Design and stability analysis of a variable structure adaptive backstepping controller

This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS‐ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS‐ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

具有模糊监督控制器的积分变结构间接自适应控制

针对一类不确定非线性系统, 基于变结构控制原理, 并利用具有非线性可调参数的模糊系统去逼近过程未知函数, 提出一种具有模糊监督控制器的积分变结构间接自适应控制方案. 该方案通过监督控制器保证闭环系统所有信号有界. 进一步, 通过引入最优逼近误差的自适应补偿项来消除建模误差的影响. 理论分析证明了跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

Smooth indirect adaptive sliding mode control

In this paper, an indirect approach to the dual‐mode adaptive robust controller (DMARC) is proposed, which combines the typical transient and robustness properties of variable structure systems with a smooth control signal in steady state, typical of conventional adaptive controllers, as model reference adaptive controller. The aim of this indirect version, here named indirect DMARC, is to provide a more intuitive controller design, based on physical plant parameters, as resistances, inertia moments, capacitances, and so on, maintaining DMARC properties. In this paper, a stability analysis for the proposed controller and simulations to an unstable second‐order plant will be presented. Copyright © 2013 John Wiley & Sons, Ltd.     

Robustness analysis of discrete-time indirect model reference adaptive control with normalized adaptive laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control (MRAC) with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter axe also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.     

高频增益符号未知时的变结构模型参考自适应控制:任意相对阶的控制律设计

讨论被控对象相对阶大于1且高频增益符号未知时的变结构模型参考自适应控制问题,从而将相对阶为1时的结果推广到任意相对阶.首先对关键信号构造监控函数,并在此基础上提出了一种控制信号切换律.进而证明,当被控对象相对阶大于1、高频增益符号未知时,在监控函数的监测下,相关控制信号经至多有限次切换后将停止切换,跟踪误差将收敛到一个残集内,且该残集可通过减小某些设计参数而变得任意小.特别,本文证明,与相对阶为1时相同,当对象相对阶大于1时,若系统的某些初始条件为零,则至多只需要一次切换.     

Direct adaptive control using an adaptive reference model

Direct model reference adaptive control is considered when the plant-model matching conditions are violated due to large changes in the plant or incorrect knowledge of the plant's mathematical structure. Because of the mismatch, the plant can no longer track the original reference model, but may be able to track a modified reference model that still provides satisfactory performance. The proposed approach uses a time-varying ‘adaptive’ reference model that reflects the achievable performance of the changed plant. The approach consists of direct adaptation of state feedback gains for state tracking and simultaneous estimation of the plant-model mismatch. The reference model adapts to the changed plant, and is redesigned if the estimated plant-model mismatch exceeds a bound determined via robust stability and/or performance criteria. The resulting controller offers asymptotic state tracking in the presence of plant-model mismatch as well as matched parameter deviations.     

Tracking and parameter identification for model reference adaptive control

We provide barrier Lyapunov functions for model reference adaptive control algorithms, allowing us to prove robustness in the input‐to‐state stability framework and to compute rates of exponential convergence of the tracking and parameter identification errors to zero. Our results ensure identification of all entries of the unknown weight and control effectiveness matrices. We provide easily checked sufficient conditions for our relaxed persistency of excitation conditions to hold. Our illustrative numerical example demonstrates the performance of the control methods.     

Direct and indirect model reference adaptive control

The paper considers the control of an unknown linear time-invariant plant using Direct and Indirect Model Reference Adaptive Control. Employing a specific controller structure and the concept of positive realness, adaptive laws are derived using Indirect Control which are identical to those obtained in the case of Direct Control. The stability questions that arise are also shown to be the same. Simulation results using the new scheme are presented for the control of both stable and unstable plants.     

Robust model reference adaptive control for transient performance enhancement

To circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L₂‐norm and Cauchy‐Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high‐gain adaptation. In addition, the frequency‐domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high‐gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.     

一类非线性系统的积分变结构模糊自适应跟踪控制

针对一类具有未知常数控制增益的不确定非线性系统,基于变结构控制原理,并利用具有非线性可调参数的模糊系统逼近等价控制,提出一种具有监督控制器的积分变结构模糊自适应跟踪控制策略.该策略通过监督控制器保证闭环系统所有信号有界.进一步,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响.理论分析证明了跟踪误差能够收敛到零.仿真结果表明了该方法的有效性.     

Robust variable structure model reference adaptive control

A new variable structure model reference adaptive control scheme is proposed in this paper to achieve robustness to bounded disturbance. A key feature of this scheme is that the knowledge of neither the upper bound on the disturbance nor the upper bound on the norm of the matching controller parameters is required. Another advantage of the scheme is its zero output error tracking     

间接型的混杂模型参考自适应控制

针对相对阶为1的理想系统,本文考虑了具有混杂自适应律的间接型模型参考自适应控制问题.通过建立系统和控制器的离散参数估计和它们的插值四者之间关系的性质,严格地分析了闭环系统的稳定性,证明了闭环系统中所有的信号都一致有界,并且跟踪误差渐进收敛于零.     

一种具有强鲁棒性的模型参考自适应控制系统

提出一种模型参考自适应控制系统．该系统只要求知道对象阶次的上界,不要求对象严格正实和最小相位,并且允许存在建模误差和作用在对象任何部位的大幅值高频干扰．系统的强鲁棒性来源于特殊的系统结构和对信号的良好滤波．Lyapunov稳定性理论证明了系统的渐近稳定性,Matlab仿真验证了系统的强鲁棒性．     

An adaptive variable structure control for a class of nonlinear systems

Motivated by the recent advance in adaptive output-feedback control for a class of nonlinear systems which can be transformed into the so-called output-feedback form [7,10,11], an adaptive structure controller is proposed in this paper to solve the nonlinear model reference adaptive control problem. It is shown that an asymptotic output tracking performance can be achieved for this class of nonlinear system even if some nonlinearity is not available or some unknown parameters are fast time-varying.     

Improving transient performance of adaptive control via a modified reference model and novel adaptation

This paper presents a new model reference adaptive control (MRAC) framework for a class of nonlinear systems to address the improvement of transient performance. The main idea is to introduce a nonlinear compensator to reshape the closed‐loop system transient, and to suggest a new adaptive law with guaranteed convergence. The compensator captures the unknown system dynamics and modifies the given nominal reference model and the control action. This modified controlled system can approach the response of the ideal reference model. The transient is easily tuned by a new design parameter of this compensator. The nominal adaptive law is augmented by new leakage terms containing the parameter estimation errors. This allows for fast, smooth and exponential convergence of both the tracking error and parameter estimation, which again improves overall reference model following. We also show that the required excitation condition for the estimation convergence is equivalent to the classical persistent excitation (PE) condition. In this respect, this paper provides an intuitive and numerically feasible approach to online validate the PE condition. The salient feature of the suggested methodology is that the rapid suppression of uncertainties in the controlled system can be achieved without using a large, high‐gain induced, learning rate in the adaptive laws. Extensive simulations are given to show the effectiveness and the improved response of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamical adaptive integral backstepping variable structure controller design for uncertain systems and experimental application

In this study, a dynamical adaptive integral backstepping variable structure control (DAIBVSC) system based on the Lyapunov stability theorem is proposed for the trajectory tracking control of a nonlinear uncertain mechatronic system with disturbances. In this control scheme, no prior knowledge is required on the uncertain parameters and disturbances because it is estimated by two types of dynamical adaptive laws. These adaptive laws are integrated into the dynamical adaptive integral backstepping control and variable structure control (VSC) parts of the DAIBVSC. The dynamical adaptive law in the dynamical adaptive integral backstepping control part updates parametric uncertainties, while the other in the VSC part adapts upper bounds of non‐parametric uncertainties and disturbances. In order to achieve a more robust output tracking and better parameter adaptation, the control system is extended by one integrator and sliding surface is augmented by an integral action. Experimental evaluation of the DAIBVSC is conducted with respect to performance and robustness to parametric uncertainties. Experimental results of the DAIBVSC are compared with those of a traditional VSC. The proposed DAIBVSC exhibits satisfactory output tracking performance, good estimation of the uncertain parameters and can reject disturbances with a chattering free control law. Copyright © 2017 John Wiley & Sons, Ltd.     

一类非线性时滞系统的鲁棒间接自适应控制

针对一类不确定非线性时滞系统,基于变结构控制原理,利用多层神经网络逼近的能力,提出具有投影算法的间接自适应控制方案。该方案通过监督控制器保证闭环系统所有信号有界,并引入综合误差的自适应补偿项来消除建模误差的影响。理论分析证明跟踪误差收敛到零,仿真结果表明该方法有的效性。     

滑模预测离散变结构控制

研究了不确定离散时间系统的变结构控制设计问题,提出了基于滑模预测思想的离散变结构控制系统设计新思路.该方法综合考虑抖振、鲁棒性以及控制量约束等指标要求,利用当前及过去时刻的滑模信息预测未来时刻的滑模动态,实现了滚动优化求解.仿真结果表明,该方法可有效消除抖振现象,并能够保证闭环系统的鲁棒稳定性.     

直升机强跟踪自适应变稳控制器设计

变稳控制是直升机飞行模拟的关键技术之一, 气动参数的不确定性是其设计的困难所在. 对此, 提出了利用双目标直升机模型构造原型直升机的强跟踪自适应变稳控制器, 它将强跟踪的反馈补偿机构和自适应控制参数设计相分离, 简化了控制设计, 同时实现了提高自适应参数修正过程的系统稳定裕度和显著降低跟踪误差的目的. 仿真实验结果验证了所提出方法的有效性和可行性.     

Delta算子系统的全程滑模变结构控制

将全程滑模变结构控制思想引入Delta算子系统,给出了一种设计全程滑模控制方法．系统轨线一开始就位于切换面上,消除了非滑动模态运动,从而增强了系统的鲁棒性．利用Delta算子的离散特性求出系统不确定性近似值,从而在控制器设计过程中消去不确定项．仿真结果验证了该方法的有效性．