An efficient algorithm for low-order direct discrete-time implementation of fractional order transfer functions

Fractional order systems become increasingly popular due to their versatility in modelling and control applications across various disciplines. However, the bottleneck in deploying these tools in practice is related to their implementation on real-life systems. Numerical approximations are employed but their complexity no longer match the attractive simplicity of the original fractional order systems. This paper proposes a low-order, computationally stable and efficient method for direct approximation of general order (fractional order) systems in the form of discrete-time rational transfer functions, e.g. processes, controllers. A fair comparison to other direct discretization methods is presented, demonstrating its added value with respect to the state of art.     

An efficient numerical scheme for solving fractional infinite-horizon optimal control problems

This paper presents an efficient numerical method to solve fractional infinite-horizon optimal control problems, where the dynamic control system depends on Caputo fractional derivatives. First, by a suitable change of variable, we transform the fractional infinite-horizon optimal control problem to a finite-horizon one. Then, with the help of an approximation, we replace the Caputo derivative to integer order derivative. According to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for state, costate and control functions where these trial solutions are constructed by using two-layered perceptron neural network. Some numerical results are introduced to explain our main results.     

基于主曲线的书法字动态重现算法

如何高效逼真地动态重现书法作品的创作过程日益成为亟需解决的问题,因此文中提出基于主曲线的书法字动态重现方法,解决当前细化算法在提取骨架时存在的无效分支较多、不能保证笔画的连续性和准确性的问题.结合书法字自身结构对主曲线算法进行改进和优化.对书法图像进行骨架提取、骨架追踪、笔顺获取等处理,结合骨架信息和二值图像实现笔画宽度复原,针对笔画宽度存在的“肿瘤”问题,提出“角点剔除法”进行修正,结合HTML5的Canvas绘图技术进行书法字动态书写过程.在模拟数据集上的实验表明,文中算法的书法动态重现取得较好效果.     

Formal modeling and verification of fractional order linear systems

This paper presents a formalization of a fractional order linear system in a higher-order logic (HOL) theorem proving system. Based on the formalization of the Grünwald–Letnikov (GL) definition, we formally specify and verify the linear and superposition properties of fractional order systems. The proof provides a rigor and solid underpinnings for verifying concrete fractional order linear control systems. Our implementation in HOL demonstrates the effectiveness of our approach in practical applications.     

Stochastic response of fractionally damped beams

This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system.Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional derivative order. Finally, the fractional derivative term introduces in the system dynamics both effective damping and effective stiffness frequency dependent terms.     

Dustiness Quantification of Powders by the Fractional Release Rate

The handling of dispersed solids may lead to undesirable release of dust particles. Size and quantity of the particles transferred into the gas with time depend on the binding and separating forces in the powder. These in turn are determined by characteristic parameters of the powder and of the process. Analogous to the well‐known “fractional collection efficiency” describing the dust separation, a newly defined “fractional release rate” to quantify the release of dust is introduced. The application is demonstrated by an example and the way to further development of this innovative approach is demonstrated.     

Lot scheduling on a single machine

In a practical situation, a manufacturer receives different orders from its customers. Different orders may contain different quantities of the product. Therefore, the manufacturer has to decide how to group these orders into different lots based on the capacity of the lot processing machine (such as integrated circuit tester, heated container, etc.) and then decides the sequence of these lots. In this paper, we study a lot scheduling problem with orders which can be split. The objective is to minimize the total completion time of all orders. We show that this problem can be solved in polynomial time.     

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.     

Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator

A two-link robotic manipulator is a Multi-Input Multi-Output (MIMO), highly nonlinear and coupled system. Therefore, designing an efficient controller for this system is a challenging task for the control engineers. In this paper, the Fractional Order Fuzzy Proportional-Integral-Derivative (FOFPID) controller for a two-link planar rigid robotic manipulator for trajectory tracking problem is investigated. Robustness testing of FOFPID controller for model uncertainties, disturbance rejection and noise suppression is also investigated. To study the effectiveness of FOFPID controller, its performance is compared with other three controllers namely Fuzzy PID (FPID), Fractional Order PID (FOPID) and conventional PID. For tuning of parameters of all the controllers, Cuckoo Search Algorithm (CSA) optimization technique was used. Two performance indices namely Integral of Absolute Error (IAE) and Integral of Absolute Change in Controller Output (IACCO) having equal weightage for both the links are considered for minimization. Numerical simulation results clearly indicate the superiority of FOFPID controller over the other controllers for trajectory tracking, model uncertainties, disturbance rejection and noise suppression.