Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

基于干扰观测器的电液伺服系统反馈线性化滑模控制

为抑制电液伺服系统中各种非线性因素及不确定干扰,提出了基于输入输出反馈线性化的滑模控制与非线性干扰观测器相结合的控制策略以提高其位置控制跟踪精度。以电液振动台为试验对象,建立其非线性控制模型,利用李雅普诺夫稳定性理论保证了位置闭环系统的全局稳定性。利用MATLAB/Simulink对设计的控制器进行了仿真验证,结果验证了提出的控制器的可行性。为了模拟实际环境下存在不确定干扰,在位置电液系统基础上增加了电液加载系统,开展了试验研究。结果表明,该控制器能有效的提高干扰下电液伺服系统的位置跟踪性能。     

Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation

This paper proposes a new non-fragile stochastic control method to investigate the robust sampled-data synchronization problem for uncertain chaotic Lurie systems (CLSs) with time-varying delays. The controller gain fluctuation and time-varying uncertain parameters are supposed to be random and satisfy certain Bernoulli distributed white noise sequences. Moreover, by choosing an appropriate Lyapunov-Krasovskii functional (LKF), which takes full advantage of the available information about the actual sampling pattern and the nonlinear condition, a novel synchronization criterion is developed for analyzing the corresponding synchronization error system. Furthermore, based on the most powerful free-matrix-based integral inequality (FMBII), the desired non-fragile sampled-data estimator controller is obtained in terms of the solution of linear matrix inequalities. Finally, three numerical simulation examples of Chua's circuit and neural network are provided to show the effectiveness and superiorities of the proposed theoretical results.     

Iterative learning-based decentralized adaptive tracker for large-scale systems: a digital redesign approach

In this paper, a digital redesign methodology of the iterative learning-based decentralized adaptive tracker is proposed to improve the dynamic performance of sampled-data linear large-scale control systems consisting of N interconnected multi-input multi-output subsystems, so that the system output will follow any trajectory which may not be presented by the analytic reference model initially. To overcome the interference of each sub-system and simplify the controller design, the proposed model reference decentralized adaptive control scheme constructs a decoupled well-designed reference model first. Then, according to the well-designed model, this paper develops a digital decentralized adaptive tracker based on the optimal analog control and prediction-based digital redesign technique for the sampled-data large-scale coupling system. In order to enhance the tracking performance of the digital tracker at specified sampling instants, we apply the iterative learning control (ILC) to train the control input via continual learning. As a result, the proposed iterative learning-based decentralized adaptive tracker not only has robust closed-loop decoupled property but also possesses good tracking performance at both transient and steady state. Besides, evolutionary programming is applied to search for a good learning gain to speed up the learning process of ILC.     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

四旋翼不确定干扰前馈补偿与反步滑模姿态控制

针对四旋翼控制中由外部不确定干扰和系统参数不确定引起的具有时变特性的不确定界干扰问题,设计一种不确定干扰前馈补偿的反步滑模姿态抗干扰控制方法。采用牛顿欧拉方法建立带不确定干扰的四旋翼6自由度动力学模型,然后采用非线性干扰观测器对姿态系统中的不确定干扰进行观测估计,进而基于不确定干扰估计量的前馈补偿设计反步滑模控制器,最后通过Lyapunov理论验证了系统的稳定性。仿真结果表明,所设计的控制器可以有效解决外部干扰和系统参数不确定导致的系统高阶不确定性问题,实现不确定干扰下的四旋翼鲁棒控制,同时改善传统滑模中控制输入不连续的情况。通过仿真与抗干扰飞行实验验证了所设计的控制策略在应对快时变特性干扰时具有较好的鲁棒性。     

H∞ output-feedback fuzzy proportional-integral control of fully delayed input/output systems

This paper presents the output-feedback fuzzy proportional-integral (PI) controller design for uncertain nonlinear systems with both fully delayed input and output. Based on the Takagi–Sugeno (T–S) fuzzy model representation, the output-feedback PI control is realized via parallel distributed PI compensation and novel LMI gain design. Although the T–S fuzzy PI controller is simple, asymptotic output regulation is assured to overcome the effect of uncertainty, state delay, and full input/output delays. When considering disturbance and measurement noise, the control performance is achieved by robust gain design. Furthermore, state observers and bilinear matrix inequality conditions are removed in this paper. Finally, time-delay Chua׳s circuit system and a continuous-time stirred tank reactor are taken as applications to show the expected performance.     

State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities

This paper presents three fuzzy adaptive controllers for a class of uncertain multivariable nonlinear systems with both sector nonlinearities and dead zones: two first controllers are state feedbacks and the last controller is an output feedback. The design of the first controller concerns systems with symmetric and positive definite control–gain matrix, while the second control design is extended to the case of nonsymmetric control–gain matrix thanks to an appropriate decomposition, namely the product of a symmetric positive definite matrix, a diagonal matrix with diagonal entries +1 or ?1, and a unity upper triangular matrix. The third controller is an output feedback extension of the second controller. In this controller, a high-gain observer is incorporated to estimate the unmeasurable states. An appropriate adaptive fuzzy logic system is used to reasonably approximate the uncertain functions. A Lyapunov approach is adopted to derive the parameter adaptation laws and prove the stability of those control systems as well as the exponential convergence of their underlying tracking errors within an adjustable region. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.     

Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach

Robust control of a class of uncertain systems that have disturbances and uncertainties not satisfying “matching” condition is investigated in this paper via a disturbance observer based control (DOBC) approach. In the context of this paper, “matched” disturbances/uncertainties stand for the disturbances/uncertainties entering the system through the same channels as control inputs. By properly designing a disturbance compensation gain, a novel composite controller is proposed to counteract the “mismatched” lumped disturbances from the output channels. The proposed method significantly extends the applicability of the DOBC methods. Rigorous stability analysis of the closed-loop system with the proposed method is established under mild assumptions. The proposed method is applied to a nonlinear MAGnetic LEViation (MAGLEV) suspension system. Simulation shows that compared to the widely used integral control method, the proposed method provides significantly improved disturbance rejection and robustness against load variation.     

电液比例系统的H∞鲁棒性控制设计

针对电液比例系统中系统控制数学模型参数时变要求控制器鲁棒性强的特点,通过分析电液比例系统的物理模型,利用线性分式变换(LFT)方法,引入乘性不确定性参数,给出了参数时变的电液比例模型,并得出了具有参数不确定性系统状态空间函数模型。运用线性矩阵不等式(LM I)的H∞控制器的处理方法,设计出基于H∞控制的电液比例系统控制器。利用该控制器可有效的抑制参数时变对系统输出的影响。仿真表明该控制器在较大不确定参数的变动下,控制器仍然能够使系统具有较好的输出性能,结果说明该鲁棒控制器的有效性。     

人-车闭环中电动助力转向系统的基本特性分析

建立详细的四自由度电动助力转向(EPS)系统机械电气模型,考虑Fiala轮胎模型和二自由度整车模型,引入以转向盘输入角为反馈信号的驾驶员模型,构建装备EPS系统的人-车非线性闭环系统模型。采用模糊控制器确定目标电流并通过PID控制和脉冲宽度调制(PWM)实现其跟踪控制,构建电流闭环控制,并采用基于非线性控制设计(NCD)的单纯形自寻优法对参数进行优化。通过仿真计算,以转向盘输入转矩以及整车的横摆角速度、侧向加速度为指标,研究分析了EPS系统在人-车非线性闭环系统中的基本特性。     

Robust control of uncertain feedback linearizable systems based on adaptive disturbance estimation

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance.     

Output feedback model predictive control of hydraulic systems with disturbances compensation

Enhancing the robustness of output feedback control has always been an important issue in hydraulic servo systems. In this paper, an output feedback model predictive controller (MPC) with the integration of an extended state observer (ESO) is proposed for hydraulic systems. The ESO was designed to estimate not only the unmeasured system states but also the disturbances, which will be synthesized into the design of the output prediction equation. Based on the mechanism of receding horizon and repeating optimization of MPC, the output prediction equation will be updated in real time and the future behavior of the system will be accurately predicted since the disturbances are compensated effectively. Hence, the ability of the traditional MPC to suppress disturbances will be improved evidently. The experiment results show that the proposed controller has high-performance nature and strong robustness against various model uncertainties, which verifies the effectiveness of the proposed control strategy.     

电液力伺服系统自适应抗扰控制研究

考虑到电液伺服系统中存有各种非线性因素、不确定干扰以及参数时变,为了提高干扰下电液力伺服系统的控制精度,以电液伺服振动实验台作为控制对象,构建其非线性模型,同时使用参数自适应率对不定参数进行补偿,并在反演控制器中引入滑模控制以降低系统的干扰敏感性,利用Lyapunov理论保证闭环系统的全局稳定。对设计的控制器进行实验,模拟在有未知外部位置干扰下的力控制,提升系统的稳定性。实验结果证明,此控制方法能够有效地提升电液力伺服系统的抗干扰跟踪性能。     

Quasi-minimal active disturbance rejection control of MIMO perturbed linear systems based on differential neural networks and the attractive ellipsoid method

This study addresses the problem of designing an output-based controller to stabilize multi-input multi-output (MIMO) systems in the presence of parametric disturbances as well as uncertainties in the state model and output noise measurements. The controller design includes a linear state transformation which separates uncertainties matched to the control input and the unmatched ones. A differential neural network (DNN) observer produces a nonlinear approximation of the matched perturbation and the unknown states simultaneously in the transformed coordinates. This study proposes the use of the Attractive Ellipsoid Method (AEM) to optimize the gains of the controller and the gain observer in the DNN structure. As a consequence, the obtained control input minimizes the convergence zone for the estimation error. Moreover, the control design uses the estimated disturbance provided by the DNN to obtain a better performance in the stabilization task in comparison with a quasi-minimal output feedback controller based on a Luenberger observer and a sliding mode controller. Numerical results pointed out the advantages obtained by the nonlinear control based on the DNN observer. The first example deals with the stabilization of an academic linear MIMO perturbed system and the second example stabilizes the trajectories of a DC-motor into a predefined operation point.     

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.     

基于干扰抑制的汽车转向与悬架系统的集成控制

建立侧向风作用下的汽车整车横向和垂向非线性动力学模型。考虑到随机路面输入和侧向风干扰,利用L2增益干扰抑制的方法设计出电动助力转向(EPS)与主动悬架系统(ASS)的非线性输出反馈H控制器。在Matlab环境下对驾驶员—汽车—道路闭环系统进行仿真计算。结果表明,所设计的控制器能有效抑制路面随机输入和较大的侧向风干扰,改善车辆的操纵稳定性、转向轻便性和行驶平顺性。     

Decentralized output feedback stabilization for switched stochastic high-order nonlinear systems with time-varying state/input delays

This paper investigates decentralized output feedback stabilization problem for a class of switched stochastic high-order systems with time-varying state/input delays. With the help of coordinate transformations, a scaling gain is incorporated into the observers and controllers for the nominal system. Based on the homogeneous domination approach and stochastic Lyapunov–Krasovskii stability theorem, it is shown that global asymptotic stability in probability of the closed-loop system can be implemented by tuning the scaling gain. Two examples are given to demonstrate the feasibility of the proposed control method.     

Digital redesign of analog smith predictor for systems with input time delays

This paper presents a new methodology for digitally redesigning an existing analog Smith predictor control system, such that the cascaded analog controller with input delay can be implemented with a digital controller. A traditional analog Smith predictor system is reformulated into an augmented system, which is then digitally redesigned using the predicted intersampling states. The paper extends the prediction-based digital redesign method from a delay free feedback system to an input time-delay cascaded system. A tuning parameter v is optimally determined online such that in any sampling period, the output response error between the original analogously controlled time-delay system and the digitally controlled sampled-data time-delay system is significantly reduced. The proposed method gives very good performance in dealing with systems with delays in excess of several integer sampling periods and shows good robustness to sampling period selection.     

Design and analysis of a new AUV’s sliding control system based on dynamic boundary layer

The new AUV driven by multi-vectored thrusters not only has unique kinematic characteristics during the actual cruise but also exists uncertain factors such as hydrodynamic coefficients perturbation and unknown interference of tail fluid,which bring difficult to the stability of the AUV’s control system.In order to solve the nonlinear term and unmodeled dynamics existing in the new AUV’s attitude control and the disturbances caused by the external marine environment,a second-order sliding mode controller with double-loop structure that considering the dynamic characteristics of the rudder actuators is designed,which improves the robustness of the system and avoids the control failure caused by the problem that the design theory of the sliding mode controller does not match with the actual application conditions.In order to avoid the loss of the sliding mode caused by the amplitude and rate constraints of the rudder actuator in the new AUV’s attitude control,the dynamic boundary layer method is used to adjust the sliding boundary layer thickness so as to obtain the best anti-chattering effects.Then the impacts of system parameters,rudder actuator’s constraints and boundary layer on the sliding mode controller are computed and analyzed to verify the effectiveness and robustness of the sliding mode controller based on dynamic boundary layer.The computational results show that the original divergent second-order sliding mode controller can still effectively implement the AUV’s attitude control through dynamically adjusting the sliding boundary layer thickness.The dynamic boundary layer method ensures the stability of the system and does not exceed the amplitude constraint of the rudder actuator,which provides a theoretical guidance and technical support for the control system design of the new AUV in real complex sea conditions.