Discrete Walsh polynomials in the optimal control of linear digital time-varying systems

The discrete Walsh polynomials are applied to solve the digital optimal control of time-varying systems in this study. Due to the elegant properties of operational matrices of discrete Walsh polynomials, the class of digital time-varying problems can be analysed successfully. The design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of a penalty function to obtain directly computational formulations for evaluating the optimal control and state trajectory. An example is given to illustrate the usefulness of the method, and the results are very accurate.     

Discrete Walsh operational matrices for analysis and optimal control of linear digital systems

By the introduction of the shift transformation matrix, direct product matrix and summation matrix of the discrete Walsh series, the analysis of time-varying digital control systems is facilitated and the approximate solution of time-invariant digital optimal control problems is achieved of this study. The design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of penalty functions to obtain the conveniently computational formulations for evaluating the optimal control and trajectory. Three examples are illustrated by using the discrete Walsh approach.     

渐近最佳LCZ序列偶集的构造

由于最佳二进序列偶的存在空间比最佳二元序列大,为进一步扩大准同步码分多址(QS-CDMA)系统的地址码选择范围,提出了两种构造渐近最佳低相关区(LCZ)序列偶集的方法。基于最佳二进序列偶与改造后的Walsh序列集（或m序列的循环移位序列集）和二元二值周期自相关序列偶的循环移位序列偶集,构造一类渐近最佳LCZ序列偶集,构造的渐进最佳LCZ序列偶集具有更多不同的参数组合,可为实际的工程应用提供更多的选择。     

Fixed-point digital IIR filter design using two-stage ensemble evolutionary algorithm

The research on optimal design of infinite-impulse response (IIR) filter design based on various optimization techniques, including evolutionary algorithms (EAs), has gained much attention in recent years. Previously, the parameters of digital IIR filters are encoded with floating-point representations. It is known that a fixed-point representation can effectively save computational resources and is more convenient for direct realization on hardware. Inherently, compared with the floating-point representation, the fixed-point representation would make the search space miss much useful gradient information and therefore, surely rises new challenges for continuous EAs. In this paper, we first analyze the fitness landscape properties of optimal digital IIR filter design. Based on the fitness landscape investigation, a two-stage ensemble evolutionary algorithm (TEEA) is applied to digital IIR filter design with fixed-point representation. In order to fully evaluate the performance of TEEA, we experimentally compare it with five state-of-the-art EAs on four types of digital IIR filters with different settings. Based on the experimental results, we can conclude that TEEA has higher convergence speed, better exploration, and higher success rate. In order to benchmark TEEA further, we apply it to some more difficult problems with shorter word length or higher order. We can find that TEEA can provide satisfying performance on these hard tasks as well.     

Model reduction of digital systems using discrete Walsh series

This study discusses the application of discrete Walsh series expansion to reduce the order of a linear time-invariant digital system described byz-transfer function. The approach is based on matching the discrete Walsh spectra to determine both the coefficients of the denominator and numerator of the reduced model. The proposed method is simple for computation, can preserve the dynamic characteristic of the original model satisfactorily, and guarantees to have the same zero initial response as the original system.     

Research in progress

The research in the department is concerned mainly with computer-aided design. The fields in which c.a.d. is being applied include: the application of the Rademacher/Walsh transform to digital circuit synthesis; system simulation by digital filter methods; picture processing; and the design of optimal switching networks by linear programming techniques. A theoretical study of the properties of certain orthogonal transforms is also being carried out. Some of this research is outlined in the following sections.     

Active Disturbance Rejection Control System Design for a Morphing Wing Structure

Control system design for a morphing wing structure, which is proposed by NextGen Aeronautics, Inc., is investigated in this paper. The dynamic model of the morphing wing, developed based on the Euler‐Lagrange equation, is nonlinear, multivariable coupled, over‐actuated and uncertain. The allocation‐decoupling controller is designed based on control efficiency and decoupling matrices. For each decoupled subsystem, nonlinear and linear active disturbance rejection control (ADRC) systems are designed and compared. The time‐optimal property and the convergence of nonlinear ADRC are analyzed theoretically based on the isochronic region and Lyapunov theories. The simulation results of the developed control systems show satisfactory performances of decoupling and extreme tolerance of internal uncertainty and external disturbance. The comparison of nonlinear and linear ADRC systems demonstrate that the nonlinear system can provide a little better performance while the linear system can greatly simplify the design procedure. The results indicate that, the methods of control system design proposed in this paper are practical and effective for motion control of complex uncertain dynamical systems.     

On Walsh code assignment

We consider the problem of orthogonal variable spreading Walsh code assignments. The aim is to provide assignments that can avoid both complicated signaling from the BS to the users and blind rate and code detection amongst a great number of possible codes. The assignments considered here use partitioning of all users into several pools. Each pool can use its own codes, which are different for different pools. Each user has only a few codes assigned to it within the pool. We state the problem as a combinatorial one expressed in terms of a binary n × k matrix M where n is the number of users and k is the number of Walsh codes in the pool. A solution to the problem is given as a construction of a matrix M which has the assignment property defined in the paper. Two constructions of such M are presented under different conditions on n and k. The first construction is optimal in the sense that it gives the minimal number of Walsh codes — assigned to each user for given n and k. The optimality follows from a proved necessary condition for the existence ofM with the assignment property. In addition, we propose a simple algorithm of optimal assignment for the first construction.     

A simple method of Walsh spectra multiplication

The paper presents a new easy method to obtain the product of the Walsh spectra of two functions. The method makes use of both the spectra of Walsh and block-pulse functions (b.p.f.s). The proposed method can be easily implemented with a digital computer. It will be very useful in the analysis and optimal control of time varying systems via Walsh functions.     

Hybrid crafting: towards an integrated practice of crafting with physical and digital components

With current digital technologies, people have large archives of digital media, such as images and audio files, but there are only limited means to include these media in creative practices of crafting and making. Nevertheless, studies have shown that crafting with digital media often makes these media more cherished and that people enjoy being creative with their digital media. This paper aims to open up the way for novel means for crafting, which include digital media in integrations with physical construction, here called ‘hybrid crafting’. Notions of hybrid crafting were explored to inform the design of products or systems that may support these new crafting practices. We designed ‘Materialise’—a building set that allows for the inclusion of digital images and audio files in physical constructions by using tangible building blocks that can display images or play audio files, alongside a variety of other physical components—and used this set in four hands-on creative workshops to gain insight into how people go about doing hybrid crafting; whether hybrid crafting is desirable; what the characteristics of hybrid crafting are; and how we may design to support these practices. By reflecting on the findings from these workshops, we provide concrete guidelines for the design of novel hybrid crafting products or systems that address craft context, process and result. We aim to open up the design space to designing for hybrid crafting because these new practices provide interesting new challenges and opportunities for future crafting that can lead to novel forms of creative expression.     

Design approach to low-cost process control

The design of a control package for industrial use on small-scale processes is discussed. A modular system is described, made up of intelligent satellite and peripheral controllers plus various cards to provide communication with the industrial plant itself. The design is intended for operators who have little or no experience of computing. It is based on a language called paracode, an interpretive language structured to provide a number of control sequences which can run independently of each other or in parallel. Two applications of the design—a clean-in-place system and a beer-fermentation controller—are used as illustrations.     

发动机总成悬置系统解耦方法研究

目前汽车发动机动力总成悬置系统设计的主要任务是选择悬置元件的刚度、位置和角度,使悬置系统自由振动模态频率避开发动机怠速激励力频率与车身自振频率,并尽量提高各模态振型的解耦程度,从而提高悬置系统隔振效果.悬置系统按预定频率严格解耦设计是使设计出的悬置系统模态频率完全等于按汽车设计频率规划预定的频率,并使各模态的振型严格解耦,即各向振动能量的解耦度等于1.本文从悬置系统的自由振动方程出发给出了对悬置系统按预定频率严格解耦设计的方程组,可以利用广义逆矩阵的理论求该方程组的解,亦可通过方程组构造函数进而求出该方程组的解,从而提供比当前的悬置系统模态优化设计更为简便高效的优化设计方法.相应的算例验证了本文提出的按预定频率严格解耦设计方程和求解方法的正确性.     

Fast gaussian random number generation using linear transformations

We develop a method for generating pseudorandom sequences with Gaussian distribution. The method is based on completely uniformly distributed sequences and linear transformations, such as the Fourier transform and Walsh transform. We obtain some discrepancy estimates and make a numerical comparison of these two transformations. Furthermore, we show how this method can be used for testing randomness. We remark that similar approaches are due to Gut, Egorov and Il’in [7], Yuen [26] and Rader [21]. The authors are supported by the Austrian-Hungarian Scientific Cooperation Programme, Project Nr. 10U3 This author is supported by the Austrian Science Foundation, Project Nr. P10223-PHY     

乙烯裂解炉炉管出口温度控制系统设计及应用

乙烯裂解炉炉管出口温度控制系统中存在着多变量耦合情况,导致在实际生产中很难实现对各组炉管温度的精确控制.针对这种情况,本文提出了一种基于可逆解耦策略和内模PID控制原理的多变量控制系统设计方案.文中首先介绍乙烯裂解炉的结构,并对其工作原理和生产的工艺流程作了简单说明;其次根据现场得到的数据并进行滤波,去趋势项等处理,运用预报误差算法(PEM)进行系统辨识,建立了过程的多变量输入输出模型;再次,介绍了可逆解耦方法的基本原理和实现过程,并针对辨识得到的模型,采用该方法设计系统的解耦环节.它可以避免采用传统解耦方法时的复杂运算过程,能够较为快捷地得到解耦参数矩阵.最后,针对解耦后的被控系统设计控制器.由于内模控制具有结构简单,控制性能良好等特点,本文中采用内模控制原理设计带滤波器形式的PID控制器,并给出了滤波系数等相关参数值.同时,对模型存在失配的情况和模型匹配时采用传统单回路控制策略的情况,以及不对系统解耦而直接设计PID控制器进行控制的情况分别进行仿真,并比较了仿真结果.分析表明,系统解耦后,对其控制时的静态误差消除时间大大缩短,动态性能得到改善,从而实现了对裂解炉炉管出口温度快速准确控制的要求,说明了该方案的有效性.     

Walsh变换核矩阵的简单生成及其应用

本文讨论了Walsh函数的Walsh序、Paley序与Hadamard序相应的变换核矩阵的相互转化关系，给出了三类序的Walsh变换核矩阵的生成算法，且生成算法简单，还给出了Matlab生成该类矩阵的Matlab程序，并将几类矩阵的转换置换矩阵应用到图像信息的加密置乱中，置乱效果很好。     

Optimal Decoupling Control Method and Its Application to a Ball Mill Coal-pulverizing System

The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneously provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking (LQT) control method.      

Decoupling Controller with Disturbance Observer for LTI MIMO Systems

In this paper, a decoupling multivariable control strategy for linear time‐invariant (LTI) multi‐input/multi‐output (MIMO) systems is proposed. The strategy includes a multivariable disturbance observer (MDOB) and a decoupling controller. This MDOB is introduced to improve the system performances when the system encounters severe external disturbances. H₂ optimal scheme is utilized to design the MDOB filter. The controller is developed based on an inverse control method, through which the design process can be simplified. Simulation results certify the effectiveness of the proposed control strategy.     

Digital decoupling controller design for multiple time-delay continuous-time transfer function matrices

This paper presents an extended adjoint decoupling method to conduct the digital decoupling controller design for the continuous-time transfer function matrices with multiple (integer/fractional) time delays in both the denominator and the numerator matrix. First, based on the sampled unit-step response data of the afore-mentioned multiple time-delay system, the conventional balanced model-reduction method is utilised to construct an approximated discrete-time model of the original (known/unknown) multiple time-delay continuous-time transfer function matrix. Then, a digital decoupling controller is designed by utilising the extended adjoint decoupling method together with the conventional discrete-time root-locus method. An illustrative example is given to demonstrate the effectiveness of the proposed method.     

Analysis of non-linear singular system from fluid dynamics using extended runge-kutta methods

A non-linear singular system from fluid dynamics has been analysed by considering various possibilities using three different fourth order extended Runge–Kutta (RK) methods based on arithmetic mean, harmonic mean and heronian mean. It is observed that the extended RK methods suit well for the nuclear reactor core problem, when compared to the Single Term Walsh Series (STWS) method [1,10]. The simple and direct methods presented here can easily be implemented in a digital computer.