一类相似广义互联系统的导数-输出反馈鲁棒控制器设计

以广义系统中受限系统等价概念和导数反馈- 输出反馈为基础,定义了一类广义互联系统的相似结构,提出了相似性研究的新方向.这类系 统具有不满足匹配条件的非线性不确定互联项.设计了导数-输出反馈鲁棒分散控制器,使互 联系统在平衡点处渐近稳定.由于控制器本身也具有相似结构,因此易于工程实现.     

STABILIZATION OF A CLASS OF NONLINEAR NON‐MINIMUM PHASE SYSTEMS

This paper tackles the problem of stabilization of a class of non‐minimum phase nonlinear systems which have zero dynamics with an eigenvalue zero of multiplicity 2. By adding some new terms, called cross terms, we are able to generalize the concept of the Lyapunov function with a homogeneous derivative along the trajectory, which was introduced in [4], to produce a suitable Lyapunov function. The Lyapunov function assures that the stability of an approximate system, which consists of some lower order terms of a nonlinear system with an eigenvalue zero of multiplicity 2, implies the stability of the whole system. Applying these to non‐minimum phase zero dynamics of nonlinear systems with such a center, a sufficient condition and a design method of state feedback control are obtained for stabilizing the systems.     

An Inexpensive Digital Integrator for Gas Chromatography

SUMMARY

An inexpensive gas chromatographic integrator with digital readout is described. The device is precise to ±1 count and shows linear response to within ±2%. It is directly compatible with flame ionization detectors and is easily adapted to thermal conductivity detectors.     

关于一类微积分计算方法的探究

通过对一类微积分计算方法的探究,从本质上分析所形成的思维模式,给出了一元微分以及积分区域为圆的二重积分通过平移变换简单巧妙的计算方法.由此可以类比出多元微分,以及多重积分的计算方法.     

含氮黄酮类衍生物的合成研究进展

黄酮类化合物不仅是一种天然的食品添加剂,而且具有抗氧化、抗菌、抗癌等活性.但因大部分天然黄酮的脂溶性或水溶性较差,致使其生物利用度较低.引入含氮基团,可有效地提高其药理活性和溶解性.综述了含氮黄酮类化合物合成的新进展.     

Numerical solutions of fractional advection–diffusion equations with a kind of new generalized fractional derivative

In the current paper, the numerical solutions for a class of fractional advection–diffusion equations with a kind of new generalized time-fractional derivative proposed last year are discussed in a bounded domain. The fractional derivative is defined in the Caputo type. The numerical solutions are obtained by using the finite difference method. The stability of numerical scheme is also investigated. Numerical examples are solved with different fractional orders and step sizes, which illustrate that the numerical scheme is stable, simple and effective for solving the generalized advection–diffusion equations. The order of convergence of the numerical scheme is evaluated numerically, and the first-order convergence rate has been observed.     

Root isolation methods based upon lagrangian interpolation

Two new methods for root isolation are presented. The methods apply to certain real-valued functions of one real variable. Each method takes a function and an interval and returns a set of subintervals in which roots are likely to occur. The methods are proven correct in exact arithmetic, i.e., each root of the function on the interval will be found in one of the subintervals returned. Both methods are based upon Lagrangian interpolation. The first method uses linear interpolation, requires that the function have two continuous derivatives and requires that the user give a bound on the absolute value of the second derivative. The second method uses quadratic interpolation and has similar requirements on the third derivative. The methods use only functional evaluations and the given bounds on derivatives; no other information about the function is required. An implementation is discussed and sample test cases are given which demonstrate the efficiency and utility of the methods. Future research on the use of the methods is also considered.     

Improved single-neuron PID controller for DC motor applied in robot system

An improved single-neuron proportional integral derivative (PID) controller and a new method to build the DC motor system were presented in the article. In the simulation, the robot arm is considered as an external load to DC motor. Both the motor module and the load module are created in Simulink to achieve simulation results closer to real robot system. In this way, it can well verify the performance of the improved single-neuron PID controller, which is a combined controller of normal PID controller and single-neuron PID controller. Besides, an intelligent switcher can help to realize the function of choosing a better control algorithm according to motor’s velocity output. Simulated results confirm the rapid and stable response of the improved PID controller. Moreover, the improved single-neuron PID controller has an excellent ability to overcome the load impact and supress the jamming signals. At last, a GUI interface platform is built to make the controller easier to be applied in other robot systems.     

一类高次分数阶微分方程正解的存在唯一性

研究Caputo型导数下的一类高次分数阶微分方程.首先给出等价于微分方程解的积分形式,然后利用格林函数的性质和混合单调算子不动点理论证明了这类分数阶微分方程正解的存在唯一性.     

变时间分数阶非定常对流扩散方程的数值分析

考虑变时间分数阶非定常对流扩散方程的数值逼近问题,首先,采用分段线性插值法结合对一阶时间导数的一个二阶近似离散Coimbra变时间分数阶导数,然后,用中心差分离散一阶空间分数阶导数和二阶空间分数阶导数。最后,用数值例子验证了提出的数值方法,说明了数值方法的有效性。