Search results for: Optimal control

Authors: Rooholah Hasanizadeh, Saadan Zokaei

Abstract:

In the context of sensor networks, where every few dB saving counts, the novel node cooperation schemes are reviewed where MIMO techniques play a leading role. These methods could be treated as joint approach for designing physical layer of their communication scenarios. Then we analyzed the BER performance of transmission diversity schemes under a general fading channel model and proposed a power allocation strategy to the transmitting sensor nodes. This approach is then compared to an equal-power assignment method and its performance enhancement is verified by the simulation. Another key point of the contribution lies in the combination of optimal power allocation and sensor nodes- cooperation in a transmission diversity regime (MISO). Numerical results are given through figures to demonstrate the optimality and efficiency of proposed combined approach.

Keywords: Optimal power allocation, cooperative MISO scheme, sensor networks, diversity branch.

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Authors: Abdelaziz Sahbani, Kamel Ben Saad, Mohamed Benrejeb

Abstract:

This paper proposes a Fuzzy Sliding Mode Control (FSMC) as a control strategy for Buck-Boost DC-DC converter. The proposed fuzzy controller specifies changes in the control signal based on the knowledge of the surface and the surface change to satisfy the sliding mode stability and attraction conditions. The performances of the proposed fuzzy sliding controller are compared to those obtained by a classical sliding mode controller. The satisfactory simulation results show the efficiency of the proposed control law which reduces the chattering phenomenon. Moreover, the obtained results prove the robustness of the proposed control law against variation of the load resistance and the input voltage of the studied converter.

Keywords: Buck Boost converter, Sliding Mode Control, Fuzzy Sliding Mode Control, robustness, chattering.

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Authors: İres İskender, Ahmet Karaarslan

Abstract:

In this study, the performance of a high-frequency arc welding machine including a two-switch inverter is analyzed. The control of the system is achieved using two different control techniques i- fuzzy logic control (FLC) ii- state space averaging based sliding control. Fuzzy logic control does not need accurate mathematical model of a plant and can be used in nonlinear applications. The second method needs the mathematical model of the system. In this method the state space equations of the system are derived for two different “on" and “off" states of the switches. The derived state equations are combined with the sliding control rule considering the duty-cycle of the converter. The performance of the system is analyzed by simulating the system using SIMULINK tool box of MATLAB. The simulation results show that fuzzy logic controller is more robust and less sensitive to parameter variations.

Keywords: Fuzzy logic, arc welding, sliding state space control, PWM, current control.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Benmabrouk. Zaineb, Ben Hamed. Mouna, Lassaad. Sbita

Abstract:

This paper discusses the development of wireless structure control of an induction motor scalar drives. This was realised up on the wireless WiFi networks. This strategy of control is ensured by the use of Wireless ad hoc networks and a virtual network interface based on VNC which is used to make possible to take the remote control of a PC connected on a wireless Ethernet network. Verification of the proposed strategy of control is provided by experimental realistic tests on scalar controlled induction motor drives. The experimental results of the implementations with their analysis are detailed.

Keywords: Digital drives, Induction motor, Remote control, Virtual Network Computing VNC, Wireless Local Area NetworkWiFi.

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Authors: Marios M. Hadjiandreou, Raul Conejeros, Ian Wilson

Abstract:

This study presents a mathematical modeling approach to the planning of HIV therapies on an individual basis. The model replicates clinical data from typical-progressors to AIDS for all stages of the disease with good agreement. Clinical data from rapid-progressors and long-term non-progressors is also matched by estimation of immune system parameters only. The ability of the model to reproduce these phenomena validates the formulation, a fact which is exploited in the investigation of effective therapies. The therapy investigation suggests that, unlike continuous therapy, structured treatment interruptions (STIs) are able to control the increase in both the drug-sensitive and drug-resistant virus population and, hence, prevent the ultimate progression from HIV to AIDS. The optimization results further suggest that even patients characterised by the same progression type can respond very differently to the same treatment and that the latter should be designed on a case-by-case basis. Such a methodology is presented here.

Keywords: AIDS, chemotherapy, mathematical modeling, optimal control, progression.

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Authors: I. Goual, M. S. Goual, M. K. Gueddouda, Taïbi Saïd, Abou-Bekr Nabil, A. Ferhat

Abstract:

The aim of the paper is to study the hydro-mechanical behavior of a tuff and calcareous sand mixture. A first experimental phase was carried out in order to find the optimal mixture. This showed that the material composed of 80% tuff and 20% calcareous sand provides the maximum mechanical strength. The second experimental phase concerns the study of the drying-wetting behavior of the optimal mixture was carried out on slurry samples and compacted samples at the MPO. Experimental results let to deduce the parameters necessary for the prediction of the hydro-mechanical behavior of pavement formulated from tuff and calcareous sand mixtures, related to moisture. This optimal mixture satisfies the regulation rules and hence constitutes a good local eco-material, abundantly available, for the conception of pavements.

Keywords: Tuff, sandy calcareous, road engineering, hydro mechanical behaviour, suction.

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Authors: Ahmed Abbas Helmy, M. R. M. Rizk, Mohamed El-Sayed

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A model predictive controller based on recursive learning is proposed. In this SISO adaptive controller, a model is automatically updated using simple recursive equations. The identified models are then stored in the memory to be re-used in the future. The decision for model update is taken based on a new control performance index. The new controller allows the use of simple linear model predictive controllers in the control of nonlinear time varying processes.

Keywords: Adaptive control, model predictive control, dynamic matrix control, online model identification

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Authors: Qasim M. Kriri

Abstract:

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: Parameter linear programming, objective function, sensitivity analysis, optimize profit.

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Authors: László Lengyel, Tihamér Levendovszky, Hassan Charaf

Abstract:

This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations out of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This work discusses the termination properties of VCFL and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual Model Transformation, OCL, Termination Properties, UML.

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Authors: J. Fei

Abstract:

This paper presents the adaptive control scheme with sliding mode compensator for vibration control problem in the presence of disturbance. The dynamic model of the flexible cantilever beam using finite element modeling is derived. The adaptive control with sliding mode compensator using output feedback for output tracking is developed to reject the external disturbance, and to improve the tracking performance. Satisfactory simulation results verify that the effectiveness of adaptive control scheme with sliding mode compensator.

Keywords: finite element model, adaptive control, sliding modecontrol, vibration suppression

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Authors: S. Abouda, F. Nollet, A. Chaari, N. Essounbouli, Y. Koubaa

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In this paper we propose the study of a centrifugal pump control system driven by a three-phase induction motor, which is supplied by a PhotoVoltaic PV generator. The system includes solar panel, a DC / DC converter equipped with its MPPT control, a voltage inverter to three-phase Pulse Width Modulation - PWM and a centrifugal pump driven by a three phase induction motor. In order to control the flow of the centrifugal pump, a Direct Torque Control - DTC of the induction machine is used. To illustrate the performances of the control, simulation results are carried out using Matlab/Simulink.

Keywords: Photovoltaic generators, Maximum power point tracking (MPPT), DC/DC converters, Induction motor, Direct torque control (DTC).

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Authors: Satyendra Pratap Singh, S. P. Singh

Abstract:

This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: Gravitational Search Algorithm (GSA), Law of Motion, Law of Gravity, Observability, Phasor Measurement Unit.

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Authors: M. Shakir Saat, M. Noh Ahmad, Dr, Amat Amir

Abstract:

A cart-ball system is a challenging system from the control engineering point of view. This is due to the nonlinearities, multivariable, and non-minimum phase behavior present in this system. This paper is concerned with the problem of modeling and control of such system. The objective of control strategy is to place the cart at a desired position while balancing the ball on the top of the arc-shaped track fixed on the cart. A State-Feedback Controller (SFC) with a pole-placement method will be designed in order to control the system. At first, the mathematical model of a cart-ball system in the state-space form is developed. Then, the linearization of a model will be established in order to design a SFC. The integral control strategy will be performed as to control the cart position of a system. Simulation work is then performed using MATLAB/SIMULINK software in order to study the performance of SFC when applied to the system.

Keywords: Cart-Ball System, Integral Control, Pole-PlacementMethod, State-Feedback Controller.

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

Abstract:

In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: Autonomous vehicles, convoy, nonlinear control, nonlinear observer, sliding mode.

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Authors: S. Sutha, N. Kamaraj

Abstract:

In deregulated operating regime power system security is an issue that needs due thoughtfulness from researchers in the horizon of unbundling of generation and transmission. Electric power systems are exposed to various contingencies. Network contingencies often contribute to overloading of branches, violation of voltages and also leading to problems of security/stability. To maintain the security of the systems, it is desirable to estimate the effect of contingencies and pertinent control measurement can be taken on to improve the system security. This paper presents the application of particle swarm optimization algorithm to find the optimal location of multi type FACTS devices in a power system in order to eliminate or alleviate the line over loads. The optimizations are performed on the parameters, namely the location of the devices, their types, their settings and installation cost of FACTS devices for single and multiple contingencies. TCSC, SVC and UPFC are considered and modeled for steady state analysis. The selection of UPFC and TCSC suitable location uses the criteria on the basis of improved system security. The effectiveness of the proposed method is tested for IEEE 6 bus and IEEE 30 bus test systems.

Keywords: Contingency Severity Index, Particle Swarm Optimization, Performance Index, Static Security Assessment.

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Authors: O. Sotolongo-Grau, D. Rodriguez-Perez, J. A. Santos-Miranda, M. M. Desco, O. Sotolongo-Costa, J. C. Antoranz

Abstract:

The use of the oncologic index ISTER allows for a more effective planning of the radiotherapic facilities in the hospitals. Any change in the radiotherapy treatment, due to unexpected stops, may be adapted by recalculating the doses to the new treatment duration while keeping the optimal prognosis. The results obtained in a simulation model on millions of patients allow the definition of optimal success probability algorithms.

Keywords: Mathematical model, radiation oncology, dynamical systems applications.

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Authors: Kazuya Sato, Toru Kasahara, Junji Kuroda, Tomoyuki Izu

Abstract:

In this paper, an autonomous hovering control method of multicopter using only Web camera is proposed. Recently, various control method of an autonomous flight for multicopter are proposed. But, in the previous proposed methods, a motion capture system (i. e., OptiTrack) and laser range finder are often used to measure the position and posture of multicopter. To achieve an autonomous flight control of multicopter with simple equipments, we propose an autonomous flight control method using AR marker and Web camera. AR marker can measure the position of multicopter with Cartesian coordinate in three dimensional, then its position connects with aileron, elevator, and accelerator throttle operation. A simple PID control method is applied to the each operation and adjust the controller gains. Experimental results are given to show the effectiveness of our proposed method. Moreover, another simple operation method for autonomous flight control multicopter is also proposed.

Keywords: Autonomous hovering control, multicopter, Web camera.

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Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

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In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: Optimal linear quadratic tracker, proportional plus integral observer, state estimator, disturbance estimator.

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Authors: Ahmed Rekik, Mourad Zribi, Ahmed Ben Hamida, Mohamed Benjelloun

Abstract:

This paper presents an optimal and unsupervised satellite image segmentation approach based on Pearson system and k-Means Clustering Algorithm Initialization. Such method could be considered as original by the fact that it utilised K-Means clustering algorithm for an optimal initialisation of image class number on one hand and it exploited Pearson system for an optimal statistical distributions- affectation of each considered class on the other hand. Satellite image exploitation requires the use of different approaches, especially those founded on the unsupervised statistical segmentation principle. Such approaches necessitate definition of several parameters like image class number, class variables- estimation and generalised mixture distributions. Use of statistical images- attributes assured convincing and promoting results under the condition of having an optimal initialisation step with appropriated statistical distributions- affectation. Pearson system associated with a k-means clustering algorithm and Stochastic Expectation-Maximization 'SEM' algorithm could be adapted to such problem. For each image-s class, Pearson system attributes one distribution type according to different parameters and especially the Skewness 'β1' and the kurtosis 'β2'. The different adapted algorithms, K-Means clustering algorithm, SEM algorithm and Pearson system algorithm, are then applied to satellite image segmentation problem. Efficiency of those combined algorithms was firstly validated with the Mean Quadratic Error 'MQE' evaluation, and secondly with visual inspection along several comparisons of these unsupervised images- segmentation.

Keywords: Unsupervised classification, Pearson system, Satellite image, Segmentation.

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Authors: Santi Behera, M. Tripathy, J. K. Satapathy

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Power systems are operating under stressed condition due to continuous increase in demand of load. This can lead to voltage instability problem when face additional load increase or contingency. In order to avoid voltage instability suitable size of reactive power compensation at optimal location in the system is required which improves the load margin. This work aims at obtaining optimal size as well as location of compensation in the 39- bus New England system with the help of Bacteria Foraging and Genetic algorithms. To reduce the computational time the work identifies weak candidate buses in the system, and then picks only two of them to take part in the optimization. The objective function is based on a recently proposed voltage stability index which takes into account the weighted average sensitivity index is a simpler and faster approach than the conventional CPF algorithm. BFOA has been found to give better results compared to GA.

Keywords: BFOA, GA, SSVSL, WASI.

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Authors: R. Srinivasa Rao, S. V. L. Narasimham

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This paper presents a novel approach for optimal reconfiguration of radial distribution systems. Optimal reconfiguration involves the selection of the best set of branches to be opened, one each from each loop, such that the resulting radial distribution system gets the desired performance. In this paper an algorithm is proposed based on simple heuristic rules and identified an effective switch status configuration of distribution system for the minimum loss reduction. This proposed algorithm consists of two parts; one is to determine the best switching combinations in all loops with minimum computational effort and the other is simple optimum power loss calculation of the best switching combination found in part one by load flows. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 33-bus system. The results show that the performance of the proposed method is better than that of the other methods.

Keywords: Distribution system, network reconfiguration, powerloss reduction, radial network, heuristic technique.

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Authors: Myungraee Cha, Jun Seok Kim, Seung Hwan Park, Jun-Geol Baek

Abstract:

In manufacturing industries, development of measurement leads to increase the number of monitoring variables and eventually the importance of multivariate control comes to the fore. Statistical process control (SPC) is one of the most widely used as multivariate control chart. Nevertheless, SPC is restricted to apply in processes because its assumption of data as following specific distribution. Unfortunately, process data are composed by the mixture of several processes and it is hard to estimate as one certain distribution. To alternative conventional SPC, therefore, nonparametric control chart come into the picture because of the strength of nonparametric control chart, the absence of parameter estimation. SVDD based control chart is one of the nonparametric control charts having the advantage of flexible control boundary. However,basic concept of SVDD has been an oversight to the important of data characteristic, density distribution. Therefore, we proposed DW-SVDD (Density Weighted SVDD) to cover up the weakness of conventional SVDD. DW-SVDD makes a new attempt to consider dense of data as introducing the notion of density Weight. We extend as control chart using new proposed SVDD and a simulation study of various distributional data is conducted to demonstrate the improvement of performance.

Keywords: Density estimation, Multivariate control chart, Oneclass classification, Support vector data description (SVDD)

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Authors: H. Iranmanesh, M. R. Skandari, M. Allahverdiloo

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Project managers are the ultimate responsible for the overall characteristics of a project, i.e. they should deliver the project on time with minimum cost and with maximum quality. It is vital for any manager to decide a trade-off between these conflicting objectives and they will be benefited of any scientific decision support tool. Our work will try to determine optimal solutions (rather than a single optimal solution) from which the project manager will select his desirable choice to run the project. In this paper, the problem in project scheduling notated as (1,T|cpm,disc,mu|curve:quality,time,cost) will be studied. The problem is multi-objective and the purpose is finding the Pareto optimal front of time, cost and quality of a project (curve:quality,time,cost), whose activities belong to a start to finish activity relationship network (cpm) and they can be done in different possible modes (mu) which are non-continuous or discrete (disc), and each mode has a different cost, time and quality . The project is constrained to a non-renewable resource i.e. money (1,T). Because the problem is NP-Hard, to solve the problem, a meta-heuristic is developed based on a version of genetic algorithm specially adapted to solve multi-objective problems namely FastPGA. A sample project with 30 activities is generated and then solved by the proposed method.

Keywords: FastPGA, Multi-Execution Activity Mode, ParetoOptimality, Project Scheduling, Time-Cost-Quality Trade-Off.

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Authors: A. Elakkary, A. Echchatbi, N. Elalami

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In this paper, we are interested in attitude control of a satellite, which using wheels of reaction, by state feedback. First, we develop a method allowing us to put the control and its integral in the state-feedback form. Then, by using the theorem of Gronwall- Bellman, we put the sufficient conditions so that the nonlinear system modeling the satellite is stabilisable and observed by state feedback.

Keywords: Satellite, attitude control, state feedback, attitude stabilization.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

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Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Govind Shay Sharma, Randhir Singh Baghel

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The stock management of raw materials and finished goods is a significant issue for industries in fulfilling customer demand. Optimization of inventory strategies is crucial to enhancing customer service, reducing lead times and costs, and meeting market demand. This paper suggests finding an approach to predict the optimum stock level by utilizing past stocks and forecasting the required quantities. In this paper, we utilized Artificial Neural Network (ANN) to determine the optimal value. The objective of this paper is to discuss the optimized ANN that can find the best solution for the inventory model. In the context of the paper, we mentioned that the k-means algorithm is employed to create homogeneous groups of items. These groups likely exhibit similar characteristics or attributes that make them suitable for being managed using uniform inventory control policies. The paper proposes a method that uses the neural fit algorithm to control the cost of inventory.

Keywords: Artificial Neural Network, inventory management, optimization, distributor center.

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Authors: M.Saleem Khan, Khaled Benkrid

Abstract:

This paper presents a time control liquids mixing system in the tanks as an application of fuzzy time control discrete model. The system is designed for a wide range of industrial applications. The simulation design of control system has three inputs: volume, viscosity, and selection of product, along with the three external control adjustments for the system calibration or to take over the control of the system autonomously in local or distributed environment. There are four controlling elements: rotatory motor, grinding motor, heating and cooling units, and valves selection, each with time frame limit. The system consists of three controlled variables measurement through its sensing mechanism for feed back control. This design also facilitates the liquids mixing system to grind certain materials in tanks and mix with fluids under required temperature controlled environment to achieve certain viscous level. Design of: fuzzifier, inference engine, rule base, deffuzifiers, and discrete event control system, is discussed. Time control fuzzy rules are formulated, applied and tested using MATLAB simulation for the system.

Keywords: Fuzzy time control, industrial application and timecontrol systems, adjustment of Fuzzy system, liquids mixing system, design of fuzzy time control DEV system.

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Authors: Seyed Mohammad Hosseini, Amirhossein Moghanian

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The main purpose of this research was to design a biomimetic system by freeze-drying method for evaluating the effect of adding 5 and 10 mol. % of zinc (Zn) in 58S bioactive glass and gelatin (5ZnBG/G and 10ZnBG/G) in terms of structural and biological changes. The structural analyses of samples were performed by X-Ray Diffraction (XRD), scanning electron microscopy (SEM) and Fourier-transform infrared (FTIR) spectroscopy. Also, 3-(4,5dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) and alkaline phosphatase (ALP) activity tests were carried out for investigation of MC3T3-E1 cell behaviors. The SEM results demonstrated the spherical shape of the formed hydroxyapatite (HA) phases and also HA characteristic peaks were detected by XRD spectroscopy after 3 days of immersion in the simulated body fluid (SBF) solution. Meanwhile, FTIR spectra proved that the intensity of P–O peaks for 5ZnBG/G was more than 10ZnBG/G and control samples. Moreover, the results of ALP activity test illustrated that the optimal amount of Zn (5ZnBG/G) caused a considerable enhancement in bone cell growth. Taken together, the scaffold with 5 mol.% Zn was introduced as an optimal sample because of its higher biocompatibility, in vitro bioactivity and growth of MC3T3-E1 cells in comparison with other samples in bone tissue engineering.

Keywords: Scaffold, gelatin, modified bioactive glass, ALP, bone tissue engineering.

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Authors: Rita SahaRay, Ganesh Dutta

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In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n ≡ 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs providing estimation of all main effects orthogonal to the block effects. In practice, such orthogonal estimation of main effects is often a desirable condition. In the wider class of all available m two level even sized blocked main effects plans, where the factors do not occur at high and low levels equally often in each block, E-optimal designs are also characterized. Simple construction methods based on Hadamard matrices and Kronecker product for these optimal designs are presented.

Keywords: Design matrix, Hadamard matrix, Kronecker product, type 1 criteria, type 2 criteria.

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