Sliding mode control for an aerodynamic missile based on backstepping design

In order to solve the mismatched uncertainties of a class of nonlinear systems,a control method of sliding mode control (SMC) based on the backstepping design is proposed. It introduces SMC in to the last step of backstepping design to modify the backstepping algorithm. This combination not only enables the generalization of the backstepping design to be applied to more general nonlinear systems, but also makes the SMC method become effective in solving the mismatched uncertainties. The SMC based on the backstepping design is applied to the flight control system design of an aerodynamic missile. The control system is researched through simulation. The simulation results show the effectiveness of the proposed control method.     

不确定非线性系统的自适应反推高阶终端滑模控制

针对一类非匹配不确定非线性系统,提出一种神经网络自适应反推高阶终端滑模控制方案.反推设计的前1步利用神经网络逼近未知非线性函数,结合动态面控制设计虚拟控制律,避免传统反推设计存在的计算复杂性问题,并抑制非匹配不确定性的影响;第步结合非奇异终端滑模设计高阶滑模控制律,去除控制抖振,使系统对于匹配和非匹配不确定性均具有鲁棒性.理论分析证明了闭环系统状态半全局一致终结有界,仿真结果表明了所提出方法的有效性.     

非匹配不确定非线性系统的自适应反演滑模控制

针对一类具有非匹配不确定性的最小相位仿射非线性系统,研究其在未知扰动作用下的调节问题。基于自适应反演设计方法和变结构控制设计了控制方案,实现不确定系统的鲁棒调节。与经典反演设计相比,本方案允许非参数化不确定性,增强了控制系统的鲁棒性。     

基于NDOB的匹配/非匹配不确定性系统滑模控制

针对一类n阶匹配与非匹配不确定性和扰动共存的系统,提出了一种新颖的基于非线性干扰观测器的滑模控制方法。将非匹配扰动的估计值融入到滑模面,设计了集成扰动观测的滑模控制。与传统的滑模控制方法相比,该方法在匹配与非匹配不确定性和扰动出现时具有较好的抑制能力,并能有效地抑制切换增益所引起的抖振现象。利用李雅普诺夫理论和输入-输出稳定性概念严格证明了闭环系统的稳定性。最后通过两个仿真实例验证了所提控制方法的有效性。     

Discrete-time adaptive sliding mode control for uncertain systems based on multi-rate output measurement

This article presents the design of a discrete-time adaptive sliding mode control (SMC) for uncertain systems using the noisy multi-rate output measurement. It is assumed that the dynamic systems are described by a discrete-time state equation with mismatched uncertainties. The proposed discrete-time adaptive SMC is composed of the equivalent and the nonlinear switching controls, and it is derived based on a new sliding surface. A new least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed without the information of the statistics for the measurement noises and the initial state. In the design of the proposed discrete-time adaptive SMC, the un-measurable states and the uncertainties are, respectively, replaced as their estimates obtained from the proposed LSE, and the sliding coefficient matrices are selected such that the states for the systems are ultimately bounded, and the effect of the external disturbances to give the states is reduced as small as possible. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

非匹配不确定系统的自适应反步非奇异快速终端滑模控制

针对一类n阶非匹配不确定系统,提出一种自适应反步非奇异快速终端滑模控制方法.控制的前n-1步采用自适应反步控制策略,消除非匹配不确定性的影响;最后一步利用误差的积分构造非奇异快速终端滑模面,设计控制律使系统第n个状态有限时间收敛.该方法对系统中匹配和非匹配不确定项均具有鲁棒性,比自适应反步终端滑模方法具有更快的收敛速度.理论分析证明了闭环系统的稳定性,仿真结果验证了该方法的有效性.     

基于块控原理的变结构控制

针对一类非匹配不确定性的线性系统 ,基于块控原理 ,提出了一种变结构控制设计方法 .利用反演设计方法来处理系统中的非匹配不确定性 ,再用变结构控制方法来改善系统的性能 .仿真实例证明了所提出的方法的正确性和有效性     

A New Adaptive Sliding Mode Control of Uncertain Nonlinear Systems

In this paper, a new adaptive sliding mode control is proposed to control nonlinear systems with parametric uncertainties and matched and unmatched external disturbances. The proposed method first combines immersion and invariance (I&I) adaptive scheme with sliding mode control (SMC), which preserves the advantages of the two methods. The proposed method is different from the approach of combining the backstepping adaptive scheme and sliding mode control in the parameter estimation law, which allows for prescribed dynamics to be assigned to the estimation error and is easier to tune. Finally, the method is applied to control a class of power systems, and simulation results show the advantages of the proposed method.     

基于反步法的一类非线性切换系统控制器设计

研究一类子系统是纯反馈非线性系统的切换系统控制器设计问题．基于多Lyapunov函数和反步法,提出一种状态反馈控制律及切换规则设计方法。通过递推设计可得到使非线性切换系统稳定的反馈控制律和切换规则．将所提出的方法应用于该类非线性切换系统含有不确定性的情形,仿真算例结果表明了所提出方法的有效性．     

基于神经网络的严反馈块非线性系统的鲁棒控制

针对非匹配不确定性的严反馈块非线性系统,基于神经网络提出一种鲁棒控制方法．利用Lyapunov稳定性定理推导出RBF神经网络的全调节律,用于处理系统中的非线性参数不确定性,提高了神经网络的在线逼近能力;采用神经网络和鲁棒控制方法,利用已知信息的同时,对控制系数矩阵未知时的设计问题进行处理,避免了控制器可能的奇异问题;引入非线性跟踪微分器,解决了Backstepping设计中的“计算膨胀”问题．运用Lyapunov稳定性定理证明了闭环系统的所有信号均最终一致有界．     

块控非线性系统自适应神经网络控制

针对一类含有非匹配不确定性的块控型多输入多输出非线性系统,提出一种基于反演技术和RBF神经网络的控制系统设计方案.通过引入一种改进型的Lyapunov函数,避免了控制矩阵未知情况下可能出现的奇异问题.在控制系统设计过程中,充分应用鲁棒自适应控制技术,解决了多输入多输出结构不确定性所带来的设计难题,得到了系统所有状态量将全局指数收敛至原点附近一个邻域的结论.最后的仿真结果表明了设计方案的正确性.     

非线性不确定系统的非奇异快速终端滑模控制

针对存在非匹配干扰的非线性系统,设计了一种基于干扰观测器和反步法的非奇异快速终端滑模控制.引入非线性干扰观测器估计系统的不确定性,利用反步的思想处理高阶非线性系统,从而可以将非线性干扰观测器估计的干扰值引入反步法的虚拟控制量中,同时设计一种新颖的非奇异快速终端滑模控制律保证系统的收敛速度和精度.利用Lyapunov函数从理论上证明了所设计的控制器可以保证闭环系统的有限时间收敛.最后通过数值仿真验证了所设计的控制方法的有效性.     

A New Robust Adaptive Control of Uncertain Nonlinear Systems and Pendulum Application

A new robust adaptive control of uncertain nonlinear systems is proposed in this paper. The proposed method combines sliding mode control with the immersion and invariance (I&I) adaptive scheme, and it has more available degrees of freedom than using the backstepping scheme. Via the proposed method, a class of nonlinear systems with mismatched parametric perturbations can be rendered asymptotically stable and the performance of the system can also be improved. Finally, the proposed method is applied to a simple pendulum with motor dynamics, and simulation results show the effectiveness and performance of the proposed method.     

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

This paper addresses the control problem of adaptive backstepping control for a class of nonlinear active suspension systems considering the model uncertainties and actuator input delays and presents a novel adaptive backstepping‐based controller design method. Based on the established nonlinear active suspension model, a projector operator–based adaptive control law is first developed to estimate the uncertain sprung‐mass online, and then the desirable controller design and stability analysis are conducted by combining backstepping technique and Lyapunov stability theory, which can not only deal with the actuator input delay but also achieve better dynamics performances and safety constraints requirements of the closed‐loop control system. Furthermore, the relationship between the input delay and the state variables of this vehicle suspension system is derived to present a simple and effective method of calculating the critical input delay. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller.     

一种基于反步法的鲁棒自适应终端滑模控制

针对不确定严格反馈块控非线性系统, 提出了一种基于反步法的鲁棒自适应终端滑模变结构控制方法. 系统的未知不确定及外界干扰由模糊系统在线逼近, 利用反步法设计了变结构控制的终端滑模面, 并由此得到了鲁棒自适应终端滑模控制器, 使系统的跟踪误差在有限时间内趋于给定轨迹的任意小的邻域内. 通过Lyapunov定理证明了闭环系统所有信号最终有界. 对某战斗机6自由度机动仿真结果表明, 该方法具有强鲁棒性.     

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.     

Adaptive Fuzzy Control for Nonlinear Time‐Delay Systems with Dynamical Uncertainties

In this paper, an adaptive fuzzy backstepping robust control approach is proposed for a class of SISO nonlinear strict‐feedback systems. The nonlinear systems addressed in this paper are assumed to possess three uncertainties: (i) the unstructured uncertainties; (ii) the time delays; and (iii) the dynamics uncertainties. In adaptive backstepping recursive design, fuzzy logic systems are used to approximate the unstructured uncertainties. A nonlinear damping technique and Lyapunov–Krasovskii functions are introduced to cancel the effects of the dynamics uncertainties and deal with the time delays, respectively. Combining the backstepping technique and a small gain approach, a stable adaptive fuzzy robust control approach is developed. It is proved that all the signals of the closed‐loop system are semi‐golablly uniformaly ultimately bounded (SUUB). The effectiveness of the proposed approach is illustrated by a simulation example.     

Robust stabilization of uncertain nonholonomic systems with strong nonlinear drifts

This paper investigates the robust stabilization of the nonholonomic control systems with strongly non- linear uncertainties. In order to make the state scaling effective and to prevent the finite time escape phenomenon from happening, the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization. The recursive integrator backstepping technique is applied to the design of the robust controller. The simulation example demonstrates the efficiency and robust features of the proposed method.     

Adaptive output feedback control for nonholonomic systems with uncertain chained form

The output feedback adaptive control problem is investigated for nonholonomic systems with strongly nonlinear uncertainties and unknown virtual control directions. A nonlinear output feedback switching controller based on the output measurement of the first subsystem is employed in order to make the state scaling effective and ensure the convergence of the system states. The novel observer/estimator is introduced for state and unknown parameter estimates. The integrator backstepping technique by the use of a constructive recursive is applied to the design of the adaptive controller and to overcome the unknown virtual control directions. The simulation result validates the effectiveness of the proposed scheme.     

Adaptive backstepping control for an engine cooling system with guaranteed parameter convergence under mismatched parameter uncertainties

This paper proposes a novel adaptive backstepping control for a special class of nonlinear systems with both matched and mismatched unknown parameters. The parameter update laws resemble a nonlinear reduced-order disturbance observer. Thus, the convergence of the estimated parameter values to the true ones is guaranteed. In each recursive design step, only single parameter update law is required in comparison to the existing standard adaptive backstepping techniques based on overparametrization and tuning functions. To make a fair comparison with the overparametrization and tuning function methods, a second-order nonlinear engine cooling system is taken as a benchmark problem. This system is subject to both matched and mismatched state-dependent lumped disturbances. Moreover, the proposed model-based controllers are compared with a classical PI control by using performance metrics, i.e., root-mean-square error and control effort. The comparative analysis based on these performance metrics, simulations as well as experiments highlights the effectiveness of the proposed novel adaptive backstepping control in terms of asymptotic tracking, global stability and guaranteed parameter convergence.