Feedback diagonal canonical form and its application to stabilization of nonlinear systems

~~Feedback diagonal canonical form and its application to stabilization of nonlinear systems1. Aeyels, D., Stabilization of a class of non-linear systems by a smooth feedback control, Sys. Contr. Lett., 1985, 5: 289-294. 2. Behtash, S., Dastry, D., Stabilization of non-linear systems with uncontrollable linearization, IEEE Trans. Aut. Contr., 1988, 33(6): 585-590. 3. Byrnes, C. I., Isidori, A., Willems, J. C., Passivity, feedback equivalence, and the global stabilization of …     

基于Smith的非最小相位对象PID控制器设计

针对具有非最小相位时滞的过程,基于Smith预估控制思想,提出一种改进控制方案,对右半平面零点和纯滞后同时进行补偿,使闭环特征方程中不含右半平面零点,从而简化控制器设计。根据期望闭环传函,解析得出PID控制器形式,综合负调、响应时间、ISE以及鲁棒性要求整定控制器参数,针对Smith控制抗扰性较差提出了抗扰性设计。仿真结果表明,该方案对于具有非最小相位时滞的对象有较好的控制效果,并且在模型失配和有干扰输入的情况下,有较好的鲁棒性和抗扰性。     

Analytical design of active disturbance rejection control for nonlinear uncertain systems with delay

For first-order nonlinear uncertain systems with delay, the analytical design of active disturbance rejection control (ADRC) with matched time delay is rigorously studied. The conditions of stabilizing the closed-loop system are studied in the form of parameters’ explicit sets such that the tuning laws of ADRC can be directly obtained and intuitively demonstrated in engineering practice. The necessary and sufficient condition of the asymptotical stability for the closed-loop system in the case of linear time-invariant is explicitly given. The condition of stabilizing the closed-loop system with nonlinear uncertain dynamics is quantitatively presented. Moreover, the water tank experiment illustrates the proposed tuning laws.     

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

This paper deals with the problem of active disturbance rejection control (ADRC) design for a class of uncertain nonlinear systems with sporadic measurements. A novel extended state observer (ESO) is designed in a cascade form consisting of a continuous time estimator, a continuous observation error predictor, and a reset compensator. The proposed ESO estimates not only the system state but also the total uncertainty, which may include the effects of the external perturbation, the parametric uncertainty, and the unknown nonlinear dynamics. Such a reset compensator, whose state is reset to zero whenever a new measurement arrives, is used to calibrate the predictor. Due to the cascade structure, the resulting error dynamics system is presented in a non-hybrid form, and accordingly, analyzed in a general sampled-data system framework. Based on the output of the ESO, a continuous ADRC law is then developed. The convergence of the resulting closed-loop system is proved under given conditions. Two numerical simulations demonstrate the effectiveness of the proposed control method.      

Robust flat filtering DSP based control of the boost converter

The article deals with the design and implementation of a flat filter tracking digital controller for a boost dc-dc power converter. A highly perturbed switched boost converter circuit is shown to be efficiently controlled, in a trajectory tracking task for its non-minimum phase output, by means of a suitable linear filter, here addressed as a flat filter. Flat filtering is a natural robust version of generalized proportional integral control (GPIC) by which the effects of arbitrary time varying exogenous disturbances, unknown endogenous nonlinearities and un-modeled dynamics can be jointly attenuated in a conceptually similar fashion to observer-based active disturbance rejection control (ADRC) and algebraic identification based model free control (MFC) but: a) without using extended state observers and b) respecting the original system order in a time-varying simplified model while avoiding algebraic estimation techniques. The proposed control technique based on the TMS320F28335 digital signal processor chip is tested by means of realistic simulations and experimental setup.     

倒立摆的自抗扰解耦控制方法研究

针对高阶次、多变量、强耦合的倒立摆系统,提出了基于自抗扰解耦控制方法对其进行控制。该方法采用双通道复合控制的方式,突破摆角和小台车相耦合作用的定位控制难点,完成摆角和小台车精确定位控制。采用该方法无需进行精确的输入变量与输出变量配对,只需要对控制作用的耦合矩阵进行静态解耦,分别构建控制通道。对于模型摄动造成的影响和各子对象间的动态耦合作用可由状态观测器（ESO,extended state observer）来估计并反馈到控制器以进行补偿。最终通过调节控制系统的相关参数,达到摆角和小台车位移相耦合作用的定位控制。仿真结果表明：该方法能够完成摆角和小台车位移相耦合作用的定位控制,瞬态性能和稳态性能好,超调量小,具有良好的控制效果。     

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.     

Output tracking for nonlinear non-minimum phase systems and application to PVTOL aircraft

In this paper, we consider a class of multi-input multi-output (MIMO) nonlinear non-minimum phase systems. For such nonlinear system, an output tracking control approach based on decomposition is presented and applied to a planar vertical takeoff and landing (PVTOL) aircraft. The external dynamics of the system can be separated into minimum-phase and non-minimum-phase parts. The internal dynamics of the system is separated to linear part and nonlinear part, and the linear part of the internal dynamics is only related with the non-minimum phase part of the external dynamics and the states of itself. Consequently, two low-dimensional controllers are designed separately to stabilize the two subsystems, and make the overall closed-loop system stable in spite of the existence of disturbances. Through this method, the design of the controller parameters is very simple. The theoretical results are confirmed by computer simulations.     

离散型自抗扰控制器在四旋翼飞行姿态控制中的应用

本文首先介绍了自抗扰控制器的结构组成,包括跟踪微分器、扩张状态观测器以及非线性状态误差反馈律,及各部分的典型算法.针对四旋翼盘旋系统的姿态控制问题,设计了3种离散型自抗扰控制器,搭建了仿真结构图,并进行了参数整定,得到了优良的仿真结果.进而在实际装置上进行试验,调试出了令人满意的姿态实时控制结果.实时控制结果表明,文中所设计的自抗扰控制器可以满足控制精度及快速性的要求,并且具有抗干扰性能、稳定控制能力以及对非线性强耦合系统的解耦能力.最后,总结并分析了3种自抗扰控制器的优缺点及适用范围.     

飞机俯仰运动自抗扰控制器设计

提出了利用自抗扰控制器在大包线范围内设计飞机俯仰运动控制器的新方法．利用二阶自抗扰控制器补偿系统模型扰动和外扰，实现了纵向运动俯仰角变量的跟踪控制．自抗扰控制器直接依据飞机的非线性模型，符合飞机动力学模型摄动大的特点，在很大的包线范围内不需要改变控制器的结构和参数，简化了飞行控制律的设计过程．大包线范围内的仿真结果表明，系统具有良好的动态和稳态性能，控制器具有很强的鲁棒性，为解决大包线范围内的飞行控制问题提供了一种有效的新途径．     

非仿射纯反馈系统的间接自适应神经网络控制

针对非仿射纯反馈系统,提出了一种新的设计方案.与现有文献中方法不同,该方案不是直接利用逼近技巧构建理想的反馈控制器.首先通过自抗扰思想将非仿射纯反馈系统转化成含有未知控制系数以及未知非线性的仿射系统,并且证明了可行性.然后结合微分器和全调节径向基函数神经网络,利用自适应反演技巧设计了自抗扰控制器,微分器的引入避免了传统反演的计算复杂性.最后,从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致有界,并且证明了系统状态渐进收敛到零点的残集内.仿真例子验证了算法的有效性.     

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.      

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凋、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。     

具有多层感知器力矩补偿的机器人自抗扰控制

本文针对机器人系统的控制特性, 提出了一种基于自抗扰控制(ADRC)的关节控制算法, 该算法可以克服 传统控制算法中存在的如系统抗干扰能力弱, 控制性能受限于建模精度, 动态性能与稳态性能难以兼顾, 控制律设 计较为复杂等问题. 针对受控系统特性给出了一套实际控制器的完整设计方法与参数整定方法, 并根据控制性能指 标设计优化函数完成了最优控制参数的优化, 在系统参数辨识的基础上利用多层感知器(MLP)设计了对建模不确 定性的补偿网络. 数值仿真和实验结果均表明该算法能够实现机器人快速稳定的轨迹跟踪, 具有良好的控制精度 与很强的抗干扰能力, 此外该算法不依赖于精确的系统模型, 降低了实际设计和应用的难度, 具有很好的工程应用 价值.     

Fractional-order unstable pole-zero cancellation in linear feedback systems

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.     

双质量弹簧基准问题自抗扰控制研究

本文研究了自抗扰控制(ADRC)方法在双质量弹簧基准问题的应用.传统的自抗扰控制方法倾向于使用高增益控制来抑制扰动和模型不确定性,但是对于双质量弹簧基准问题,高增益在评分中受到较大惩罚,而且对于模型参数变化没有足够的鲁棒性.为解决这一问题,本文对ADRC设计提出了两种改进方案.首先,为了减小控制信号的幅度,将扩张状态观测器(ESO)的一个极点配置在原点.其次,采用阻尼比来调整带宽.结果表明,所提出的ADRC设计可以很好地解决双质量弹簧基准系统的控制问题.     

Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.     

Control design for arbitrary complex nonlinear discrete-time systems based on direct NNMRAC strategy

A novel scheme of neural network model reference adaptive control is proposed for arbitrary complex nonlinear discrete-time systems, i.e., non-minimum phase system, time-delay system and minimum phase system. An improved nearest neighbor clustering algorithm using an optimization strategy is introduced as the on-line learning algorithm to regulate the parameters of the RBFNN, which can simplify the neural network structure and accelerate the convergence speed. The clustering radius can be regulated automatically to guarantee the rationality of radius. Through constructing the pseudo-plant, the direct NNMRAC is also effective to the nonlinear non-minimum phase system. With the help of simulations, the control strategy based on direct RBFNN model reference adaptive control can not only make the multi-dimension nonlinear plants track multi-dimension reference signals quickly, but also endow the control systems with satisfying robustness.