ADAPTIVE SLIDING MODE BACKSTEPPING CONTROL OF NONLINEAR SYSTEMS WITH UNMATCHED UNCERTAINTY

This paper considers an adaptive backstepping algorithm for designing the control for a class of nonlinear continuous uncertain processes with disturbances that can be converted to a parametric semi‐strict feedback form. Sliding mode control using a combined adaptive backstepping sliding mode control (SMC) algorithm, is also studied. The algorithm follows a systematic procedure for the design of adaptive control laws for the output tracking of nonlinear systems with matched and unmatched uncertainty.     

A modified direct adaptive robust motion trajectory tracking controller of a pneumatic system

In this study, we developed and tested a high-precision motion trajectory tracking controller of a pneumatic cylinder driven by four costless on/off solenoid valves rather than by a proportional directional control valve. The relationship between the pulse width modulation （PWM） of a signal＇s duty cycle and control law was determined experimentally, and a mathematical model of the whole system established. Owing to unknown disturbances and unmodeled dynamics, there are considerable uncertain nonlinearities and parametric uncertainties in this pneumatic system. A modified direct adaptive robust controller （DARC） was constructed to cope with these issues. The controller employs a gradient type adaptation law based on discontinuous projection mapping to guarantee that estimated unknown model parameters stay within a known bounded region, and uses a deterministic robust control strategy to weaken the effects of unmodeled dynamics, disturbances, and parameter estimation errors. By using discontinuous projection mapping, the parameter adaptation law and the robust control law can be synthesized separately. A recursive backstepping technology is applied to account for unmatched model uncertainties. Kalman filters were designed sepa- rately to estimate the motion states and the derivative of the intermediate control law in synthesizing the deterministic robust control law. Experimental results illustrate the effectiveness of the proposed controller.     

单元机组的非线性自适应反演综合控制

针对同时考虑参数不确定性和外界干扰的单元机组整体模型(锅炉–汽轮机–发电机模型),提出了一种基于自适应反演法和协调无源性理论的非线性综合控制策略.首先,针对预处理后的被控对象各子系统,采用反演法得到汽门控制输入,然后以高压侧电压为控制目标对励磁部分进行优化设计,最后逐步递推设计燃料控制器.在控制律设计过程中,为克服模型参数的不确定性,避免可能出现的参数漂移,通过引入充分光滑投影算子设计了参数自适应律.同时,借助在控制律中添加阻尼项,以有效抑制外界干扰对控制品质的影响.仿真分析和变负荷实验的结果表明,本文所设计的综合控制策略同时优化了单元机组的有功和无功响应特性,使其具有良好的负荷跟踪性能、抗干扰能力和对模型不确定参数的鲁棒性.     

不匹配不确定性系统的近似变结构输出跟踪控制

针对一类具有不匹配不确定性的非线性系统,提出一种结合变结构控制方法及自适应控制方法输出跟踪控制器。首先提出一种保证不确定性系统跟踪误差指数稳定的近似变结构控制器;进而得到一种具有不确定性范数上界估计能力的自适应近似变结构控制器,并证明了所提出的自适应近似变结构控制器使跟踪误差在时间趋于无穷时收敛于零。     

干扰下的无人直升机自适应反步法鲁棒跟踪控制

针对无人直升机干扰下的鲁棒轨迹跟踪问题,设计了一种自适应反步控制方法.鉴于作用在直升机上的干扰是产生跟踪误差的主要原因,该方法的主要思想是寻求一种方法来补偿这种干扰.首先,将未建模动态如外部阵风干扰、配平误差、机身、垂尾、平尾以及其他可忽略的动态产生的力和力矩看成一种组合干扰,从而建立了一个方便反步法控制器设计的简化模型.当设计好反步法控制器后,设计了一个非线性自适应律来估计这种组合干扰,并通过将干扰估计值整合到反步控制器中,使得闭环跟踪系统的鲁棒稳定性得到了保证,即基于李雅普诺夫稳定性理论证明了所设的控制器对于干扰主动阻隔,特别是低频干扰的主动阻隔是有效的.最后,两个仿真研究验证了该方法是优于常规反步法和积分反步法的.     

Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays

In this paper, an adaptive backstepping tracking control scheme is proposed for a class of nonlinear state time‐varying delay systems, which are subject to parametric uncertainties and external disturbances. The bounds of the time delays and their derivatives are assumed to be unknown. Tuning functions method is exploited to construct the control law and adaptive laws. Unknown time‐varying delays are compensated by using appropriate Lyapunov–Krasovskii functional. It is shown that the proposed controller can guarantee the boundedness of all the closed‐loop signals. The tracking performance can be adjusted by choosing suitable design parameters. At the end, a simulation example is provided to illustrate the effectiveness of the design procedure. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive Dynamic Surface control of An electrohydraulic Actuator with Friction Compensation

In this paper, an adaptive nonlinear control scheme with a friction observer for position control of an electrohydraulic actuator is proposed. The observer based on the LuGre friction model is employed to compensate for the friction. Adaptation laws are used to handle parameter uncertainties in the actuator and friction model. The control law including dynamics of the observer is developed through a backstepping‐like dynamic surface control (DSC) technique. Experimental results have illustrated the success of the control scheme. The results also show that the adaptive DSC controller has better tracking performance than an adaptive backstepping and conventional PI controllers.     

一类非匹配不确定非线性系统的鲁棒跟踪控制制

针对一类半严格反馈型不确定非线性系统,提出一种鲁棒反演滑模变结构控制方法.采用反演控制方法设计了使前n-1阶子系统稳定的虚拟控制律,抑制非匹配不确定性的影响;在第n步设计了一种连续可导的滑模变结构控制律,消除控制抖振,实现了对存在未知不确定性及扰动系统的鲁棒输出跟踪.通过Lyapunov定理证明了闭环系统所有信号最终有界.仿真结果验证了该方法的有效性.     

Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach

In this paper, a direct adaptive fuzzy robust control approach is proposed for single input and single output (SISO) strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamical disturbances. No prior knowledge of the boundary of the nonlinear uncertainties is required. Fuzzy logic systems are used to approximate the intermediate stabilizing functions, and a stable direct adaptive fuzzy backstepping robust control approach is developed by combining the backstepping technique with the fuzzy adaptive control theory. The stability of the closed-loop system and the convergence of the system output are proved based on the small-gain theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

Adaptive Backstepping Tracking Control of a 6-DOF Unmanned Helicopter

This paper presents an adaptive backstepping control design for a class of unmanned helicopters with parametric uncertainties. The control objective is to let the helicopter track some pre-defined position and yaw trajectories. In order to facilitate the control design, we divide the helicopter's dynamic model into three subsystems. The proposed controller combines the backstepping method with online parameter update laws to achieve the control objective. The global asymptotical stability (GAS) of the closed-loop system is proved by a Lyapunov based stability analysis. Numerical simulations demonstrate that the controller can achieve good tracking performance in the presence of parametric uncertainties.      

Robust output tracking of nonlinear systems with mismatched uncertainties

The problem of robust output tracking for a class of uncertain nonlinear systems which do not satisfy the conventional matching condition is considered. The main assumption on the uncertainty is that the triangularity condition is satisfied. Based on backstepping method and input/output linearization approach, we propose a class of non-adaptive state feedback controllers which can guarantee exponential stability of the tracking error for the uncertain nonlinear systems first. Next, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we design a class of adaptive robust controllers. It is shown that under the proposed adaptive robust control the tracking error of the controlled system converges to zero as time approaches infinity.     

Variable Structure Control of Robot Manipulators with Perturbation Estimator

The idea of perturbation compensation is incorporated in variable structure control (VSC) of robot manipulators to cancel the effects of system parametric uncertainties and external disturbances and hence alleviate control chattering. By using the dynamic response of the robot as characterized by the sliding function, a technique is proposed to deduce the system perturbation signal. For practical implementation, a perturbation estimator is introduced to approximate the system uncertainties. Estimates of the bounds on modelling errors and external disturbances are not required while signal measurement uncertainties can be accommodated. The suggested VSC law ensures that the robot control system reaches the sliding mode in finite time and with prescribed transient behaviour. Detailed computer simulation results are presented to demonstrate the effectiveness of this new approach.     

Adaptive control and constrained control allocation for overactuated ocean surface vessels

In this article, the constrained control allocation is proposed for overactuated ocean surface vessels with parametric uncertainties and unknown external disturbances. The constrained control allocation is transformed into a convex quadratic programming problem and a recurrent neural network is employed to solve it. To complete the control allocation, the control command is derived via the backstepping method. Adaptive tracking control is proposed for the full-state feedback case using the backstepping technique and the Lyapunov synthesis. It is proved that the proposed adaptive tracking control is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system. Then, the obtained control command is distributed to each actuator of overactuated ocean vessels. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control and the constrained control allocation scheme.     

Robust adaptive control for a nonholonomic mobile robot with unknown parameters

A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.     

Robust Tracking Control Of The Variable Stiffness Actuator Based On The Lever Mechanism

This paper is concerned with the design of a robust adaptive tracking control scheme for a class of variable stiffness actuators (VSAs) based on the lever mechanisms. For these VSAs based on the lever mechanisms, the AwAS‐II developed at Italian Institute of Technology (IIT) is chosen as the study object, and it is an enhanced version of the original realization AwAS (actuator with adjustable stiffness). Firstly, for the dynamic model of the AwAS‐II system in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance and input saturation constraints, by using the coordinate transformations and the static state feedback linearization, the state space model of the AwAS‐II system with composite disturbances and input saturation constraints is transformed into an uncertain multiple‐input multiple‐output (MIMO) linear system with lumped disturbances and input saturation constraints. Subsequently, a combination of the feedback linearization, disturbance observer, sliding mode control and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the AwAS‐II system. Under the proposed controller, the semi‐global uniformly ultimately bounded stability of the closed‐loop system has been proved via Lyapunov stability analysis. Simulation results illustrate the effectiveness and the robustness of the proposed robust adaptive tracking control scheme.     

Discrete-time robust backstepping adaptive control for nonlineartime-varying systems

This paper studies the problem of adaptive control for a class of nonlinear time-varying discrete-time systems with nonparametric uncertainties. The plant parameters considered here are not necessarily slowly time-varying in a uniform way. They are allowed to have a finite number of big jumps. By using the backstepping procedures with parameter projection update laws, a robust adaptive controller can be designed to achieve adaptive tracking of a reference signal for this class of systems. It is shown that the proposed controller can guarantee the global boundedness of the states of the whole adaptive system in the presence of parametric and nonparametric uncertainties. It can also ensure that the tracking error falls within a compact set whose size is proportional to the size of the uncertainties and disturbances. In the ideal case when there is no nonparametric uncertainties and time-varying parameters, perfect tracking can be achieved     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Inverse optimal adaptive backstepping control for spacecraft rendezvous on elliptical orbits

The spacecraft rendezvous problem with the target spacecraft on an arbitrary elliptical orbit is addressed using adaptive backstepping control. The relative motion of two spacecrafts is established based on the Lawden equations. In order to take the parametric uncertainties into consideration, an adaptive backstepping controller is proposed in this paper, which is optimal with respect to a family of cost functionals. With Lyapunov analysis, the proposed control laws can guarantee the globally asymptotic stability of the whole system and estimate the upper bounds of uncertain model parameters at the same time. Furthermore, a group of modified control laws is obtained, which stabilises the closed-loop system under input constraints. Finally, simulation results are presented to validate the effectiveness of the proposed approach.     

空天飞空天飞行器的自适应变论域模糊预测控制行器的自适应变论域模糊预测控制

考虑一类非线性不确定系统的变论域模糊预测控制问题.根据跟踪误差在线调整伸缩因子,使变论域模糊系统一致逼近被控对象中的未知干扰和不确定因素.通过引入鲁棒自适应控制器,消除了模糊建模误差,提高了系统的动态性能.基于泰勒展开的非线性预测控制律,避免了繁重的计算负担.基于Lyapunov理论,给出了伸缩因子的σ调整律,并证明了闭环系统一致最终有界.最后,将该算法用于空天飞行器(ASV)姿态控制系统的设计,仿真结果表明了该算法的有效性.