数学分析课程中的数学方法教学初探

本文提出数学分析课程教学中应重视的两种基本数学思想方法——优化控制法和反演变换法,并结合教材说明它们的教学过程。

配电网中光伏电源的无功电压控制

建立光伏电源并网仿真模型,首先注入纯有功功率,研究并网光伏电源对系统各个节点电压分布的影响;然后应用各种控制方法在不同电源功率和不同负载情况下分别进行仿真实验,研究各类控制方法的稳态适应性;比较各种控制方法在电源功率有阶跃变化情况下的响应时间,研究其动态响应,提出优化无功功率控制法,然后通过逆变器并网实验,验证控制方法的可行性;最后总结控制方法,指出各自的适用场合和无功电压控制法的缺陷。

乙醇催化偶合制备C_(4)烯烃的优化模型

文章以乙醇作为原料,通过在催化剂不同组合及温度条件的影响下,探索乙醇催化偶合制备C_(4)烯烃的最佳工艺条件.利用MATLAB、Excel及SPSS软件对数据进行处理,拟合出催化剂组合在不同温度下与乙醇转化率及C_(4)烯烃的选择性关系,从而建立数学模型.采用控制变量法,对于催化剂不同组合中Co/SiO_(2)和HAP装料比与乙醇转化率、C_(4)烯烃的选择性之间的相关性进行分析.利用优化模型,从而使C_(4)烯烃收率尽可能高.利用对照实验矩阵对不同实验组合进行交叉对比,并找到各组实验数据的对比组,对于缺失对照组的数据实验组提出新的实验设计.

Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

NSGA-Ⅱ based traffic signal control optimization algorithm for over-saturated intersection group

In order to improve the efficiency of traffic signal control for an over-saturated intersection group, a nondominated sorting genetic algorithm Ⅱ（NSGA-Ⅱ） based traffic signal control optimization algorithm is proposed. The throughput maximum and average queue ratio minimum for the critical route of the intersection group are selected as the optimization objectives of the traffic signal control for the over-saturated condition. The consequences of the efficiency between traffic signal timing plans generated by the proposed algorithm and a commonly utilized signal timing optimization software Synchro are compared in a VISSIM signal control application programming interfaces （SCAPI） simulation environment by using real filed observed traffic data. The simulation results indicate that the signal timing plan generated by the proposed algorithm is more efficient in managing oversaturated flows at intersection groups, and, thus, it has the capability of optimizing signal timing under the over-saturated conditions.

Some Trials of Typical Typhoon Tracks Using the Adjoint Method

In this paper, the adjoint method is applied to the statistical-dynamic model （SD-90） for the prediction of typhoon tracks along with the regularization thinking and optimal control techniques. The adjoint model and the gradient of objective function are deduced with the continual model respectively. For 4 typical typhoons, the forces and the initial velocity can be retrieved well, and the tracks of these typhoons are accurately fitted for an appropriate regularization parameter and optimal control parameter.

NECESSARY AND SUFFICIENT CONDITIONS FOR QUADRATIC STABILITY OF UNCERTAIN DISCRETE TIME SYSTEMS

The robust stability analysis of discrete time systems with fast time varying uncertainties is considered in this paper. The necessary and sufficient conditions for quadratic stability are presented. Moreover, the stability robustness index is introduced as the measurement of the stability robustness. For the systems with given uncertain parameter bounds, checking the necessary and sufficient conditions and calculating the stability robust index are converted to solving minimax problems. It is shown that the maximization can be reduced to comparisons between the functional values of the corners when the parameter region is bounded by hyperpolydredon, and any local minimum value in the minimization is exactly the global minimum.

Optimum Design of the Control System for a Laser Beam Riding Guidance Anti-Tank Missile

The optimum theory and methods were adopted to design the laser beam riding guidance anti tank missile's control system in the short run. Through building the mathematical model of system, selecting a proper method and taking advantage of computer's high speed calculation and logic traits, an optimal controller was designed. Simulation results showed that the designed control system has fair performance and it satisfies the tactical and technical requirements. The results also demonstrate that by the combination of the optimizing methods and the computer the control system could be designed as soon as possible.

Optimal fuzzy PID controller with adjustable factors based on flexible polyhedron search algorithm

A new kind of optimal fuzzy PID controller is proposed, which contains two parts. One is an on line fuzzy inference system, and the other is a conventional PID controller. In the fuzzy inference system, three adjustable factors x p, x i , and x d are introduced. Their functions are to further modify and optimize the result of the fuzzy inference so as to make the controller have the optimal control effect on a given object. The optimal values of these adjustable factors are determined based on the ITAE criterion and the Nelder and Mead′s flexible polyhedron search algorithm. This optimal fuzzy PID controller has been used to control the executive motor of the intelligent artificial leg designed by the authors. The result of computer simulation indicates that this controller is very effective and can be widely used to control different kinds of objects and processes.

Multi-domain modeling and simulation of proportional solenoid valve

A multi-domain nonlinear dynamic model of a proportional solenoid valve was presented.The electro-magnetic,mechanical and fluid subsystems of the valve were investigated,including their interactions.Governing equations of the valve were derived in the form of nonlinear state equations.By comparing the simulated and measured data,the simulation model is validated with a deviation less than 15%,which can be used for the structural design and control algorithm optimization of proportional solenoid valves.

Optimal variable structure control with sliding modes for unstable processes

In this work,a variable structure control(VSC)technique is proposed to achieve satisfactory robustness for unstable processes.Optimal values of unknown parameters of VSC are obtained using Whale optimization algorithm which was recently reported in literature.Stability analysis has been done to verify the suitability of the proposed structure for industrial processes.The proposed control strategy is applied to three different types of unstable processes including non-minimum phase and nonlinear systems.A comparative study ensures that the proposed scheme gives superior performance over the recently reported VSC system.Furthermore,the proposed method gives satisfactory results for a cart inverted pendulum system in the presence of external disturbance and noise.

Optimization of actuator/sensor position of multi-body system with quick startup and brake

A new method was put forward to optimize the position of actuator/sensor of multi-body system with quick startup and brake. Dynamical equation was established for the system with intelligent structure of piezoelectric actuators. According to the property of the modes varying with time, the performance index function was developed based on the optimal configuration principle of energy maximal dissipation, and the relevant optimal model was obtained. According to its characteristic, a float-encoding genetic algorithm, which is efficient, simple and excellent for solving the global-optimal solution of this problem, was adopted. Taking the plane manipulator as an example, the result of numerical calculation shows that, after the actuator/sensor position being optimized, the vibration amplitude of the multi-body system is reduced by 35% compared with that without optimization.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex

To solve dynamic optimization problem of chemical process (CPDOP), a hybrid differential evolution algorithm, which is integrated with Alopex and named as Alopex-DE, was proposed. In Alopex-DE, each original individual has its own symbiotic individual, which consists of control parameters. Differential evolution operator is applied for the original individuals to search the global optimization solution. Alopex algorithm is used to co-evolve the symbiotic individuals during the original individual evolution and enhance the fitness of the original individuals. Thus, control parameters are self-adaptively adjusted by Alopex to obtain the real-time optimum values for the original population. To illustrate the whole performance of Alopex-DE, several varietal DEs were applied to optimize 13 benchmark functions. The results show that the whole performance of Alopex-DE is the best. Further, Alopex-DE was applied to solve 4 typical CPDOPs, and the effect of the discrete time degree on the optimization solution was analyzed. The satisfactory result is obtained.

Optimal operation of water supply systems with tanks based on genetic algorithm

In view of the poor water supply system’s network properties, the system’s complicated network hydraulic equations were replaced by macroscopic nodal pressure model and the model of relationship between supply flow and water source head. By using pump-station pressure head and initial tank water levels as decision variables, the model of optimal allocation of water supply between pump-sources was developed. Genetic algorithm was introduced to deal with the model of optimal allocation of water supply. Methods for handling each constraint condition were put forward, and overcome the shortcoming such as premature convergence of genetic algorithm; a solving method was brought forward in which genetic algorithm was combined with simulated annealing technology and self-adaptive crossover and mutation probabilities were adopted. An application example showed the feasibility of this algorithm.

Advanced Coverage Optimization Techniques for Small Cell Clusters

Coverage challenge for small considered to be a optlmlzation is a main cell clusters which are promising solution to provide seamless cellular coverage for large indoor or outdoor areas. This paper focuses on small cell cluster coverage problems and proposes both centralized and distributed self-optimization methods. Modified Particle swarm optimization （MPSO） is introduced to centralized optimization which employs particle swarm optimization （PSO） and introduces a heuristic power control scheme to accelerate the algorithm to search tbr the global optimum solution. Distributed coverage optimization is modeled as a non-cooperative game, with a utility function considering both throughput and interference. An iterative power control algorithm is then proposed using game theory （DGT） which converges to Nash Equilibrium （NE）. Simulation results show that both MPSO and DGT have excellent performance in coverage optimization and outperform optimization using simulated annealing algorithm （SA）, reaching higher coverage ratio and throughput while with less iterations.

Genetic Optimization Algorithm of PID Decoupling Control for VAV Air-Conditioning System

Variable-air-volume (VAV) air-conditioning system is a multi-variable system and has multi coupling control loops. While all of the control loops are working together, they interfere and influence each other. A multivariable decoupling PID controller is designed for VAV air-conditioning system. Diagonal matrix decoupling method is employed to eliminate the coupling between the loop of supply air temperature and that of thermal-space air temperature. The PID controller parameters are optimized by means of an improved genetic algorithm in floating point representations to obtain better performance. The population in the improved genetic algorithm mutates before crossover, which is helpful for the convergence. Additionally the micro mutation algorithm is proposed and applied to improve the convergence during the later evolution. To search the best parameters, the optimized parameters ranges should be amplified 10 times the initial ideal parameters. The simulation and experiment results show that the decoupling control system is effective and feasible. The method can overcome the strong coupling feature of the system and has shorter governing time and less over-shoot than non-optimization PID control.

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

Abstract-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 simultaneousiy 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.

Fractional order PID control for steer-by-wire system of emergency rescue vehicle based on genetic algorithm

Aiming at dealing with the difficulty for traditional emergency rescue vehicle(ECV)to enter into limited rescue scenes,the electro-hydraulic steer-by-wire(SBW)system is introduced to achieve the multi-mode steering of the ECV.The overall structure and mathematical model of the SBW system are described at length.The fractional order proportional-integral-derivative(FOPID)controller based on fractional calculus theory is designed to control the steering cylinder’s movement in SBW system.The anti-windup problem is considered in the FOPID controller design to reduce the bad influence of saturation.Five parameters of the FOPID controller are optimized using the genetic algorithm by maximizing the fitness function which involves integral of time by absolute value error(ITAE),peak overshoot,as well as settling time.The time-domain simulations are implemented to identify the performance of the raised FOPID controller.The simulation results indicate the presented FOPID controller possesses more effective control properties than classical proportional-integral-derivative(PID)controller on the part of transient response,tracking capability and robustness.

Study on optimization control method based on artificial neural network

In the goal optimization and control optimization process the problems with common artificial neural network algorithm are unsure convergence, insufficient post-training network precision, and slow training speed, in which partial minimum value question tends to occur. This paper conducted an in-depth study on the causes of the limi-tations of the algorithm, presented a rapid artificial neural network algorithm, which is characterized by integrating multiple algorithms and by using their complementary advan-tages. The salient feature of the method is self-organization, which can effectively prevent the optimized results from tending to be partial minimum values. Overall optimization can be achieved with this method, goal function can be searched for in overall scope. With op-timization control of coal mine ventilator as a practical application, the paper proves that by integrating multiple artificial neural network algorithms, best control optimization and goal optimized can be achieved.