响应特性。相对于经典的反步法,前向控制是从流形的角度出发,原则上不需要Lyapunov函数,而且其设计步骤可以大大简化。本文首先将被控对象指定为一类关于输入仿射的高阶全信息非线性系统,通过对系统浸入与不变流形理论的研究,前向控制技术可以有效地实现模型降阶。这种新型的非线性控制方法不需要对模型进行线性化,仅需要在每一步构造目标系统、映射以及虚拟控制器保证闭环子系统所有信号的有界性,以及在浸入条件中系统响应特性得到传递。然而,随着系统自由度的增加,控制器设计会变得越来越复杂。出现这种弊端的原因与经典反步法类似,前向控制方法每一步设计都需要计算映射的导数,被控对象的阶数越高,计算量越增大,这就是微分膨胀现象。为了解决这样的问题,在每一步虚拟控制器设计过程中,引入一个滤波器来计算映射及其导数,保证整个控制器设计过程不涉及直接的微分运算,极大地提高了控制器计算效率。同时,利用滤波器的内稳定性可以推导出系统所有信号的有界性,而且不需要被控对象模型中的函数都是可微的。在全信息非线性系统的基础上考虑模型中出现满足不匹配条件的不确定性以及外部扰动,设计了鲁棒前向控制器。首先,结合自适应控制理论,对带有线性参数化的系统设计了自适应控制器;其次,对系统中出现的扰动以及不确定性,利用扰动观测器对其进行估计,从而得到了基于扰动观测器的鲁棒前向控制策略;然后,利用径向基函数的神经网络对模型中的不确定性以及映射的导数进行任意精度的逼近,从而得到基于神经网络的鲁棒自适应控制器。这种方式避免了大量地引入滤波器,而且不需要限制模型的线性参数化形式。在保证闭环系统稳定性的基础上,利用原系统与目标系统的浸入关系,设计了改善系统响应特性的准有限时间前向控制器。由于前向控制是基于系统浸入与不变流形理论框架提出来的,所以选取合适的目标系统与映射,在系统降阶之后状态响应特性不会改变。通过综合例如一阶或者二阶线性系统这样的低阶目标子系统的控制器获得期望的响应特性,使得高阶系统得到同样的系统性能的目的。因此,无论平衡点调节问题还是参考信号跟踪问题,在准有限时间前向控制器的作用下,系统收敛速度会更快,跟踪精度会更高,扰动抑制能力会更强。而响应速度取决于虚拟控制器增益的调节。另一方面,当高阶非线性系统出现执行器饱和时,利用双曲正切函数对饱和非线性函数进行逼近,从而得到抗饱和鲁棒前向控制器。最后,将上述提出的基于系统浸入和不变流形理论的鲁棒前向控制设计方法应用于拮抗式筋腱机械臂的控制系统设计中,设计了基于标准前向控制器、自适应前向控制器以及准有限时间前向控制器。将所设计的控制器放在拮抗式筋腱机械臂的非线性模型中进行时域仿真,经过仿真验证,本文提出的基于前向控制方法的鲁棒控制器可以保证机械臂对外部扰动和不确定性不敏感,而且可以快速跟踪期望的参考轨迹。更多还原

【Abstract】 Forwarding control technology we studied is proposed within the framework of system immersion and invariance manifold(I&I),which is a constructive control approach for a class of high-order nonlinear systems in strict-feedback form.Forwarding control strategy immersed the lower-order target dynamics into the controlled plant by selecting a mapping,such that two systems have the compliant responses.Differing from the standard backstepping method,forwarding control does not require Lyapunov function in principle from the perspective of manifold,and its controller design procedures are simplified to great extent.The plant is extended to a class of high-order full-information nonlinear systems with regard to affine input,and after the study of system immersion and invariance manifold,we are able to realize the system’s order reduction via forwarding control technology.This novel nonlinear control strategy does not require model linearization,but only needs to select target dynamics,mapping and virtual controller to ensure the boundedness of all signals of closed-loop systems,such that the system responses in the immersion conditions can be transmitted.However,controller design will become more complex as the degree of freedom of system increases.Analogous to backstepping design,forwarding control needs to compute analytic derivatives at each step of the design,and the higher the order of plant is,the larger computation load is.This is so-called “complexity of explosion”.To solve this problem,a filter is introduced into each virtual controller design to compute the mapping and its analytic derivatives such that controller is not involved with direct differential computation.This modification greatly improves controller’s computation efficiency.Meanwhile,the boundedness of all signals can be derived by using the internal stability of filters,and all functions in the model are not required differential.Uncertainties and external disturbances satisfying mismatched condition are considered in the full-information nonlinear systems and robust forwarding controller is presented.First,adaptive controller is designed for systems in the linear parameterization form by combining with traditional adaptive theory;second,when disturbance and uncertainties occur,a robust forwarding strategy based on disturbance observer is proposed,which can estimate such uncertainties by using disturbance observer;third,uncertainties and the derivatives of mappings are approximated by using racial basis function(RBF)-based neural network with arbitrary precision,and a neural network-based robust adaptive forwarding controller is proposed.This control procedure obviate to employ multiple of filters and does not require model in the form of linear parameterization.After ensuring the stabilization of closed-loop system,a new forwarding controller is proposed to improve the system performance by using the relationship between plant and target dynamics.Since forwarding control is developed within I&I’s framework,system performance will keep compliant by selecting appropriate target dynamics and mappings after system’s order reduction.Synthesizing the controller of target system,such as firstorder or second-order linear system,to obtain the desired response behavior,the original high-order system is able to have the same system performance.Therefore,with the implementation of quasi-finite-time forwarding controller,the speed of convergence will be faster,tracking precision will be higher and the attenuation of disturbance will be stronger from both regulation and trajectory tracking’s view.In particular,response speed depends on the gain of virtual controller.On the other hand,when actuator saturation occurs in the high-order nonlinear systems,robust forwarding controller is developed by using hyperbolic tangent function to approximate the saturation nonlinearity.Finally,the I&I-based robust forwarding control approaches mentioned above are applied to antagonistic tendon-driven robot,then standard forwarding controller,adaptive forwarding controller and quasi-finite-time forwarding controller are obtained.All these controllers with the nonlinear model of this robot are carried out in the simulation platform,and after verification of simulation,robust forwarding control method we discussed in this thesis makes the robot insensitive to external disturbances and uncertainties,especially tracks the expected reference signal with a fast speed.更多还原