Robust nonlinear integral control

It is well known from linear systems theory that an integral control law is needed for asymptotic set-point regulation under parameter perturbations. The note presents a similar result fur a class of nonlinear systems in the presence of an unknown equilibrium due to uncertain nonlinearities and dynamic uncertainties. Both partial state and output feedback cases are considered. Sufficient small-gain type conditions are identified for existence of linear and nonlinear control laws. A procedure for robust nonlinear integral controller design is presented and illustrated via a practical example of fan speed control     

A new integral inequality and its applications to robust control problems of uncertain nonlinear systems

In this paper, a new integral inequality is presented. By combining this integral inequality with adaptive approach, new design methods can be developed to synthesize some adaptive robust control schemes for a large class of uncertain nonlinear systems and to deal with well the unknown nonlinearities appearing in uncertain nonlinear control dynamical systems. As an application of the presented integral inequality to control theory, the robust stabilization problem is considered for a class of uncertain strict‐feedback nonlinear systems with both time‐delay and unknown dead‐zone input nonlinearities. It is shown that there are two main merits in the design method based on the integral inequality presented in this paper. The first one is that one need not estimate and know the unknown nonlinearities to synthesize some stabilizing control schemes. The second one is that the resulting feedback control schemes have rather simple structure.     

Robust sampled-data fuzzy control of nonlinear systems with parametric uncertainties: Its application to depth control of autonomous underwater vehicles

This paper presents a new direct discrete-time design methodology of a robust sampled-data fuzzy controller for a class of nonlinear system with parametric uncertainties that is exactly represented by Takagi-Sugeno (T-S) fuzzy model. Based on an exact discrete-time fuzzy model in an integral form, sufficient conditions for a robust asymptotic stabilization of the nonlinear system are investigated in the discrete-time Lyapunov sense. It is shown that the resulting sampled-data controller indeed robustly asymptotically stabilizes the nonlinear plant. To illustrate the effectiveness of the proposed methodology, an example, a sampled-data depth control of autonomous underwater vehicles (AUVs) is provided.     

倒立摆的自适应积分反步控制策略

针对直线单级倒立摆在模型参数不确定和外部扰动情况下的稳定控制问题,提出一种自适应积分反步控制策略。采用拉格朗日方程建立倒立摆系统的运动学模型,为减少稳态误差,将误差积分项引入反步法,设计了倒立摆的控制器;对含有未知参数的系统非线性状态微分方程,设计适当的Lyapunov函数推导出系统未知参数的自适应更新律,削弱了参数不确定性的影响。将自适应积分反步控制与一般的反步法控制、模糊控制及神经网络控制的仿真结果进行了对比,并在LabVIEW开发环境下进行了实物实验。结果表明,自适应积分反步法可以较为迅速且精确地完成稳定控制,较好地克服系统参数不确定及外部扰动的影响,具有较强的鲁棒性。     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

Active disturbance rejection control of nonlinear SISO Lagrangian systems via endogenous injections and exogenous feedback for trajectory tracking

This article deals with a linear classical approach for the robust output reference trajectory tracking control of nonlinear SISO Lagrangian systems with a controllable (fat) tangent linearization around an operating equilibrium point. An endogenous injections and exogenous feedback (EIEF) approach is proposed, which is naturally equivalent to the generalized proportional integral control method and to a robust classical compensation network. It is shown that the EIEF controller is also equivalent, within a frequency domain setting demanding respect for the separation principle, to the reduced order observer based active disturbance rejection control approach. The proposed linear control approach is robust with respect to total disturbances and, thus, it is efective for the linear control of the nonlinear Lagrangian system. An illustrative nonlinear rotary crane Lagrangian system example, which is non-feedback linearizable, is presented along with digital computer simulations.     

Output feedback adaptive RISE control for uncertain nonlinear systems

In this article, committed to extending the robust integral of the sign of the error (RISE) feedback control to the working condition of output feedback, a novel output feedback controller with a continuously bounded control input which combines the adaptive control and integral robust feedback will be proposed for trajectory tracking of a family of nonlinear systems subject to modeling uncertainties. A novel adaptive state observer (ASO) with disturbance rejection performance is creatively constructed to derive real-time estimation of the unmeasured state signals. Moreover, a projection-type adaption law is integrated to handle parameter uncertainties and an integral robust term is employed to deal with external disturbances. It is shown that asymptotic estimation performance and meanwhile asymptotic tracking result can eventually be derived. Simulation validations are implemented to demonstrate the high tracking performance of the presented controller. Notably, the synthesized control algorithm can be readily extended to the Euler–Lagrange systems. Typically, it can be extended to practical electromechanical equipment such as three-dimensional vector forming robots to improve the real-time forming accuracy.     

基于自组织小波小脑模型关节控制器的不确定非线性系统鲁棒自适应终端滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以良好的跟踪性能及强鲁棒性为目标,提出基于自组织小脑模型(self-organizing wavelet cerebellar model articulation controller,SOWCMAC)的鲁棒自适应积分末端(terminal)滑模控制策略.首先,将小脑模型、自组织神经网络和小波函数各自优势相结合,给出一种SOWCMAC,以保证干扰估计方法具有快速学习能力和更好的泛化能力.其次,设计两种改进的terminal滑模面构造方法,并分别给出各自的收敛时间.然后,基于SOWCMAC和改进的积分terminal滑模面,给出不确定非线性系统鲁棒自适应非奇异terminal控制器的设计过程,其中通过构造自适应鲁棒项抑制干扰估计误差对系统跟踪性能的影响,并利用Lyapunov理论证明闭环系统的稳定性.最后,将该方法应用于近空间飞行器姿态的控制仿真实验,结果表明所提出方法有效性.     

Robust nonlinear H∞-output feedback control

This paper investigates the problem of robust H_∞-output feedback control for nonlinear systems with time-varying parameter uncertainty satisfying some integral functional constraints. We address the problem of designing a compensator such that the L₂-gain of the mapping from the exogenous input noise to the penalty output is minimized or guaranteed to be less than or equal to a prescribed value. We establish the interconnection between the robust nonlinear H_∞-control problem and the nonlinear H _∞-control problem, Based on this connection, a sufficient condition for the existence of a solution to the robust nonlinear H_∞-output feedback control problem is derived in terms of a “scaled” Hamilton-Jacobi inequality     

Robust adaptive tracking control for servo mechanisms with continuous friction compensation

In this paper, a robust adaptive tracking control scheme is developed for servo mechanisms with nonlinear friction dynamics. A continuously differentiable friction model is used to capture the friction behaviors (e.g. Stribeck effect, Coulombic friction and Viscous friction). The robust integral of the sign of the error (RISE) feedback term is employed to design an innovative adaptive controller to compensate nonlinear friction and bounded disturbances. To reduce the effect of noise pollution, the desired trajectory is employed to replace the output signal in controller design. The developed adaptive controller can guarantee the asymptotic tracking performance for nonlinear servo mechanisms in the presence of nonlinear friction and bounded disturbances. Comparative experimental results are used to validate the effectiveness of the developed control algorithm.     

Robust H-infinity integral sliding mode control for a class of uncertain switched nonlinear systems

This paper develops a new method to deal with the robust H-infinity control problem for a class of uncertain switched nonlinear systems by using integral sliding mode control. A robust H-infinity integral sliding surface is constructed such that the sliding mode is robust stable with a prescribed disturbance attenuation level γ for a class of switching signals with average dwell time. Furthermore, variable structure controllers are designed to maintain the state of switched system on the sliding surface from the initial time. A numerical example is given to illustrate the effectiveness of the proposed method.     

Robust tracking control of uncertain nonlinear systems with unknown control directions

A global robust tracking control design procedure is proposed for a class of uncertain nonlinear systems. The key point is that the signs of multiplicative uncertainties, the so-called control directions, are not assumed to be known a priori. The class of systems can be of arbitrary dynamic order and the unmatched additive uncertainties need not satisfy the global Lipschitz condition. It is proved that under the proposed control, all closed-loop states are bounded and the tracking error converges to any prescribed small neighborhood of the origin. The results of this paper enlarge the class of uncertain nonlinear systems for which global robust tracking control can be designed.     

Robust fuzzy tracking control for nonlinear networked control systems with integral quadratic constraints

This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints (IQCs) are satisfied while both time-varying network-induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities (LMIs) and parallel distributed compensation (PDC). Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.     

Modeling and robust decoupling control for hypersonic scramjet vehicle

In this paper, the modeling and the robust decoupling control for a generic hypersonic scramjet vehicle are studied. Firstly, the dynamics of the hypersonic vehicle are modeled by applying the Lagrangian approach, which captures the most primary characteristics such as elastic deformation, aerodynamics, aero-heating, variable mass, effect of spherical rotating earth and their inherent interactions. Then, a robust output decoupling controller is designed by using nonlinear dynamic inversion plus the desired proportional integral dynamics, and natural time-scale separation theorem between fast and slow variables. Finally, the nonlinear simulations confirm the effectiveness of the robust decoupling controller.     

Robust dissipative control for linear systems with dissipative uncertainty and nonlinear perturbation

This paper focuses on the problem of dissipative control for linear systems which are subjected to dissipative uncertainty and matched nonlinear perturbation. Specifically, quadratic dissipative uncertainty is considered, which contains norm-bounded uncertainty, positive real uncertainty and uncertainty satisfying integral quadratic constraints (IQCs) as special cases. We develop a linear matrix inequality (LMI) approach for designing a robust nonlinear state feedback controller such that the closed-loop system is quadratic dissipative for all admissible uncertainties. Furthermore, under some condition on the dissipative uncertainty, we show that the controller also guarantees the asymptotic stability of the closed-loop system. As special cases, robust H_∞ control and robust passive control problems for systems with nonlinear perturbation and norm-bounded uncertainty (respectively, generalized positive real uncertainty) are solved using the LMI approach.     

A robust optimal sliding‐mode control approach for magnetic levitation systems

This paper presents a robust optimal sliding‐mode control approach for position tracking of a magnetic levitation system. First, a linear model that represents the nonlinear dynamics of the magnetic levitation system is derived by the feedback linearization technique. Then, the robust optimal sliding‐mode control developed from the linear model is proposed. In the proposed control scheme, the integral sliding‐mode control with robust optimal approach is developed to achieve the features of high performance in position tracking response and robustness to the matched and unmatched uncertainties. Simulation and experimental results from the computer‐controlled magnetic levitation system are illustrated to show the validity of the proposed control approach for practical applications. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust impedance control of a hydraulic suspension system

A novel robust impedance control approach is developed to control dynamic behavior of a vehicle subject to road disturbances. This behavior is predetermined as an impedance rule to achieve passenger comfort and vehicle handling by the use of a hydraulically actuated suspension system. Impedance control law is simple, free of model and efficient to apply for a broad range of road conditions. Moreover, it relates comfort to handling. This control approach can provide a desired comfort when passing a bump, and both desired comfort and handling after passing a bump. Robust position and force controls are used to implement the robust impedance control with the presence of uncertainties. A transformed proportional–integral–derivative control is proposed to perform the robust control. The system stability is analyzed and analytical results are confirmed by simulations. A quarter‐car model of suspension system and a nonlinear model of hydraulic actuator are used to simulate the control system. Copyright © 2009 John Wiley & Sons, Ltd.     

A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.     

Robust adaptive control for uncertain nonlinear systems with unknown control directions and actuator nonlinearity

A robust adaptive control scheme is proposed for a class of uncertain nonlinear systems in strict feedback form with both unknown control directions and non-symmetric dead-zone nonlinearity based on backstepping design.The conditions that the dead-zone slopes and the boundaries are equal and symmetric are removed by simplifying nonlinear dead-zone input model,the assumption that the priori knowledge of the control directions to be known is eliminated by utilizing Nussbaum-type gain technique and neural networks(NN) approximation capability.The possible controller singularity problem and the effect of dead-zone input nonlinearity are avoided perfectly by combining integral Lyapunov design with sliding mode control strategy.All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the system is proven to be converged to a small neighborhood of the origin.Simulation results demonstrate the effectiveness of the proposed control scheme.     

Adaptive PI Hermite neural control for MIMO uncertain nonlinear systems

This paper presents an adaptive PI Hermite neural control (APIHNC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The proposed APIHNC system is composed of a neural controller and a robust compensator. The neural controller uses a three-layer Hermite neural network (HNN) to online mimic an ideal controller and the robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Moreover, a proportional–integral learning algorithm is derived to speed up the convergence of the tracking error. Finally, the proposed APIHNC system is applied to an inverted double pendulums and a two-link robotic manipulator. Simulation results verify that the proposed APIHNC system can achieve high-precision tracking performance. It should be emphasized that the proposed APIHNC system is clearly and easily used for real-time applications.