Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers

One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method.     

An approach to design controllers for MIMO fractional-order plants based on parameter optimization algorithm

The parameter optimization method for multivariable systems is extended to the controller design problems for multiple input multiple output (MIMO) square fractional-order plants. The algorithm can be applied to search for the optimal parameters of integer-order controllers for fractional-order plants with or without time delays. Two examples are given to present the controller design procedures for MIMO fractional-order systems. Simulation studies show that the integer-order controllers designed are robust to plant gain variations.     

建筑结构含分数阶振动控制的最优阶次研究

为了在实际控制中获得更好的控制效果,以整数阶模型为研究对象,在控制器设计时人为地引入分数阶,通过定义控制性能指标和寻优来确定最优控制的分数阶阶次.为了建立分数阶系统和原整数阶系统之间的联系,取含分数阶状态方程和原整数阶系统状态方程一致的输出变量,并采用输出控制策略使得所设计的分数阶控制器能够应用于原整数阶模型.仿真结果表明,分数阶阶次的选择不仅影响系统控制的效果,还影响系统的稳定性,并给出了一个实例分析来说明本研究方法的可行性.     

Observation and sliding mode observer for nonlinear fractional-order system with unknown input

The main purpose of this paper is twofold. First, the observability and the left invertibility properties and the observable canonical form for nonlinear fractional-order systems are introduced. By using a transformation, we show that these properties can be deduced from an equivalent nonlinear integer-order system. Second, a step by step sliding mode observer for fault detection and estimation in nonlinear fractional-order systems is proposed. Starting with a chained fractional-order integrators form, a step by step first-order sliding mode observer is designed. The finite time convergence of the observer is established by using Lyapunov stability theory. A numerical example is given to illustrate the performance of the proposed approach.     

Finite-time projective synchronization of fractional-order chaotic systems via soft variable structure control

Journal of Mechanical Science and Technology - The finite-time projective synchronization of two fractional-order chaotic systems with control constraints is investigated in this study. A soft...     

Robust stability criterion for fractional-order systems with interval uncertain coefficients and a time-delay

This study investigates the robust stability of fractional-order systems with interval coefficients and a time-delay. By the Minkowski Sum, the vertices of value set with respect to the characteristic function of the investigated fractional-order system are offered, avoiding the calculations of the redundant vertices. Meanwhile, a function depending on the obtained vertices is defined to represent the position relationship between the origin and the value set. Based on the zero exclusion principle, we propose sufficient and necessary conditions to determine the robust stability of fractional-order systems with interval uncertain coefficients and a time-delay. Finally, illustrative examples are offered to verify the effectiveness of the proposed robust stability criterion.     

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.     

超混沌系统的动力学性质及同步问题的研究

选取一个超混沌Qi系统,详细分析其动力学性质。采取基于观测器的方法来实现系统在不同初值条件下的同结构投影同步,并采用反馈法的思想设计合适的控制器,以实现Qi系统和Liu系统不同结构之间的完全同步。通过Lyapunov稳定性定理证明控制器的合理性,并对两种同步方法进行数值仿真来证明其可行性和有效性。     

Fractional-order system identification and proportional-derivative control of a solid-core magnetic bearing

This paper presents the application of fractional-order system identification (FOSI) and proportional-derivative (PD^µ) control to a solid-core magnetic bearing (MB). A practical strategy for closed-loop incommensurate FOSI along with a modified error criterion is utilized to model the MB system and a corresponding, verification experiment is carried out. Based on the identified model, integer-order (IO) PD and fractional-order (FO) PD^µ controllers are designed and compared with the same specifications. Besides, the relation between the two categories of controllers is discussed by their feasible control zones. Final simulation and experimental results show that the FO PD^µ controller can significantly improve the transient and steady-state performance of the MB system comparing with the IO PD controller.     

A new and simple method to construct root locus of general fractional-order systems

Recently fractional-order (FO) differential equations are widely used in the areas of modeling and control. They are multivalued in nature hence their stability is defined using Riemann surfaces. The stability analysis of FO linear systems using the technique of Root Locus is the main focus of this paper. Procedure to plot root locus of FO systems in s-plane has been proposed by many authors, which are complicated, and analysis using these methods is also difficult and incomplete. In this paper, we have proposed a simple method of plotting root locus of FO systems. In the proposed method, the FO system is transformed into its integer-order counterpart and then root locus of this transformed system is plotted. It is shown with the help of examples that the root locus of this transformed system (which is obviously very easy to plot) has exactly the same shape and structure as the root locus of the original FO system. So stability of the FO system can be directly deduced and analyzed from the root locus of the transformed IO system. This proposed procedure of developing and analyzing the root locus of FO systems is much easier and straightforward than the existing methods suggested in the literature. This root locus plot is used to comment about the stability of FO system. It also gives the range for the amplifier gain k required to maintain this stability. The reliability of the method is verified with analytical calculations.     

Stability of a flat arch subjected to deterministic and stochastic loads taking into account nonlocal damping

In the example of a flat arch, a problem of vibrational stability of systems subjected to deterministic and stochastic loads is considered taking into account the geometric nonlinearity and nonlocal damping of a material, which is characteristic of certain types of composites and nanomaterials. To study the stability of arch motion within the deterministic statement of the problem (stability in the sense of Lyapunov) and the stability in the almost certain stochastic statement, a method is used which is based on the calculation of the maximal Lyapunov’s exponent. The influence of damping and loading parameters on the degree of system stability is analyzed.     

基于时域的分数阶PID预测函数励磁控制器

为了提高电力系统的稳定性,将分数阶PID算法与预测函数算法相结合,提出了一种新型的基于时域的分数阶PID预测函数励磁控制器的设计方法.该算法不仅具有分数阶PID静态误差小、上升速度快以及预测函数算法超调小、调节时间短的优点,还克服了分数阶PID调节时间长和预测函数算法静态误差大的缺点,同时还比预测函数算法多出了5个可调参数,设计更加灵活.研究结果表明该算法不仅能有效地解决机端电压偏移问题,还能有效地抑制电网低频振荡,为电力系统稳定性控制提供了一种新型有效的方法.     

On the stability of rods laying on a nonlinearly elastic bed under stochastic parametric excitation

The problem of simulating undisturbed behavior of a nonlinear system subjected to the action of deterministic and stochastic parametrical load is examined and the stability of undisturbed motion of the system is analyzed. It has been revealed that the trajectory motion of points changes greatly, if we take into account one or several components in deflection expansion while examining the deterministic and stochastic parametrical problem. In this case it is possible to stabilize the unstable undisturbed motion of the rod by superimposing the stochastic component in the form of a stationary Gaussian process with hidden periodicity to the deterministic load. By stability we mean the almost certain stability and average stability and mean square stability (stability with respect to the first- and second-order statistic moments).     

汽车非线性主动悬架系统的分数阶模糊控制

针对非线性主动悬架系统的控制问题,提出一种分数阶模糊控制方法。该方法采用分数阶微分信号作为模糊控制器输入,并根据悬架系统综合性能指标函数最小准则获得分数阶次。仿真结果表明：相比整数阶的模糊控制情形,即使车辆在不同车速和不同等级道路的行驶工况下,该分数阶模糊控制方法可以使得非线性悬架系统能够获得更优的控制效果,能进一步降低车身垂直振动加速度、动行程及轮胎形变,有效提高车辆的行驶平顺性和操纵稳定性。     

Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation

This paper proposes a new non-fragile stochastic control method to investigate the robust sampled-data synchronization problem for uncertain chaotic Lurie systems (CLSs) with time-varying delays. The controller gain fluctuation and time-varying uncertain parameters are supposed to be random and satisfy certain Bernoulli distributed white noise sequences. Moreover, by choosing an appropriate Lyapunov-Krasovskii functional (LKF), which takes full advantage of the available information about the actual sampling pattern and the nonlinear condition, a novel synchronization criterion is developed for analyzing the corresponding synchronization error system. Furthermore, based on the most powerful free-matrix-based integral inequality (FMBII), the desired non-fragile sampled-data estimator controller is obtained in terms of the solution of linear matrix inequalities. Finally, three numerical simulation examples of Chua's circuit and neural network are provided to show the effectiveness and superiorities of the proposed theoretical results.     

Stability analysis and compensation of network-induced delays in communication-based power system control: A survey

This survey is to summarize and compare existing and recently emerging approaches for the analysis and compensation of the effects of network-induced delays on the stability and performance of communication-based power control systems. Several important communication-based power control systems are briefly introduced. The deterministic and stochastic methodologies of analyzing the impacts of network-induced delays on the stability of the communication-based power control systems are summarized and compared. A variety of control approaches are reviewed and compared for mitigating the effects of network-induced delays, depending on several design requirements, such as model dependence and design difficulty. The summary and comparison of these control approaches in this survey provide researchers and utilities valuable guidance for designing advanced communication-based power control systems in the future.     

Fault tolerant synchronization of chaotic heavy symmetric gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control

In this paper, fault tolerant synchronization of chaotic gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control is investigated. Taking the general nature of faults in the slave system into account, a new synchronization scheme, namely, fault tolerant synchronization, is proposed, by which the synchronization can be achieved no matter whether the faults and disturbances occur or not. By making use of a slave observer and a Lyapunov rule-based fuzzy control, fault tolerant synchronization can be achieved. Two techniques are considered as control methods: classic Lyapunov-based control and Lyapunov rule-based fuzzy control. On the basis of Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are obtained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. Two proposed methods are compared. The Lyapunov rule-based fuzzy control can compensate for the actuator faults and disturbances occurring in the slave system. Numerical simulation results demonstrate the validity and feasibility of the proposed method for fault tolerant synchronization.     

含双重补偿的液压缸位置同步控制

非对称液压缸同步控制系统在大型、重型工业设备中应用广泛,其同步性能和响应速度直接影响设备的稳定运行。为了进一步优化对称阀控非对称液压缸同步系统,对阀控非对称液压缸进行建模分析。基于非对称液压缸特性及负载变化范围大的特点,提出了模糊补偿控制方法来提高液压缸的响应速度;针对液压缸的同步问题,设计了交叉耦合的前馈补偿控制方式来缩小同步误差。利用AMESim搭建液压回路系统模型作为控制对象,并联合Simulink搭建控制系统进行仿真。仿真结果表明:相比于改进前,在负载不断变化且具有偏载的情况下,含双重补偿的同步控制可以明显减小液压同步系统的跟踪误差与同步误差。     

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.