Adaptive complementary sliding-mode control for thrust active magnetic bearing system

An adaptive complementary sliding-mode control (ACSMC) system with a multi-input-multi-output (MIMO) recurrent Hermite neural network (RHNN) estimator is proposed to control the position of the rotor in the axial direction of a thrust active magnetic bearing (TAMB) system for the tracking of various reference trajectories in this study. First, the operating principles and dynamic model of the TAMB system using a linearized electromagnetic force model is derived. Then, a conventional sliding-mode control (SMC) system is designed for the tracking of various reference trajectories. Moreover, a complementary sliding-mode control (CSMC) system is adopted to reduce the guaranteed ultimate bound of the tracking error by half while using the saturation function as compared with the SMC. Furthermore, since the system parameters and the external disturbance are highly nonlinear and time-varying, the ACSMC is proposed to further improve the control performance and increase the robustness of the TAMB system. In the ACSMC, the MIMO RHNN estimator with estimation laws is proposed to estimate two complicated dynamic functions of the system on-line. In addition, a robust compensator is proposed to confront the minimum approximated errors and achieve the robustness. Finally, some experimental results for the tracking of various reference trajectories show that the control performance of the ACSMC is significantly improved comparing with the SMC and CSMC.     

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.     

Robust Dynamic Sliding-Mode Control Using Adaptive RENN for Magnetic Levitation System

In this paper, a robust dynamic sliding mode control system (RDSMC) using a recurrent Elman neural network (RENN) is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties. First, a dynamic model of the magnetic levitation system is derived. Then, a proportional–integral–derivative (PID)-type sliding-mode control system (SMC) is adopted for tracking of the reference trajectories. Moreover, a new PID-type dynamic sliding-mode control system (DSMC) is proposed to reduce the chattering phenomenon. However, due to the hardware being limited and the uncertainty bound being unknown of the switching function for the DSMC, an RDSMC is proposed to improve the control performance and further increase the robustness of the magnetic levitation system. In the RDSMC, an RENN estimator is used to estimate an unknown nonlinear function of lumped uncertainty online and replace the switching function in the hitting control of the DSMC directly. The adaptive learning algorithms that trained the parameters of the RENN online are derived using Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher order terms in Taylor series. Finally, some experimental results of tracking the various periodic trajectories demonstrate the validity of the proposed RDSMC for practical applications.      

H∞ decentralized fuzzy model reference tracking controldesign for nonlinear interconnected systems

In general, due to the interactions among subsystems, it is difficult to design an H_∞ decentralized controller for nonlinear interconnected systems. The model reference tracking control problem of nonlinear interconnected systems is studied via H_∞ decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H∞ model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H_∞ tracking control design problem for nonlinear interconnected systems. The problem of H _∞ decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

非线性互联系统的分散混合自适应智能控制

针对一类高阶互联MIMO非线性系统，利用TS模糊系统和神经网络的通用逼近能力，在神经网络控制器中引入模糊基函数，提出一种分散混合自适应智能控制器设计的新方案．基于等价控制思想，设计分散自适应控制器，无需计算TS模型．通过对不确定项进行自适应估计，取消了其存在已知上界的假设．通过理论分析，证明了闭环智能控制系统所有信号有界，跟踪误差收敛到零．     

Wavelet CMAC for MIMO uncertain nonlinear systems using a modified social ski-driver algorithm

This study uses a Mexican hat wavelet membership function for a cerebellar model articulation controller (CMAC) to develop a more efficient adaptive controller for multiple input multiple output (MIMO) uncertain nonlinear systems. The main controller is called the adaptive Mexican hat wavelet CMAC (MWCMAC), and an auxiliary controller is used to remove the residual error. For the MWCMAC, the online learning laws are derived from the gradient descent method. In addition, the learning rate values are very important and have a great impact on the performance of the control system; however, they are difficult to choose accurately. Therefore, a modified social ski driver (SSD) algorithm is proposed to find optimal learning rates for the control parameters. Finally, a magnetic ball levitation system and a nine-link biped robot are used to illustrate the effectiveness of the proposed SSD-based MWCMAC control system. The comparisons with other existing control algorithms have shown the superiority of the proposed control system.     

非线性相似组合系统的鲁棒输出跟踪控制*

研究一类具有相似结构的非线性不确定组合系统的分散输出跟踪控制问题,利用的相似结构,提出一种设计具有相似结构的分散滑模控制器的方法,所设计的控制器,对于所有允许的不确定性,均使系统输出渐近跟踪所给定的参考输出。     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式补偿后得到最终的复合控制律,实现对参考位置跟踪的快速性,准确性以及对总扰动的鲁棒性.值得注意的是,与传统EID结构中的龙伯格观测器相比,等价输入干扰滑模观测器中增加的非线性观测误差反馈项有助于提高状态估计的快速性和精确性.从理论上证明了该系统是全局一致毕竟有界的.仿真和实验结果表明,相较于基于EID观测器的模型预测控制方法和基于龙伯格观测器的积分模型预测控制方法,所提方法提高了磁悬浮球系统的跟踪性能,并且有效的抑制了系统不确定性和外部干扰.     

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     

A modeling and control approach to magnetic levitation system based on state-dependent ARX model

Magnetic levitation (Maglev) systems are usually strongly nonlinear, open-loop unstable and fast responding. In order to control the position of the steel ball in a Maglev system, a data-driven modeling approach and control strategy is presented in this paper. A state-dependent AutoRegressive with eXogenous input (SD-ARX) model is built to represent the dynamic behavior between the current of electromagnetic coil and the position of the ball. State-dependent functional coefficients of the SD-ARX model are approximated by Gaussian radial basis function (RBF) neural networks. The model parameters are identified offline by applying the structured nonlinear parameter optimization method (SNPOM). Based on the model, a predictive controller is designed to stabilize the magnetic levitation ball to a given position or to make it track a desired trajectory. The real-time control results of the proposed approach and the comparisons with other two approaches are given, which demonstrate that the modeling and control method presented in this paper are very effective and superior in controlling the fast-responding, strongly nonlinear and open-loop unstable system. This paper gives the real experimental evidence that the RBF-ARX model is capable of not only globally, but also locally capturing and quantifying a nonlinear and fast-response system's behavior, and the model-based predictive control strategy is able to work quite well in a wide working-range of the nonlinear system.     

Improved adaptive fuzzy backstepping control of a magnetic levitation system based on Symbiotic Organism Search

Magnetic levitation systems have become very important in many applications. Due to their instability and high nonlinearity, such systems pose a challenge to many researchers attempting to design high-performance and robust tracking control. This paper proposes an improved adaptive fuzzy backstepping control for systems with uncertain input nonlinear function (uncertain parameters and structure), and applies it to a magnetic levitation system, which is a typical representative of such systems. An adaptive fuzzy system is used to approximate unknown, partially known or uncertain input nonlinear functions of a magnetic levitation system. An adaptation law is obtained based on Ljapunov analysis in order to guarantee closed-loop stability and good tracking performance. Initial adaptive and control parameters have been initialized with Symbiotic Organism Search optimization algorithm, due to strong non-linearity and instability of the magnetic levitation system. The theoretical background of the proposed control method is verified with a simulation study and implementation on a laboratory experimental application.     

基于Backstepping方法的MIMO过程分散PID控制器设计

A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO) dynamic processes. The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops, therefore the sub-controllers can be efficiently flexibly designed in parallel prototype. The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach. As a complementary support to the design procedure, the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved. The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.     

Quasi-sliding mode based repetitive control for nonlinear continuous-time systems with rejection of periodic disturbances

A Quasi-Sliding Mode (QSM) based tracking control method for tackling Multiple-Input Multiple-Output (MIMO) nonlinear continuous-time systems with un-matching system uncertainties and exogenous disturbances is proposed. The presented Repetitive Control (RC) scheme ensures robust system stability when the system is subject to non-periodic uncertainties and exogenous disturbances. The complete rejection of periodic exogenous disturbances and a perfect tracking of non-periodic reference trajectories are achievable. In this paper, a practical application to a mass-spring-damper system is used to illustrate the validity of the proposed QSM based RC method.     

Backstepping-based Decentralized PID Controller Design for MIMO Processes

A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output(MIMO)dynamic processes.The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops,therefore the sub-controllers can be efficiently flexibly designed in parallel prototype. The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach.As a complementary support to the design procedure,the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved.The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.     

Direct adaptive neural control of nonlinear systems with extreme learning machine

A direct adaptive neural control scheme for a class of nonlinear systems is presented in the paper. The proposed control scheme incorporates a neural controller and a sliding mode controller. The neural controller is constructed based on the approximation capability of the single-hidden layer feedforward network (SLFN). The sliding mode controller is built to compensate for the modeling error of SLFN and system uncertainties. In the designed neural controller, its hidden node parameters are modified using the recently proposed neural algorithm named extreme learning machine (ELM), where they are assigned random values. However, different from the original ELM algorithm, the output weight is updated based on the Lyapunov synthesis approach to guarantee the stability of the overall control system. The proposed adaptive neural controller is finally applied to control the inverted pendulum system with two different reference trajectories. The simulation results demonstrate good tracking performance of the proposed control scheme.     

On the sliding mode control of MIMO nonlinear systems: An input‐output approach

We address the sliding mode control design problem for output reference trajectory tracking problems in the special class of MIMO flat systems known as static feedback linearizable systems. We assume unavailable system state components but rely on available inputs and measurable flat outputs. Each controller will largely ignore state and control input couplings by adopting a standard sliding mode controller scheme derived from the SISO case and used this as decoupled input‐to‐flat‐output model. The standard controller arises from a vastly simplified pure integration, additively perturbed, system. The simplified pure integration system controlled trajectories are shown to be time‐scale homotopically equivalent to those of the nonlinear flat system. The basic sliding surface coordinate function design is approached from the perspective of structural integral reconstructors requiring only the inputs and the flat outputs of the system. Integral structural reconstructors were introduced by Fliess et al for the control of linear SISO and MIMO systems, giving rise to the generalized proportional integral control method. Simulations are presented for SISO and MIMO systems and experimental results are reported for a two‐degree‐of‐freedom fully actuated robotic manipulator.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

Intelligent adaptive control for MIMO uncertain nonlinear systems

This paper investigates an intelligent adaptive control system for multiple-input–multiple-output (MIMO) uncertain nonlinear systems. This control system is comprised of a recurrent-cerebellar-model-articulation-controller (RCMAC) and an auxiliary compensation controller. RCMAC is utilized to approximate a perfect controller, and the parameters of RCMAC are on-line tuned by the derived adaptive laws based on a Lyapunov function. The auxiliary compensation controller is designed to suppress the influence of residual approximation error between the perfect controller and RCMAC. Finally, two MIMO uncertain nonlinear systems, a mass–spring–damper mechanical system and a Chua’s chaotic circuit, are performed to verify the effectiveness of the proposed control scheme. The simulation results confirm that the proposed intelligent adaptive control system can achieve favorable tracking performance with desired robustness.     

Self-sensing magnetic levitation using a LC resonant circuit

A self-sensing magnetic levitation system utilizing a LC resonant circuit is proposed by using the characteristic that the inductance of the magnetic system is varied with respect to the air gap displacement. An external capacitor is added into the electric system to make the levitation system statically stable, which much relieves the control effort required to stabilize the magnetic levitation system of having an intrinsic unstable nature. For the realization of the self-sensing magnetically levitated system, an amplitude modulation/demodulation method is used with a positive position feedback controller. Experimental results are presented to validate the proposed method.