自适应线性自抗扰控制器的设计

自抗扰控制器对于抑制不确定的扰动有良好的效果,但其控制器参数较多且整定困难。为了实现自适应的线性自抗扰控制器,对线性自抗扰控制器的参数整定策略展开了研究。首先,设计了基于观测误差的线性扩张观测器参数自适应整定算法。接着,设计了自抗扰控制器线性反馈环节的参数的自适应整定算法。最后,利用李雅普诺夫方法,证明上述自适应整定算法得到的参数可以保证扩张状态观测器的观测误差和被控系统最终输出误差都收敛至零。实验结果表明:精密气浮运动平台低速工况下,自适应线性自抗扰控制器的参数在0.8s内即可迅速完成整定计算;线性扩张观测器观测误差绝对值小于2nm;被控精密气浮运动平台的速度波动不大于5%。自适应线性自抗扰控制器实现了控制器参数在线整定,控制器的性能表现满足要求。     

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.     

Active Vibration Control of SMA Actuated Structures using Fast Output Sampling Based Sliding Mode Control

Abstract

Fast Output Sampling (FOS) based discrete sliding mode control is designed for Shape Memory Alloy (SMA) actuated structures to suppress the structural vibration. For the design of discrete sliding mode control the reaching law, method proposed by W. Gao is used. The simulation results demonstrate the performance of the controller. The proposed control technique achieves good vibration suppression. This methodology is more practical and easier to implement, since the measurement or estimation of the system states is not needed for designing the controller.     

Fault tolerant system based on non-integers order observers: Application in a heat exchanger

This work presents a fault-tolerant (FT) scheme based on the application of non-integer order observers also called fractional observers, the case of study is a double pipe countercurrent heat exchanger (HE). The aim of the FT is to detect sensors faults as soon as possible, and to provide a healthy signal in order to replace the faulty sensor signal by the fractional observer estimation. To develop the FT scheme a bank of high gain fractional order observers (HGFOO) is proposed. The Riemann-Liouville (RL) fractional derivative definition is used to solve each fractional observer. Experimental measures from a HE were used to test the performance of the fractional observers and the control scheme. The results show the robustness of the proposed observers.     

Performance optimization of linear active disturbance rejection control approach by modified bat inspired algorithm for single area load frequency control concerning high wind power penetration

The linear active disturbance approach is employed to deal with the load frequency control issue of a single area wind power system based on doubly fed induction generator, and the performance of the control law is optimized by using the bat-inspired algorithm. The load frequency control issue has become more challenging in a complex power system based on wind energy conversion system due to the varying feature of the wind penetration, and sustaining the balance between the power generation and demand by rejecting the internal uncertainties in the process model and the external disturbances simultaneously. In the framework of the presented linear active disturbance rejection control approach, by constructing an extended state observer, the total disturbance, including all the unmodelled dynamics in the process model and the external disturbances, can be estimated in real time and then compensated by a simple linear PD control law. The controller parameters tuning is then simplified into the optimization of the two bandwidths: observer bandwidth, and the controller bandwidth. Then, this issue can be achieved by employing the heuristic modified bat inspired algorithm based on the optimization of the proposed performance index. The effectiveness of the proposed approach is validated by the extensive simulation examples of the load frequency control issue involved in the single area power system, taking into account different wind penetration, as well as the external disturbances. The performance robustness of the proposed approach against the parameters perturbation in the process model is also demonstrated via the Monte-Carlo method. The performance superiority of the proposed approach over the conventional Proportional Integral and Fuzzy-Proportional Integral based controller even in the presence of external disturbances and uncertainty in power system parameters under different cases of high wind penetration is also validated from the simulation results.     

H∞ observer-based event-triggered sliding mode control for a class of discrete-time nonlinear networked systems with quantizations

This paper investigates the problem of H_∞ observer-based event-triggered sliding mode control (SMC) for a class of uncertain discrete-time Lipschitz nonlinear networked systems with quantizations occurring in both input and output channels. The event-triggered strategy is used to save the limited network bandwidth. Then, based on the zero-order-hold (ZOH) measurement, a state observer is designed to reconstruct the system state, which facilitates the design of the discrete-time sliding surface. Considering the effects of quantizations, networked-induced constraints and event-triggered scheme, the nonlinear state error dynamics and sliding mode dynamics are converted into a unified linear parameter varying (LPV) time-delay system with the aid of a reformulated Lipschitz property. By using the Lyapunov-Krasovskii functional and free weighting matrix, a new sufficient condition is derived to guarantee the robust asymptotic stability of the resulting closed-loop system with prescribed H_∞ performance. And then the observer gain, event-triggering parameter and sliding mode parameter are co-designed. Furthermore, a novel SMC law is synthesized to force the trajectories of the observer system onto a pre-specified sliding mode region in a finite time. Finally, a single-link flexible joint robot example is utilized to demonstrate the effectiveness of the proposed method.     

Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

In this paper, adaptive filters are applied (in the fractional Fourier transform domain – FRFd) for denoising lightning electric-field signals, both in high and low signal-to-noise-ratio (SNR) environments. These filters are based on the concentration energy property of the fractional Fourier transform (FRFT). The proposed method integrates the advantages of leakage least mean square (LLMS) and normalized least mean square (NLMS) algorithms, including a leakage factor γ and a normalized step-size μ, in order to reduce the memory effect when tracking a non-stationary signal and also to reduce the effect of the input signal power on the algorithm performance, respectively. Parameter estimation of adaptive filters is analyzed in several case studies for various lightning-generated electric field signals. The adaptive algorithm is shown to provide better performance in low SNR environments. Finally, some analyses (in terms of temporal parameters of lightning electric-field signals) are included to demonstrate the validity of the method.     

RTDS implementation of an improved sliding mode based inverter controller for PV system

This paper proposes a novel approach for testing dynamics and control aspects of a large scale photovoltaic (PV) system in real time along with resolving design hindrances of controller parameters using Real Time Digital Simulator (RTDS). In general, the harmonic profile of a fast controller has wide distribution due to the large bandwidth of the controller. The major contribution of this paper is that the proposed control strategy gives an improved voltage harmonic profile and distribute it more around the switching frequency along with fast transient response; filter design, thus, becomes easier. The implementation of a control strategy with high bandwidth in small time steps of Real Time Digital Simulator (RTDS) is not straight forward. This paper shows a good methodology for the practitioners to implement such control scheme in RTDS. As a part of the industrial process, the controller parameters are optimized using particle swarm optimization (PSO) technique to improve the low voltage ride through (LVRT) performance under network disturbance. The response surface methodology (RSM) is well adapted to build analytical models for recovery time (R_t), maximum percentage overshoot (MPOS), settling time (T_s), and steady state error (E_ss) of the voltage profile immediate after inverter under disturbance. A systematic approach of controller parameter optimization is detailed. The transient performance of the PSO based optimization method applied to the proposed sliding mode controlled PV inverter is compared with the results from genetic algorithm (GA) based optimization technique. The reported real time implementation challenges and controller optimization procedure are applicable to other control applications in the field of renewable and distributed generation systems.     

基于并联RSO优化自抗扰的PMSM速度控制

为提高永磁同步电机调速系统的速度精度及抗干扰能力,提出一种并联降阶状态观测器优化线性自抗扰控制的方法.对传统线性扩张状态观测器进行改进,设计了降阶状态观测器.为了提升控制器在有限带宽内的抗扰动能力,设计并联型的降阶状态观测器.仿真结果表明,控制系统的速度精度和鲁棒性得到明显的提升.     

Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines

Wind power plants have nonlinear dynamics and contain many uncertainties such as unknown nonlinear disturbances and parameter uncertainties. Thus, it is a difficult task to design a robust reliable controller for this system. This paper proposes a novel robust fractional-order sliding mode (FOSM) controller for maximum power point tracking (MPPT) control of doubly fed induction generator (DFIG)-based wind energy conversion system. In order to enhance the robustness of the control system, uncertainties and disturbances are estimated using a fractional order uncertainty estimator. In the proposed method a continuous control strategy is developed to achieve the chattering free fractional order sliding-mode control, and also no knowledge of the uncertainties and disturbances or their bound is assumed. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory. Simulation results in the presence of various uncertainties were carried out to evaluate the effectiveness and robustness of the proposed control scheme.     

Modified reduced order observer based linear active disturbance rejection control for TITO systems

This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme.     

Variable-order fuzzy fractional PID controller

In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC) is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic control (FLC) could easily deal with parameter variations of control system, but the fractional-order parameters are unable to change through this way and it has confined the effectiveness of FLC. Therefore, an attempt is made in this paper to allow all the five parameters of fractional-order PID controller vary along with the transformation of system structure as the outputs of FLC, and the influence of fractional orders λ and μ on control systems has been investigated to make the fuzzy rules for VOFFLC. Four simulation results of different plants are shown to verify the availability of the proposed control strategy.     

The application of fractional order control for an air-based contactless actuation system

Industry pushes towards ever faster and more accurate production of thin substrates. Contactless positioning offers advantages, especially in terms of risk of breakage and contamination. A system is considered designed for contactless positioning by floating a silicon wafer on a thin film of air. This paper focuses on the design of a control system, including actuators, sensors and control method, suitable for this purpose. Two cascaded control loops, with decoupled SISO controllers, are implemented for this moving mass controlled on a mass-spring system, which can be modelled as a fourth order system. The SISO controllers are first designed with classic loopshaping tools, which are then modified using fractional control. Two arguments based on examples in this system are given for the application of fractional control. Firstly, to increase the bandwidth of a regular mass-spring system, and secondly to control a plant which behaves fundamentally fractional, such as the moving mass in this cascaded fourth order system. By merely the application of fractionality, the bandwidths are extended by 14.6 % and 62 %, for the inner and outer loop respectively. A closed-loop positioning bandwidth of the wafer of 60 Hz is achieved, resulting in a positioning error of 104 nm (2σ value), which is limited by sensor noise and pressure disturbances. This paper shows how the extension of classic loopshaping tools with fractional control can directly improve the performance, without adding to the complicatedness of the control system. Moreover it demonstrates a working concept of a novel type of contactless actuator.     

A novel interval type-2 fractional order fuzzy PID controller: Design,performance evaluation,and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.     

Active disturbance rejection control based human gait tracking for lower extremity rehabilitation exoskeleton

This paper presents an active disturbance rejection control (ADRC) based strategy, which is applied to track the human gait trajectory for a lower limb rehabilitation exoskeleton. The desired human gait trajectory is derived from the Clinical Gait Analysis (CGA). In ADRC, the total external disturbance can be estimated by the extended state observer (ESO) and canceled by the designed control law. The observer bandwidth and the controller bandwidth are determined by the practical principles. We simulated the proposed methodology in MATLAB. The numerical simulation shows the tracking error comparison and the estimated errors of the extended state observer. Two experimental tests were carried out to prove the performance of the algorithm presented in this paper. The experiment results show that the proposed ADRC behaves a better performance than the regular proportional integral derivative (PID) controller. With the proposed ADRC, the rehabilitation system is capable of tracking the target gait more accurately.     

Robust stability and stabilization of fractional order linear systems with positive real uncertainty

This paper investigates the robust stability and stabilization of fractional order linear systems with positive real uncertainty. Firstly, sufficient conditions for the asymptotical stability of such uncertain fractional order systems are presented. Secondly, the existence conditions and design methods of the state feedback controller, static output feedback controller and observer-based controller for asymptotically stabilizing such uncertain fractional order systems are derived. The results are obtained in terms of linear matrix inequalities. Finally, some numerical examples are given to validate the proposed theoretical results.     

Robust fast controller design via nonlinear fractional differential equations

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods.     

基于扩张状态观测器的快速步进/凝视成像机构控制

提出一种基于扩张状态观测器并引入加速度补偿策略的控制器设计方案,以实现快速步进/凝视成像机构对控制性能的高要求。首先,阐述了扩张状态观测器理论,对其特性进行了详细分析,并设计了以成像机构为被控对象的三阶线性扩张状态观测器。通过将观测器置于速度内环反馈通道,设计了基于扩张状态观测器的位置和速度双回路控制器。在此基础上,利用观测器输出的加速度估计值,提出加速度补偿策略,并设计了补偿环节。实验结果表明,与无加速度补偿环节相比,引入加速度补偿后,成像机构每次步进调节时间由76ms减小到33ms,凝视期间的角位置精度由约0.07°减小到0.01°以内,速度波动减小约2~3倍,成像机构的控制性能明显改善。控制器设计简单,需整定参数少,对于提高同类控制系统性能具有较高的实用价值。     

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=_Kpx(t)+_KIIα(x(t))$u\left(t\right)=K_{p}x\left(t\right)+K_I{\mathfrak{I}}_{\alpha }\left(x\right(t\left)\right)$. The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n−1$n-1$ (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.