Robust observer‐based output feedback controller for nonlinear systems with uncertain triangular and nontriangular nonlinearities and diagonal terms

In this paper, we provide a robust observer‐based output feedback control scheme for a class of nonlinear systems where there are uncertain triangular and nontriangular nonlinearities, nontrivial diagonal terms, and external disturbance. The presence of diagonal terms is the main generalized feature over the existing results. In order to handle the diagonal terms, there is a gain‐scaling factor in the proposed controller. Through the analysis, we show that all states and observer errors of the controlled system remain bounded. Moreover, the ultimate bounds of some states and observer errors can be made (arbitrarily) small by adjusting the gain‐scaling factor reflecting on the structure of nonlinearities and external disturbance. The validity of our control scheme is experimentally verified via the ball position control of an electromagnetic levitation system.     

Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

We consider a global regulation problem of a class of feedforward nonlinear systems with uncertain delays by output feedback. The considered system is a generalized feedforward time-delay nonlinear system in the sense that an additional uncertain constant delay exists in the main control input to the system and feedforward nonlinearity includes states and input which have uncertain time-varying delays. Moreover, when feedforward nonlinearity satisfies some restrictive condition, we extend our control problem to the case such that the delay in the main control input is also a time-varying delay. To globally regulate the considered system, we develop an output feedback controller whose gain-scaling factor involves an adaptive dynamic. Two examples are given for illustration.     

Robust fuzzy tracking control for robotic manipulators

In this paper, a stable adaptive fuzzy-based tracking control is developed for robot systems with parameter uncertainties and external disturbance. First, a fuzzy logic system is introduced to approximate the unknown robotic dynamics by using adaptive algorithm. Next, the effect of system uncertainties and external disturbance is removed by employing an integral sliding mode control algorithm. Consequently, a hybrid fuzzy adaptive robust controller is developed such that the resulting closed-loop robot system is stable and the trajectory tracking performance is guaranteed. The proposed controller is appropriate for the robust tracking of robotic systems with system uncertainties. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

Disturbance observer-based tracking control with prescribed performance specifications for a class of nonlinear systems subject to mismatched disturbances

This work investigates simultaneous prescribed performance tracking control and mismatched disturbance rejection problems for a class of strict-feedback nonlinear systems. A novel control scheme combining prescribed performance control, disturbance observer technique, and backstepping method is proposed. The disturbance estimations are introduced into the design of virtual control law design in each step to compensate the mismatched disturbances. To further improve the control performance, a prescribed performance function characterizing the error convergence rate, maximum overshoot, and steady-state error is used to construct the composite controller. The proposed controller guarantees transient and steady-state performance specifications of tracking error and provides much better disturbance attenuation ability simultaneously. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that all the states in the resulting closed-loop system are stable, and the tracking error evolves within the prescribed performance boundaries and asymptotically converges to zero even in the presence of mismatched external disturbances. Finally, theoretical results are illustrated and demonstrated by two simulation examples.     

On Robust Approximate Feedback Linearization: Control with Two Gain-scaling Factors

In this paper, we consider a problem of global stabilization for a class of approximately feedback linearized nonlinear systems. In order to handle more nonlinearity over the existing results, we provide a new feedback controller with two gain-scaling factors and we show that more nonlinearity can be treated by our control scheme. Moreover, we analytically show that the considered nonlinear systems can be stabilized by the proposed controller. Through comparison practical examples, we illustrate the improved features of our proposed control method.

     

具有外部扰动的PMSM系统的无模型自适应预测控制

针对于一类具有强耦合、负载不确定性和外界干扰的永磁同步电机(PMSM)系统,本文研究了基于无模型自适应预测控制(MFAPC)问题,并提出了一种新颖的MFAPC方案来实现有外界扰动的PMSM系统的速度追踪任务.所提出控制方案的主要优势在于仅使用了被控系统的输入/输出数据,并且对外界干扰具有较强的鲁棒性.此外,还讨论了闭环系统跟踪误差的收敛性以及有界输入有界输出的稳定性.最后,通过与传统的PI控制方案、原型无模型自适应控制(MFAC)方案的仿真结果相比较,验证了所提出MFAPC方案的有效性和优越性.     

具有未知输入干扰的补偿控制

针对系统存在干扰波形已知但干扰幅值未知或幅值无界的一类外界干扰,提出了一种实现干扰补偿的控制策略,并给出了具体的设计过程。通过对原系统构造一个新的系统输出并为其设计状态观测器,进而实现对状态和干扰的同时估计。此外,并将干扰的估计信息引入到控制律当中,从而实现系统对外界干扰的补偿控制,保证系统状态有界。仿真结果验证了这一控制方法的有效性。     

Improved Controller Design with Two Gain-scaling Factors for Global Asymptotic Stabilization of Nonlinear Systems via Matrix Inequality Approach

In this paper, we consider a problem of global asymptotic stabilization for nonlinear systems with the perturbed nonlinearity. We provide a stabilizing controller with two gain-scaling factors and a new controller design method with matrix inequality approach. In particular, we provide a new procedure for selecting gain-scaling factors which are associated with stabilizing the closed-loop system. As a result, our proposed control method widens the class of considered nonlinear systems and yields better control performance over the existing methods. Via several comparison examples, we illustrate the improved features of the proposed control method over the existing ones.

     

具有输入饱和的近空间飞行器鲁棒控制

针对近空间飞行器这一类存在外部扰动,输入饱和和参数不确定的多输入多输出线性系统,提出了一种基于干扰观测器的抗饱和鲁棒控制方案.将干扰观测器与抗饱和控制技术相结合,从而消除系统存在的未知外部扰动、输入饱和和不确定性对系统控制的影响.首先,设计干扰观测器对线性外部系统产生的未知扰动进行估计.然后根据干扰观测器输出,通过超前抗饱和方法设计抗饱和补偿器,并将其加入到鲁棒控制器的设计中,保证闭环系统存在输入饱和、未知外部扰动和参数不确定情况下的稳定性.为便于设计,干扰观测器、抗饱和补偿器和控制器设计矩阵均通过求解线性矩阵不等式得到.最后,将提出的鲁棒抗饱和控制方法应用于近空间飞行器,仿真结果验证了该控制方案的有效性.     

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.     

非仿射纯反馈非线性系统的自抗扰控制

针对一类具有外部扰动的不确定非仿射纯反馈非线性系统,结合反演和自抗扰技术,提出了一种新的控制设计方案,该方案中反演设计的每一步引入了自抗扰设计,同时采用微分器和扩展状态观测器分别估计虚拟控制的导数和系统的未知部分.与现有设计方法不同,它不是直接利用逼近定理来构建理想的控制器.该方案设计过程简单,并且通过输入状态稳定性分析证明了系统状态能渐近收敛到原点的任意小邻域内.仿真结果证实了该方法的有效性.     

Robust H∞ Tracking Control of Uncertain Robotic Systems with Periodic Disturbances

This paper addresses the problem of designing robust tracking control for a large class of uncertain robotic systems. A more general model of the external disturbance is employed in the sense that the external disturbance can be expressed as the sum of a modeled disturbance and an unmodeled disturbance, for example, any periodic disturbance can be expressed in this general form. An adaptive neural network system is constructed to approximate the behavior of unknown robot dynamics. An adaptive control algorithm is designed to estimate the behavior of the modeled disturbance, and in turn the robust H_∞ control algorithm is required to attenuate the effects of the unmodeled disturbance only. Consequently, an intelligent adaptive/robust tracking control scheme is constructed such that an H_∞ tracking control is achieved in the sense that all the states and signals of the closed‐loop system are bounded and the effect due to the unmodeled disturbance on the tracking error can be attenuated to any preassigned level. Finally, simulations are provided to demonstrate the effectiveness and performance of the proposed control algorithm.     

Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Algebraic estimation and active disturbance rejection in the control of flat systems

This paper proposes a feedback method for the control of uncertain systems with unknown external disturbances, which includes an algebraic estimator and relies on the Active Disturbance Rejection Control (ADRC) approach. The proposed estimator considers a generalized disturbance in order to deal with systems which may simultaneously present time varying parameters, external disturbances, un-modeled dynamics, and process noise. The on-line estimated disturbance is obtained by means of differential algebraic methods and it is used as the major part of an on-line feedback cancellation scheme aiming at linearization and uncertainty suppression. The algebraic estimator proposed in the paper makes unnecessary the use of classical extended state observers, which are widely used in ADRC. The speed of response and reliability of the proposed algebraic disturbance estimator-based control scheme was experimentally tested on three laboratory systems, including a system of directly-coupled DC motors, a roto-magnet system, and a disc and beam system, showing that the experimental results are in excellent agreement with the predictions of the theory.     

A nonregressor nonlinear disturbance observer-based adaptive control scheme for an underwater manipulator

A new nonlinear disturbance observer-based tracking control scheme for an underwater manipulator is presented in this paper. This observer overcomes the disadvantages of existing disturbance observers, which are designed or analyzed by the linear system techniques. It can be applied in underwater manipulator systems for various purposes such as payload compensation, interaction effects compensation, underwater current or external disturbance compensation, and independent system control. The performance of the proposed tracking control scheme is demonstrated numerically by the payload compensation and interaction effects compensation for a two degrees of freedom vertical underwater manipulator.     

Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control

A novel direct adaptive interval type-2 fuzzy neural network (FNN) controller in which linguistic fuzzy control rules can be directly incorporated into the controller is developed to synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances, in this paper. By incorporating direct adaptive interval type-2 FNN control scheme and sliding mode approach, two non-identical chaotic systems can be synchronized based on Lyapunov stability criterion. Moreover, the chattering phenomena of the control efforts can be reduced and the external disturbance on the synchronization error can be attenuated. The stability of the proposed overall adaptive control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded. From the simulation example, to synchronize two non-identical Chua’s chaotic circuits, it has been shown that type-2 FNN controllers have the potential to overcome the limitations of tpe-1 FNN controllers when training data is corrupted by high levels of uncertainty.     

Robust tracking enhancement of robot systems including motordynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance     

Stabilization and Tracking Control of X‐Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control

A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X‐Z inverted pendulum known as a special underactuated, non‐feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower‐order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X‐Z inverted pendulum, including a comparative simulation with an all‐state‐feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques.     

Adaptive backstepping controller design for nonlinear uncertain systems using fuzzy neural systems

In this article, we propose an adaptive backstepping control scheme using fuzzy neural networks (FNNs), ABC_FNN, for a class of nonlinear non-affine systems in non-triangular form. The nonlinear non-affine system contains the uncertainty, external disturbance or parameters variations. Two kinds of FNN systems are used to estimate the unknown system functions. According to the FNN estimations, the adaptive backstepping control (ABC_FNN) signal can be generated by backstepping design procedure such that the system output follows the desired trajectory. To ensure robustness and performance, a proportional-integral-surface function and robust controller are designed to improve the control performance. Based on the Lyapunov stability theory, the stability of a closed-loop system is guaranteed and the adaptive laws of the FNN parameters are obtained. This approach is also valid for nonlinear affine system with uncertainty or disturbance. The uncertainty and disturbance terms are estimated by FNNs and treated by the ABC_FNN scheme. Finally, the effectiveness of the proposed ABC_FNN is demonstrated through the simulation of controlling a nonlinear non-affine system and the continuously stirred tank reactor plant to demonstrate the performances of our approach.     

Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.