Model-based feedforward precompensation and VS-type robust nonlinear postcompensation for uncertain robotic systems with/without knowledge of uncertainty bounds(I)

In this paper, a robust motion tracking control algorithm for robotic manipulators is proposed where the higher-order system uncertainties are taken into account. The control structure consists of two main parts: a model-based precompensation part and a robust nonlinear controller one. Specifically, with knowledge of possible upper bounds on uncertainties, we propose the nonadaptive version of robust controller. Stability and robustness issues of the controllers have been investigated via a Lyapunov method and it is shown that the proposed control algorithms are highly robust in the presence of significant system uncertainties. Finally, the computer simulation results are presented to validate the proposed algorithm.     

Identification of uncertain nonlinear systems for robust fuzzy control

In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by S?krjanc et al. (2005) [11] and [12]. With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.     

Lyapunov theory based robust control of complicated nonlinear mechanical systems with uncertainty

This paper presents a robust control approach for nonlinear uncertain crane systems with a three DOF framework. We deal with an overhead crane in which a trolley located on the top is moved to x- and y-axes independently. We first approximate the nonlinear system model through feedback linearization transformation to simply construct a PD control and then design a robust control system for compensating control deviation feasibly occurring due to modeling error or system perturbation in practice. An adaptive control rule is analytically derived by using Lyapunov stability theory given bounds of system perturbation. We accomplish numerical simulation for evaluating the proposed methodology and demonstrate its superiority by comparing with the traditional control strategy. This paper was recommended for publication in revised form by Associate Editor Dong Hwan Kim Hyun Cheol Cho received a B.S. from the Pukyong National University in 1997, a M.S. from the Dong-A University, Korea in 1999, and a Ph.D. from University of Nevada-Reno, USA in 2006. He is currently a post-doc researcher in the Dept. of Electrical Engineering, Dong-A University. His research interests are in the areas of control systems, neural networks, stochastic process, and signal processing.     

Design of H(infinity) robust fault detection filter for linear uncertain time-delay systems

In this paper, the robust fault detection filter design problem for linear time-delay systems with both unknown inputs and parameter uncertainties is studied. Using a multiobjective optimization technique, a new performance index is introduced, which takes into account the robustness of the fault detection filter against disturbances and sensitivity to faults simultaneously. The reference residual model is then designed based on this performance index to formulate the robust fault detection filter design problem as an H(infinity) model-matching problem. By applying robust H(infinity) optimization control technique, the existence condition of the robust fault detection filter for linear time-delay systems with both unknown inputs and parameter uncertainties is presented in terms of linear matrix inequality formulation, independently of time delay. In order to detect the fault, an adaptive threshold which depends on the inputs is finally determined. An illustrative design example is used to demonstrate the validity of the proposed approach.     

一类不确定性时滞系统的鲁棒控制器设计

本文讨论了一类非匹配时滞系统的鲁棒自适应控制和非线性控制问题.所讨论系统包含时滞及不确定性扰动项,且扰动项关于具有未知增益的高阶多项式函数有界而不是关于线性函数有界.利用Lyapunov-Krasovskii方法提出了保证系统渐近稳定的自适应控制器设计方法,相应的控制器是时滞依赖的.并利用Razumikhin引理给出了能使系统一致最终有界稳定的时滞独立的控制器设计方法.     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.     

基于神经网络的一类不确定非线性系统自适应H∞跟踪控制

基于神经网络针对一类具有输入不确定性的非线性系统提出了一种H∞自适应跟踪控制方法.控制器由等效控制器、H∞控制器及参数自适应控制器三部分组成.H∞控制器用于减弱外部及神经网络的逼近误差对跟踪性能的影响,参数自适应控制器用于抑制输入干扰对跟踪性能的影响.所设计的控制器不仅保证了整个闭环系统的稳定性,而且使外部干扰及神经网络的逼近误差对跟踪的影响减小到给定的性能指标.最后给出一个算例验证了该方法的有效性.     

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.     

Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.     

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.     

Robust Control of multi-echelon production-distribution systems with limited decision policy (II)

A typical production-distribution system consist of three main echelons representing the retailer, distributors, and a factory each with an on-site warehouse. The system is sufficiently general and realistic to represent many industrial situations. However, decision functions and parameters have been selected to apply particularly to the production and distribution of consumer durables. The flows included in the model are materials orders, and those information flows needed to support the material and order-rate decisions.     

Calculation and tuning of controllers for nonlinear systems with different-rate processes

A method for calculating the parameters of controllers for nonlinear nonstationary dynamic systems is proposed. The structure of the controller is a generalization of the structure of proportional-integral and proportional-integral-differential controllers. The method is applicable to unstable nonlinear systems with incomplete information on the plant model. The method is based on the deliberate formation of different-rate processes in a control system in which the stability of fast processes is provided by choosing the controller parameters, and the slow processes formed correspond to the reference model of the desired behavior of a nonlinear system. An example of the results of numerical simulation is given.     

Comment on “Further improvement on delay-range-dependent robust absolute stability for Lur׳e uncertain systems with interval time-varying delays” by P. Liu [ISA Trans. 58(2015)58–66]

In a recent paper (ISA Transactions (2015)58: 58–66), an integral inequality has been proposed to reduce the conservativeness of stability conditions for Lur׳e uncertain systems. We point out that there exist some errors in Theorems 1–8, and the correct theorems are presented. Finally, the allowable maximum admissible upper bound (MAUB) listed in Table 1, Table 2, Table 3, Table 4, Table 5 have been recalculated by using the correct results.     

Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2)

This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 <α<2. By using the Mittag-Leffler function, Laplace transform and the Gronwall–Bellman lemma, one sufficient condition is attained for the local asymptotical stability of a class of fractional order nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.     

Dynamic characterization of noise and vibration transmission paths in linear cyclic systems (II)

Linear cyclic systems (LCS’s) are a class of systems whose dynamic behavior changes periodically. Such a cyclic behavior is ubiquitous in systems with fundamentally repetitive motion. Yet, the knowledge of the noise and vibration transmission paths in LCS’s is quite limited due to the time-varying nature of their dynamics. The first part of this two-part paper derives a generic expression that describes how the noise and/or vibration are transmitted between two (or multiple) points in the LCS’s. In Part II, experimental validation of the theoretical development of Part I is provided. The noise and vibration transmission paths of the scroll and rotary compressors (two typical LCS’s) are examined to show that the LCS’s indeed generate a series of amplitude modulated input signals at the output, where the carrier frequencies are harmonic multiples of the LCS’ fundamental frequency. The criterion proposed in Part I to determine how well a given LCS can be approximated as a linear time-invariant systems (LTIS) is applied to the noise and vibration transmission paths of the two compressors. Furthermore, the implications of the experimental validations/applications are discussed in order to assess the applicability of the noise/vibration source and transmission path identification techniques based on the assumption that the system under consideration is linear and time-invariant.     

Determination of the saturation thickness and albedo factors for mercury(II) oxide and lead(II) oxide

It is important to know the saturation thickness and reflecting power of a target for accurate x-ray analysis. In the present work, the saturation thickness was determined by using photons scattered from mercury(II) oxide and lead(II) oxide targets. Also, albedo factors (albedo number, albedo energy and albedo dose) were determined experimentally. Mercury(II) oxide and lead(II) oxide were excited by 59.54 keV gamma rays emitted from a ²⁴¹Am annular radioactive source with 5 Ci activity by energy dispersive x-ray fluorescence. The scattered and emitted x-rays were counted by a high-purity germanium detector with a resolution of 182 eV at 5.9 keV at a scattering angle of 168^o. The saturation thickness decreased with the increasing mean atomic number. The albedo factors decreased with increasing target thickness.