A Programmable logic controller (PLC) uses the digital logic circuits and their operating concepts in its hardware structure and its programming instructions and algorithms. Therefore, the deep understanding of these two items is staple for the development of control applications using the PLC. This target is only possible through the practical sensing of the various components or instructions of these two items and their applications. In this work, a user-friendly and re-configurable ladder, digital logic learning and application development design and testing platform has been designed and implemented using a Programmable Logic Controller (PLC), Human Machine Interface panel (HMI), four magnetic contactors, one Single-phase power line controller and one Variable Frequency Drive (VFD) unit. The PLC role is to implement the ladder and digital logic functions. The HMI role is to establish the virtual circuit wiring and also to drive and monitor the developed application in real time mode of application. The magnetic contactors are to play the role of industrial field actuators or to link the developed application control circuit to another field actuator like three phase induction motor. The Single -phase power line controller is to support an application like that of the soft starter. The VFD is to support induction motor driven applications like that of cut-to-length process in which steel coils are uncoiled and passed through cutting blade to be cut into required lengths. The proposed platform has been tested through the development of 14 application examples. The test results proved the validity of the proposed platform.
In this paper ternary logic is encoded into binary and certain processes were conducted on binary logic after which the binary is decoded to ternary. General purpose digital devices were used and the circuit is designed back to front starting from ternary logic provided by transistor pairs at output side back to front end. This provided easier design technique in this particular paper. Practical and simulation results are recorded. K eyw ords: Logic, ternary- binary conversion, coding, decoding. تشفير المنطق الثالثي رونق علي حبيب جامعة الب صرة / كلية الهندسة / العراق الخالصة في هذا البحث يتم تشفير المنطق الثالثي الى ثنائي ويتم اجراء بعض العمليات على المنطق الثنائي التي يتم بعدها االعادة الى الشفرة الثالثية . استخدمت النبائط الرقمية لالغراض العامة (general purpose devices) في تصميم الدائرة الذ ي يتم من مرحلة االخراج (output) الى مرحلة االدخال (input) بدءا من المنطق الثالثي باستخدام ازواج الترانزستور في جهة االخراج والعودة الى جهة االدخال . هذا يجعل تقنية التصميم اسهل ( في هذا البحث خاصة ). ولقد تم تسجيل النتائج العملية ونتائج المحاكاة للدائرة العمل . ية اﻟﻤﺠﻠﺔ اﻟﻌﺮاﻗﻴﺔ ﻟﻠﻬﻨﺪﺳﺔ اﻟﻜﻬﺮﺑﺎﺋﻴﺔ واﻻﻟﻜﺘﺮوﻧﻴﺔ Iraq J. Electrical and Electronic Engineering ﻡﺠﻠﺪ 10 ، اﻟﻌﺪد 1 ، 2014 Vol.10 No.1 , 2014 24
This paper presents a method for improving the speed profile of a three phase induction motor in direct torque control (DTC) drive system using a proposed fuzzy logic based speed controller. A complete simulation of the conventional DTC and closed-loop for speed control of three phase induction motor was tested using well known Matlab/Simulink software package. The speed control of the induction motor is done by using the conventional proportional integral (PI) controller and the proposed fuzzy logic based controller. The proposed fuzzy logic controller has a nature of (PI) to determine the torque reference for the motor. The dynamic response has been clearly tested for both conventional and the proposed fuzzy logic based speed controllers. The simulation results showed a better dynamic performance of the induction motor when using the proposed fuzzy logic based speed controller compared with the conventional type with a fixed (PI) controller.
Efficient energy collection from photovoltaic (PV) systems in environments that change is still a challenge, especially when partial shading conditions (PSC) come into play. This research shows a new method called Maximum Power Point Tracking (MPPT) that uses fuzzy logic and neural networks to make PV systems more flexible and accurate when they are exposed to PSC. Our method uses a fuzzy logic controller (FLC) that is specifically made to deal with uncertainty and imprecision. This is different from other MPPT methods that have trouble with the nonlinearity and transient dynamics of PSC. At the same time, an artificial neural network (ANN) is taught to guess where the Global Maximum Power Point (GMPP) is most likely to be by looking at patterns of changes in irradiance and temperature from the past. The fuzzy controller fine-tunes the ANN’s prediction, ensuring robust and precise MPPT operation. We used MATLAB/Simulink to run a lot of simulations to make sure our proposed method would work. The results showed that combining fuzzy logic with neural networks is much better than using traditional MPPT algorithms in terms of speed, stability, and response to changing shading patterns. This innovative technique proposes a dual-layered control mechanism where the robustness of fuzzy logic and the predictive power of neural networks converge to form a resilient and efficient MPPT system, marking a significant advancement in PV technology.
The power quality problems can be defined as the difference between the quality of power supplied and the quality of power required. Recently a large interest has been focused on a power quality domain due to: disturbances caused by non-linear loads and Increase in number of electronic devices. Power quality measures the fitness of the electric power transmitted from generation to industrial, domestic and commercial consumers. At least 50% of power quality problems are of voltage quality type. Voltage sag is the serious power quality issues for the electric power industry and leads to the damage of sensitive equipments like, computers, programmable logic controller (PLC), adjustable speed drives (ADS). The prime goal of this paper is to investigate the performance of the Fuzzy Logic controller based DVR in reduction the power disturbances to restore the load voltage to the nominal value and reduce the THD to a permissible value which is 5% for the system less than 69Kv. The modeling and simulation of a power distribution system have been achieved using MATLABL/Simulink. Different faults conditions and power disturbances with linear and non-linear loads are created with the proposed system, which are initiated at a duration of 0.8sec and kept till 0.95sec.
In this work, a new architecture is designed for fuzzy logic system. The proposed architecture is implemented on field programed gate array (FPGA). The hardware designed fuzzy systemimproves the excution speed with very high speed up factor using low cost availble kits such as FPGA. The implementation of the proposed architecture uses very low amount of logic elements and logic array blocks as proven when implementing the proposed architucture on FPGA.
Power transformer protective relay should block the tripping during magnetizing inrush and rapidly operate the tripping during internal faults. Recently, the frequency environment of power system has been made more complicated and the quantity of 2nd frequency component in inrush state has been decreased because of the improvement of core steel. And then, traditional approaches will likely be maloperated in the case of magnetizing inrush with low second harmonic component and internal faults with high second harmonic component. This paper proposes a new relaying algorithm to enhance the fault detection sensitivities of conventional techniques by using a fuzzy logic approach. The proposed fuzzy-based relaying algorithm consists of flux-differential current derivative curve, harmonic restraint, and percentage differential characteristic curve. The proposed relaying was tested with MATLAB simulation software and showed a fast and accurate trip operation.
The increasing demand for electricity due to population expansion has led to frequent interruptions in electrical power, so there are backup power lines everywhere, especially in the sectors of education, health, banking, transportation and communications. DC sources are beginning to become widely spread in terms of low maintenance requirements, no need for refueling, and no pollutant emission in these institutions. The problems of DC systems are; losses in DC system components, and change in output voltage as loads change. This research presents a power system that generates 1760W AC power from batteries bank, the system consists of a twin inverter to reduce losses in switches and filters, and thus improving the efficiency and the power factor of the system, and fuzzy logic controllers to regulate the output voltage of the converter and inverter. Modeling and simulation in MATLAB / Simulink showed obtaining a constant load voltage with acceptable values of total harmonics distortion (THD) under different conditions of loads and batteries.
In this work, a healthcare monitoring system-based Internet of Medical Things (IoMT) is proposed, implemented, analyze it by artificial intelligence using fuzzy logic. Atmega microcontroller was used to achieve the function of the proposed work and provide the area for monitoring and Analytic(decision) to the caretakers or doctors through putting the results in the platform. In this paper, the heart rate pulse sensor and infrared temperature sensor are chosen, which give skin temperature and room temperature to provide their results to the caretaker. The decision that gives the patient is in a normal state, or the fuzzy logic does an abnormal state or risk state. The fuzzy logic is used for it accurate and fast in processing data and gives a result very closer to the reality in smart health services. IoMT enables the doctors and caretakers to monitor the patient easily at any time and any place by using their intelligent laptops, tablets, and phones. Finally, the proposed system can contribute to the construction of a wide healthcare monitoring system in the unit or in the department that follows on for the hospital. Therefore, Doctors can improve the accuracy of the diagnosis, as they receive all the patient data necessary.
A theoretical analysis is presented to calculate the signal phase shift and the gain coefficient associated with two-wave mixing in photorefractive crystals subjected to an external electric field. The relative position of the induced-refractive index grating with respect to the fringe pattern of the two input optical beams leads to a coupling effect between the phase and intensity of these beams. An optical logic operation system that is based on photorefractive two-wave mixing is introduced. This system uses the fringe-shifting techniques that are executed by a Mach-Zehnder interferometer. The proposed system configurations are capable of producing all the basic 16 two-operand Boolean functions simultaneously at different output planes.
This paper presents and discusses a buck DC/DC converter control based on fuzzy logic approach, in which the fuzzy controller has been driven by voltage error signal and a current error signal for which the load current has been taken as a reference one. The validity of the proposed approach has been examined through starting the buck DC/DC converter at different loading and input voltages (to monitor the starting performances), exposing the converter into large load resistance and input voltage step variations (to explore its dynamic performance), in addition to step and smooth variation in the reference voltage (to see its ability in readjusting its operating point to comply with the new setting). The simulation results presented an excellent load & line regulations abilities in addition to a good reference tracking ability. It also showed the possibility of using the buck converter as smooth variable voltage source (under smooth reference voltage variations).
In this paper an integrated electronic system has been designed, constructed and tested. The system utilizes an interface card through the parallel port in addition to some auxiliary circuits to perform fuzzy control operations for DC motor speed control with load and no load. Software is written using (C++ language Ver. 3.1) to display the image as control panel for different types of both conventional and fuzzy control. The main task of the software is to simulate: first, how to find out the correct parameters for fuzzy logic controller (membership’s function, rules and scaling factor). Second, how to evaluate the gain factors (K P , K I and K D ) by Ziegler-Nichols method. When executing any type of control process the efficiency is estimated by drawing the relative speed response for this control.
Navigational sensors are evolving both on a commercial and research level. However, the limitation still lies in the accuracy of the respective sensors. For a navigation system to reach a certain accuracy, multi sensors or fusion sensors are used. In this paper, a framework of fuzzy sensor data fusing is proposed to obtain an optimised navigational system. Different types of sensors without a known state of inaccuracy can be fused using the same method proposed. This is demonstrated by fusing compass/accelerometer and GPS signal. GPS is prone to inaccuracies due to environmental factors. These inaccuracies are available in the extracted NMEA protocols as SNR and HDOP. Dead reckoning sensors on the other hand do not depend on external radio signal coverage and can be used in areas with low coverage, but the errors are unbounded and have an accumulative effect over time.
This paper deals with the navigation of a mobile robot in unknown environment using artificial potential field method. The aim of this paper is to develop a complete method that allows the mobile robot to reach its goal while avoiding unknown obstacles on its path. An approach proposed is introduced in this paper based on combing the artificial potential field method with fuzzy logic controller to solve drawbacks of artificial potential field method such as local minima problems, make an effective motion planner and improve the quality of the trajectory of mobile robot.
Soft computing control system have been applied in various applications particularly in the fields of robotics controls. The advantage of having a soft computing controls methods is that it enable more flexibility to the control system compared with conventional model based controls system. In this paper, a UAV airship is controlled using fuzzy logic for its propulsion and steering system. The airship is tested on a simulation level before test flight. The prototype airship has on board GPS and compass for telemetry and transmitted to the ground control system via a wireless link.
This paper present an adaptation mechanism for fuzzy logic controller FLC in order to perfect the response performance against small rotation angles of real D.C. motor with unknown parameters. A supervisor fuzzy controller SFC is designed to continuously adjust, on-line, the universe of discourse UOD of the basic fuzzy controller BFC input variables based on position error and change of position error. Performance of the proposed adaptive fuzzy controller is compared with corresponding conventional FLC in terms of several performance measures such rise time, settling time, peak overshoot, and steady state error. The system design and implementation are carried out using LabVIEW 2009 with NI PCI-6251 data acquisition DAQ card. The practical results demonstrate using self tuning FLC scheme grant a better performance as compared with conventional FLC which is incapable of rotating a motor if the rotation angle is being small.
In this paper, we present a new programmable chaotic circuit based on the dynamical chaotic system introduced by E. Lorenz. The design and realization of the model are accomplished by using a programmable logic controller (PLC). The system can be modeled and realized with a structured texted. The nonlinear differential equations of Lorenz model are solved numerically. The generated chaotic signal by using PLC is applied to a single- phase induction motor via a variable frequency drive to create a chaotic perturbation in the experiments of liquid mixing. Colorization liquid experiments shows that the generated chaotic motion effectively makes an enhancement of the mixing process in the stirred-tank mixer model in our laboratory.
A self learning fuzzy logic controller for ship steering systems is proposed in this paper. Due to the high nonlinearity of ship steering system, the performances of traditional control algorithms are not satisfactory in fact. An intelligent control system is designed for controlling the direction heading of ships to improve the high e ffi ciency of transportation, the convenience of manoeuvring ships, and the safety of navigation. The design of fuzzy controllers is usually performed in an ad hoc manner where it is hard to justify the choice of some fuzzy control parameters such as the parameters of membership function. In this paper, self tuning algorithm is used to adjust the parameters of fuzzy controller. Simulation results show that the efficiency of proposed algorithm to design a fuzzy controller for ship steering system.
Energy limitations have become fundamental challenge for designing WSNs. Network lifetime is the most interested and important metric in WSNs. Many works have been developed for prolonging networks lifetime, in which one of the important work is the control of transmission power. This paper proposes a new fuzzy transmission power control technique that operate together with routing protocols for prolonging WSNs lifetime. Dijkstra shortest path routing is considered as the main routing protocol in this work. This paper mainly focuses on transmission power control scheme for prolonging WSNs lifetime. A performance comparison is depicted for maximum and controlled transmission power. Simulation results show an increase in network lifetime equals to 3.4776 for the proposed fuzzy control. The performance of the proposed fuzzy control technique involves a good improvement and contribution in the field of prolonging networks lifetime by using transmission power control.
The Intelligent Control of Vibration Energy Harvesting system is presented in this paper. The harvesting systems use a me- chanical vibration to generate electrical energy in a suitable form for use. Proportional-Integrated-derivative controller and Fuzzy Logic controller have been suggested; their parameters are optimized using a new heuristic algorithm, the Camel Trav- eling Algorithm(CTA). The proposed circuit Simulink model was constructed in Matlab facilities, and the model was tested under various operating conditions. The results of the simulation using the CTA was compared with two other methods.
In this paper, optical scalable parallel and high-speed 2D data array adder for trinary signed-digit (TSD) number is proposed. The digit-decomposition-plane (DDP) coding method is used to represent the 2D TSD data arrays. The algorithm performs parallel TSD addition in constant time independent of the size of the TSD data arrays. The design describes methodology to involve two-step TSD adder. The TSD addition is expressed with several combination logic formulas that are newly derived. Optical implementation with classical optical elements is suggested for proposed TSD adder. Preliminary demonstration example is also described.
Clustering is one of the most energy-efficient techniques for extending the lifetime of wireless sensor networks (WSNs). In a clustered WSN, each sensor node transmits the data acquired from the sensing field to the leader node (cluster head). The cluster head (CH) is in charge of aggregating and routing the collected data to the Base station (BS) of the deployed network. Thereby, the selection of the optimum CH is still a crucial issue to reduce the consumed energy in each node and extend the network lifetime. To determine the optimal number of CHs, this paper proposes an Enhanced Fuzzy-based LEACH (E-FLEACH) protocol based on the Fuzzy Logic Controller (FLC). The FLC system relies on three inputs: the residual energy of each node, the distance of each node from the base station (sink node), as well as the node's centrality. The proposed protocol is implemented using the Castalia simulator in conjunction with OMNET++, and simulation results indicate that the proposed protocol outperforms the traditional LEACH protocol in terms of network lifetime, energy consumption, and stability.
The segmentation methods for image processing are studied in the presented work. Image segmentation can be defined as a vital step in digital image processing. Also, it is used in various applications including object co-segmentation, recognition tasks, medical imaging, content based image retrieval, object detection, machine vision and video surveillance. A lot of approaches were created for image segmentation. In addition, the main goal of segmentation is to facilitate and alter the image representation into something which is more important and simply to be analyzed. The approaches of image segmentation are splitting the images into a few parts on the basis of image’s features including texture, color, pixel intensity value and so on. With regard to the presented study, many approaches of image segmentation are reviewed and discussed. The techniques of segmentation might be categorized into six classes: First, thresholding segmentation techniques such as global thresholding (iterative thresholding, minimum error thresholding, otsu's, optimal thresholding, histogram concave analysis and entropy based thresholding), local thresholding (Sauvola’s approach, T.R Singh’s approach, Niblack’s approaches, Bernsen’s approach Bruckstein’s and Yanowitz method and Local Adaptive Automatic Binarization) and dynamic thresholding. Second, edge-based segmentation techniques such as gray-histogram technique, gradient based approach (laplacian of gaussian, differential coefficient approach, canny approach, prewitt approach, Roberts approach and sobel approach). Thirdly, region based segmentation approaches including Region growing techniques (seeded region growing (SRG), statistical region growing, unseeded region growing (UsRG)), also merging and region splitting approaches. Fourthly, clustering approaches, including soft clustering (fuzzy C-means clustering (FCM)) and hard clustering (K-means clustering). Fifth, deep neural network techniques such as convolution neural network, recurrent neural networks (RNNs), encoder-decoder and Auto encoder models and support vector machine. Finally, hybrid techniques such as evolutionary approaches, fuzzy logic and swarm intelligent (PSO and ABC techniques) and discusses the pros and cons of each method.
This paper examines the use of non-integer switching frequency ratios in digitally controlled DC-DC converters. In particular the execution of multiple control algorithms using a Digital Signal Processor (DSP) for this application is analyzed. The variation in delay from when the Analog to Digital Converter (ADC) samples the output voltage to when the duty cycle is updated is identified as a critical factor to be considered when implementing the digital control system. Fixing the delay to its maximum value is found to produce reasonable performance using a conventional DSP. A modification of the DSP’s interrupt control logic is proposed here that minimizes the delay and thereby yields improved performance compared with that given by a standard interrupt controller. Applying this technique to a multi-rail power supply system provides the designer with the flexibility to choose arbitrary switching frequencies for individual converters, thereby allowing optimization of the efficiency and performance of the individual converters.
In this paper, enhancing dynamic performance in power systems through load frequency control (LFC) is explored across diverse operating scenarios. A new Neural Network Model Predictive Controller (NN-MPC) specifically tailored for two-zone load frequency power systems is presented. ” Make your paper more scientific. The NN-MPC marries the predictive accuracy of neural networks with the robust capabilities of model predictive control, employing the nonlinear Levenberg-Marquardt method for optimization. Utilizing local area error deviation as feedback, the proposed controller’s efficacy is tested against a spectrum of operational conditions and systemic variations. Comparative simulations with a Fuzzy Logic Controller (FLC) reveal the proposed NN-MPC’s superior performance, underscoring its potential as a formidable solution in power system regulation.
The Fast Fourier Transform (FFT) and Inverse FFT(IFFT) are used in most of the digital signal processing applications. Real time implementation of FFT/IFFT is required in many of these applications. In this paper, an FPGA reconfigurable fixed point implementation of FFT/IFFT is presented. A manually VHDL codes are written to model the proposed FFT/IFFT processor. Two CORDIC-based FFT/IFFT processors based on radix-2and radix-4 architecture are designed. They have one butterfly processing unit. An efficient In-place memory assignment and addressing for the shared memory of FFT/IFFT processors are proposed to reduce the complexity of memory scheme. With "in-place" strategy, the outputs of butterfly operation are stored back to the same memory location of the inputs. Because of using DIF FFT, the output was to be in reverse order. To solve this issue, we have re-use the block RAM that used for storing the input sample as reordering unit to reduce hardware cost of the proposed processor. The Spartan-3E FPGA of 500,000 gates is employed to synthesize and implement the proposed architecture. The CORDIC based processors can save 40% of power consumption as compared with Xilinx logic core architectures of system generator.
According to the growing interest in the soft robotics research field, where various industrial and medical applications have been developed by employing soft robots. Our focus in this paper will be the Pneumatic Muscle Actuator (PMA), which is the heart of the soft robot. Achieving an accurate control method to adjust the actuator length to a predefined set point is a very difficult problem because of the hysteresis and nonlinearity behaviors of the PMA. So the construction and control of a 30 cm soft contractor pneumatic muscle actuator (SCPMA) were done here, and by using different strategies such as the PID controller, Bang-Bang controller, Neural network controller, and Fuzzy controller, to adjust the length of the (SCPMA) between 30 cm and 24 cm by utilizing the amount of air coming from the air compressor. All of these strategies will be theoretically implemented using the MATLAB/Simulink package. Also, the performance of these control systems will be compared with respect to the time-domain characteristics and the root mean square error (RMSE). As a result, the controller performance accuracy and robustness ranged from one controller to another, and we found that the fuzzy logic controller was one of the best strategies used here according to the simplicity of the implementation and the very accurate response obtained from this method.
This is a design of an expert system in the focused ion beam optical system by using fuzzy logic technique to build an intelligent agent. Present software has been designed as an interpretation expert system, written in Visual C# for optimizing the calculation of three electrostatic lenses column. By using such rule based engine, the axial potential distributions for electrostatic fields undergo the constraints have been used to find spot size focusing for ions in the image plane which have values are very useful for getting and designing FIB model, over ranges of ion beam angles (5, 10,30,50,75 and 100) mrad.
Microgrids (ℳ-grids) can be thought of as a small-scale electrical network comprised of a mix of Distributed Generation (DG) resources, storage devices, and a variety of load species. It provides communities with a stable, secure, and renewable energy supply in either off-grid (grid-forming) or on-grid (grid-following) mode. In this work, a control strategy of coordinated power management for a Low Voltage (LV) ℳ-grid with integration of solar Photovoltaic (PV), Battery Energy Storage System (BESS) and three phase loads operated autonomously or connected to the utility grid has been created and analyzed in the Matlab Simulink environment. The main goal expressed here is to achieve the following points: (i) grid following, grid forming modes, and resynchronization mode between them, (ii) Maximum Power Point Tracking (MPPT) from solar PV using fuzzy logic technique, and active power regulator based boost converter using a Proportional Integral (PI) controller is activated when a curtailment operation is required, (iii) ℳ-grid imbalance compensation (negative sequence) due to large single-phase load is activated, and (iv) detection and diagnosis the fault types using Discrete Wavelet Transform (DWT). Under the influence of irradiance fluctuation on solar plant, the proposed control technique demonstrates how the adopted system works in grid- following mode (PQ control), grid- formation, and grid resynchronization to seamlessly connect the ℳ-grid with the main distribution system. In this system, a power curtailment management system is introduced in the event of a significant reduction in load, allowing the control strategy to be switched from MPPT to PQ control, permitting the BESS to absorb excess power. Also, in grid-following mode, the BESS's imbalance compensation mechanism helps to reduce the negative sequence voltage that occurs at the Point of Common Coupling (PCC) bus as a result of an imbalance in the grid's power supply. In addition to the features described above, this system made use of DWT to detect and diagnose various fault conditions.
Nowadays, renewable energy is being used increasingly because of the global warming and destruction of the environment. Therefore, the studies are concentrating on gain of maximum power from this energy such as the solar energy. A sun tracker is device which rotates a photovoltaic (PV) panel to the sun to get the maximum power. Disturbances which are originated by passing the clouds are one of great challenges in design of the controller in addition to the losses power due to energy consumption in the motors and lifetime limitation of the sun tracker. In this paper, the neuro-fuzzy controller has been designed and implemented using Field Programmable Gate Array (FPGA) board for dual axis sun tracker based on optical sensors to orient the PV panel by two linear actuators. The experimental results reveal that proposed controller is more robust than fuzzy logic controller and proportional- integral (PI) controller since it has been trained offline using Matlab tool box to overcome those disturbances. The proposed controller can track the sun trajectory effectively, where the experimental results reveal that dual axis sun tracker power can collect 50.6% more daily power than fixed angle panel. Whilst one axis sun tracker power can collect 39.4 % more daily power than fixed angle panel. Hence, dual axis sun tracker can collect 8 % more daily power than one axis sun tracker .
CMOS stack circuits find applications in multi-input exclusive-OR gates and barrel-shifters. Specifically, in wide fan-in CMOS NAND/NOR gates, the need arises to connect a relatively large number of NMOS/PMOS transistors in series in the pull-down network (PDN)/pull-up network (PUN). The resulting time delay is relatively high and the power consumption accordingly increases due to the need to deal with the various internal capacitances. The problem gets worse with increasing the number of inputs. In this paper, the performance of conventional static CMOS stack circuits is investigated quantitatively and a figure of merit expressing the performance is defined. The word “performance” includes the following three metrics; the average propagation delay, the power consumption, and the area. The optimum scaling factor corresponding to the best performance is determined. It is found that under the worst-case low-to-high transition at the output (that is, the input combination that results in the longest time delay in case of logic “1” at the output), there is an optimum value for the sizing of the PDN in order to minimize the average propagation delay. The proposed figure of merit is evaluated for different cases with the results discussed. The adopted models and the drawn conclusions are verified by comparison with simulation results adopting the 45 nm CMOS technology.