Order Transfer Function Research Articles

Optimization of the Control of Electromagnetic Brakes in the Stand for Tuning Internal Combustion Engines Using ID Regulators of Fractional Order

This work is aimed at developing a stand for tuning the fuel system of an internal combustion engine based on two electromagnetic retarders connected to the driving wheels of a car to simulate a load, and a microprocessor-based torque control system for each brake. In accordance with the terms of reference from the specialists of the automotive service center, such a stand should provide two main modes of operation: (1) stabilization of the speed of the drive wheels in the entire range of loads (fuel supply); (2) engine acceleration and deceleration according to linear tachograms in the range from minimum to maximum speed to determine the dependence of engine power and torque on speed. The purpose of this research is the synthesis of controllers, testing, the choice of the structural scheme, and the parameters of the control and data processing system in the stand for the precision tuning of internal combustion engines. Based on a preliminary analysis of the system, taking into account the mechanical connection of the wheels through the main gear and the car differential, the nonlinear dependence of the electromagnetic torque on the current and retarder speed, and subsequent experimental results, we obtained two types of controller—a third-order aperiodic transfer function and a fractional aperiodic transfer function of order 1.6. This made it possible to synthesize a family of controllers that ensure the operation of the stand in the required modes: synchronization of wheel speeds during engine acceleration; stabilization of the reference speed when the engine torque is changed from minimum to maximum due to fuel supply; measurement of the maximum power and torque of the internal combustion engine during the formation of a triangular tachogram with a given acceleration to compensate for the dynamic component of the torque due to mechanical inertia. The system with the PID controller configured in MATLAB in the “Tune” package has the best performance, but the smallest overshoot and the best dynamic accuracy are ensured by the PIDIγIµ fractional–integral controller, where the system is characterized by a fractional order of astaticism 1.6. Such a controller for each electromagnetic retarder serves as the basis of the microprocessor-based control, data acquisition, processing, graphical display system, and will also be used to develop a similar bench for tuning four-wheel-drive vehicles.

Control of a microgrid using robust data-driven-based controllers of distributed electric vehicles

Current advancements in power electronic converters have paved a way to shift the attention from the traditional internal combustion engine to electric vehicles (EVs). In previous research works, the EVs are normally represented by an aggregate model or a first order transfer function, and they are mostly used for the frequency regulation in microgrids (MGs). These may not be valid assumptions since the EVs consist of various distributed units and power electronic converters. To make it more practical, distributed EV models with a function of MG voltage control should be further considered. This paper proposes an approach for MG voltage and frequency regulations using data-driven-based controllers for distributed EVs. Without requiring any MG parameters, information of uncertainties with respect to operation changes are monitored such that major stability indices, i.e., damping and robustness, can be automatically calculated. Considering these indices, the adaptive control technique is applied to design the controllers. The proposed adaptive data-driven-based controller is compared to a controller designed by considering dynamics of full-converter models. Simulation results are validated in a MG with renewable energy sources and distributed EVs under various operating points and uncertainties. • Mathematical modeling and investigation of a microgrid with distributed EVs, ESSs, SPVs, and wind generators. stability. • Robust control design of the data-driven-based controllers of distributed EVs using a mixed H 2 / H ∞ . • Considering performance of the proposed distributed controllers of EVs under various operations.

Design and Robust Performance Analysis of Low-Order Approximation of Fractional PID Controller Based on an IABC Algorithm for an Automatic Voltage Regulator System

In this paper, a low-order approximation (LOA) of fractional order PID (FOPID) for an automatic voltage regulator (AVR) based on the modified artificial bee colony (ABC) is proposed. The improved artificial bee colony (IABC) high-order approximation (HOA)-based fractional order PID (IABC/HOA-FOPID) controller, which is distinguished by a significant order approximation and by an integer order transfer function, requires the use of a large number of parameters. To improve the AVR system’s performance in terms of transient and frequency response analysis, the memory capacity of the IABC/HOA-FOPID controller was lowered so that it could fit better in the corrective loop. The new robust controller is named the improved artificial bee colony (IABC) low-order approximation (LOA)-based fractional order PID (IABC/LOA-FOPID). The performance of the proposed IABC/LOA-FOPID controller was compared not only to the original ABC algorithm-tuned PID controller, but also to other controllers tuned by state-of-the-art meta-heuristic algorithms such as the improved whale optimization algorithm (IWOA), particle swarm optimization (PSO), cuckoo search (CS), many optimizing liaisons (MOL), genetic algorithm (GA), local unimodal sampling (LUS), and the tree seed algorithm (TSA). Step response, root locus, frequency response, robustness test, and disturbance rejection abilities are all compared. The simulation results and comparisons with the proposed IABC/LOA-FOPID controller and other existing controllers clearly show that the proposed IABC/LOA-FOPID controller outperforms the optimal PID controllers found by other algorithms in all the aforementioned performance tests.

Application of a Fractional Transfer Function for Simulating the Eddy Currents Effect in Electrical Systems

Some electrical devices contain a solid nonlaminated magnetic core as a component. In the case of variable magnetic flux, eddy currents arise in such a core, which should be taken into account for computer simulation if higher precision is needed. The fractional order transfer function (FOTF) based on the simple traditional model of excitation circuit of a DC machine is proposed for eddy current simulation. This model is illustrated by mathematical (based on differential equations and the Laplace operator) and structural approaches to the excitation circuit of a common DC generator with a solid core. The skin effect for more precise simulation of eddy currents is also considered by means of fractional order transfer functions in the computer models. Magnetic saturation and hysteresis were not taken into account in this case. The proposed model is simple and ensures adequate accuracy, confirmed experimentally using the FOTF Toolbox for MATLAB and Simulink. This model is distinct and proposed for the fast and accurate computer simulation of eddy currents in electrical devices with a solid magnetic core.

Approximation of Fractional Order PIλDμ-Controller Transfer Function Using Chain Fractions

The approximation of a fractional order PIλDμ-controller transfer function using a chain fraction theory is considered. Analytical expressions for the approximation of s±α components of the transfer functions of PIλDμ-controllers were obtained through the application of the chain fraction theory. Graphs of transition functions and frequency characteristics of Dμ (α = μ = 0.5) and Iλ (α = λ = −0.5) parts for five different decomposition orders were obtained and analyzed. The results showed the possibility of applying the approximation of the PIλDμ-controller transfer function by the method of chain fractions with different valuesof λ and μ. For comparison, the transfer functions with the same order polynomials, obtained by the methods of Oustaloup transformation and chain fractions, were approximated for α = ±0.5. The analysis proved the advantages of using the chain fraction method to approximate the transfer function of the PIλDμ-controller. The performed approximation opens up the possibility of developing engineering methods for the technical implementation of PIλDμ-controllers. The accuracy of the same order transfer function approximation is higher when the method of chain fractions is used. It has been established that the adequacy of the frequency characteristics of the transfer functions obtained by the chain fraction method also depends on the approximation order.

An Alternative Approach of Disturbance Rejection Control Methodology to DC-DC Boost Converter

This study presents an active disturbance rejection control (ADRC) technique for a boost converter system which is represented with a second - order transfer function. Then, linear active disturbance rejection control (LADRC) technique, wherein a linear extended state observer (LESO) is constructed to estimate both the total disturbance and the system state at the same time, has been applied to the converter. In this context, a pole placement design reduces the number of tuning parameters of LADRC to two to lessen the difficulty of parameter adjustment. The control scheme increases the tracking capability. A numerical example is provided to highlight the effectiveness of the control strategy. The tracking performance and step response are observed via several simulation studies using MATLAB/Simulink tool. It is demonstrated that the algorithm used in study is alternative way of tuning duty cycle of the boost converter instead of PID control technique. The performance of the controller is evaluated with a number of performance metrics. The tabulated results validate the controller's efficacy.

On the robust stability of commensurate fractional-order systems

Based on a recent generalised version of the Mikhailov stability criterion, this paper presents a Kharitonov–like test for a class of linear fractional–order systems described by transfer functions whose coefficients are subject to interval uncertainties. To this purpose, first the transfer function is associated with an integer-order complex polynomial function of the generalised frequency (i.e. the current coordinate along the boundary radii of the instability sector) whose coefficients are uncertain. Then the geometrical form of the value set of this characteristic polynomial is determined from the direct examination of its monomial terms. To show how the test operates, it is finally applied to two fractional–order transfer functions whose coefficients belong to given intervals.

A digraph approach to the state-space model realization of MIMO non-commensurate fractional order systems

This paper proposes a novel approach that can generate a state-space model with low inner dimension for an MIMO non-commensurate fractional order (NCFO) system. Specifically, the notion of an admissible digraph is firstly introduced associated with a fractional order transfer (function column) vector. Then, new state-space model realization conditions and corresponding procedures based on this admissible digraph are proposed for the state-space model realization of an NCFO polynomial transfer matrix. Finally, a new necessary and sufficient state-space model realization condition is proposed for the rational transfer matrix of an MIMO NCFO system, and it is shown, based on a matrix fractional description (MFD) of the given rational transfer matrix, a state-space model realization can be obtained by firstly converting it to the polynomial case and then utilizing the digraph approach for polynomial case. Symbolic and numerical examples are provided to demonstrate the main ideas and effectiveness of the proposed digraph approach.

A robust adaptive One Sample Ahead Preview controller for grid-injected currents of a grid-tied power converter with an LCL filter

This paper presents the development of a discrete-time Robust Adaptive One Sample Ahead Preview controller, based on the combination of a Robust Model Reference Adaptive Controller (RMRAC) with the One Sample Ahead Preview controller (OSAP), which is a particular case of the Deadbeat controller. This control structure is applied to grid-side current control of a grid-tied voltage-source inverter (VSI) with an LCL filter. The developed controller is robust enough to be designed considering the LCL filter as a first order model, which is commonly modelled as a third order transfer function, considering the neglected dynamics as unmodelled dynamics on controller design thanks to its adaptive identifier, which is a modified Gradient algorithm. Furthermore, the controller can deal properly with grid impedance uncertainties, which change the resonance peak frequency of the LCL filter, which affects the controller performance and can induce the closed-loop to instability, by incorporation of a majorant signal and the σ-function into the adaptive law, turning it robust. In addition, the predictive nature of the controller, which aims to regulate the current tracking in the minimum time possible (one sample) impacts straightforwardly in the reduction of harmonic distortion on grid-injected currents, improving energy quality, because the transient regime is reduced thanks to the fast dynamics of the adaptive predictive control strategy. To corroborate the controller’s performance and discuss its robustness, Hardware-in-the-Loop and experimental results using a grid-tied 5.5 kW VSI with an LCL filter are presented

Artificial neural networks with conformable transfer function for improving the performance in thermal and environmental processes

This research proposes a novel transfer function based on the hyperbolic tangent and the Khalil conformable exponential function. The non-integer order transfer function offers a suitable neural network configuration because of its ability to adapt. Consequently, this function was introduced into neural network models for three experimental cases: estimating the annular Nusselt number correlation to a helical double-pipe evaporator, the volumetric mass transfer coefficient in an electrochemical reaction, and the thermal efficiency of a solar parabolic trough collector. We found the new transfer function parameters during the training step of the neural networks. Therefore, weights and biases depend on them. We assessed the models applied to the three cases using the determination coefficient, adjusted determination coefficient, and the slope-intercept test. In addition, the MSE for the training set and the whole database were computed to show that there is no overfitting problem. The best-assessed models showed a relationship of 99%, 97%, and 95% with the experimental data for the first, second, and third cases. This novel proposal made reducing the number of neurons in the hidden layer feasible. Therefore, we show a neural network with a conformable transfer function (ANN-CTF) that learns well enough with less available information from the experimental database during its training.

Optimizing the PID Controller by Using the Genetic Algorithm

This paper aims to develop a Proportional Integral Derivative (PID) controller for the Automatic Voltage Regulator (AVR) of the Synchronous Generator, Automatic Voltage Regulator is responsible for keeping the output voltage of the Generator constant and stable. The Automatic Voltage Regulator system can be represented by a fourth order Transfer Function. The parameters of the controller are evaluated by using the Genetic Algorithm tuning method, for this method the Genetic Algorithm Optimization toolbox in MATLAB is used. A PID controller and a PID Filter controller are developed in order to come up with the optimum controller design for the system. The performance of the Genetic Algorithm based controller has been compared with the classical Ziegler-Nichols based controller. The results show that the Genetic Algorithm based controller outperforms the Ziegler-Nichols based controller, the optimum controller design is achieved by the GA based PID filter controller.

Educational aid for dynamic study of DC converter with Leverrier's and Pole clustering technique using simulation software

Abstract : In this paper, the dynamic analysis of the dc-dc converter is proposed with an educational aid to ease the process in which the study is carried out. This study's primary importance is that it can be added to the curriculum of Master's program in Electrical Engineering. This article mainly focuses on the mathematical modelling of the dc-dc converter with which the dynamic analysis is carried out to regulate the load and line condition. The main problems in the analysis of higher-order dc-dc converter is addressed with techniques available in the literature. A quadratic boost converter with DCL cell is chosen for studying the dynamic analysis with the flow of the technique proposed. The solution to the resolvent matrix of the converter is obtained using Leverrier's algorithm. The higher-order system's transfer function is reduced using the pole clustering technique to ease the controller design. Finally, the PI controller is tuned with Ziegler-Nichols tuning and it is incorporated with the converter using the reduced-order transfer function. The input to output transfer function is analyzed with the step response in MATLAB software and compared with the full order transfer function to validate the reduced-order transfer function. The closed-loop response is also validated both with full order and reduced-order system. Keywords : Bloom's taxonomy, Leverrier's algorithm, Pole clustering, DC-DC converter, dynamic, reduced-order, controller

A Novel Fractionalized PID controller Using The Sub-optimal Approximation of FOTF

In the last two decades, fractional calculus has been rediscovered by scientists and engineers and applied in an increasing number of fields, namely in the area of control theory. Recently, many research works have focused on fractional order control (FOC) and fractional systems. It has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. In This work we use the Sub-optimal Approximation of fractional order transfer function to design the parameters of PID controller and we study the performance analysis of fractionalized PID controller over integer order PID controller.

Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function

This paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractional order transfer functions (IFOTFs). Transforming an EFOTF into an equivalent fractional order differential equation, its time domain response can be obtained by solving the equation by the difference method. IFOTF cannot be transformed into an equivalent equation, so its time domain response cannot be calculated by existing difference methods. A new numerical algorithm is designed for calculating a convolution and its inverse operation, the time domain response of IFOTF can be calculated based on the algorithm. Error analysis shows that the proposed numerical algorithms are of first-order accuracy. Four calculation examples are presented, and the results are consistent with the theoretical analysis.

A Robust Adaptive Super-Twisting Sliding Mode Controller applied on grid-tied power converter with an LCL filter

This paper presents a new robust adaptive controller, totally developed on discrete-time. This controller is composed by two control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller, constituting a new control structure, nominated Robust Adaptive STSM Controller. The main advantage of this new control proposal is its high adaptability and robust performance, with fast reference tracking without chattering. The stability and robustness analysis, in discrete time, are presented, considering the overall plant, that is, in presence of matched and unmatched dynamics. To evaluate its robustness performance, the proposed controller is designed for grid-injected current control of three-phase grid-tied power converter with an LCL filter under weak grid. To validate it, the plant was partially modeled as a first order transfer function, neglecting capacitor dynamics and considering it as an additive dynamics on control design. Experimental results are presented to corroborate the controller performance and the stability analysis by means of Lyapunov Theory is provided.

Acousto-optic spatial frequency filter operating in the intermediate region of acousto-optic interaction

The characteristics of an acousto-optic spatial frequency filter designed for processing of two-dimensional images and operation in the intermediate region of acousto-optic diffraction are investigated. The advantage of such filters over filters operating in a Bragg regime is the possibility of operation at significantly lower acoustic frequencies, which allows the passband of spatial frequencies to be increased and the limiting resolution to be decreased. Transfer functions of diffraction orders are obtained. The use of the first diffraction order is demonstrated to allow selection of the two-dimensional image contour. The two-dimensional image edge enhancement of the image transmitted by optical emission at a wavelength of 0.63×10−4cm is experimentally demonstrated using a TeO2 spatial filter operating at a frequency of 15 MHz.

Shifting Method for Identification of TITO Systems using Decentralized Relay Feedback

In this paper, the relay shifting method is extended to identification of systems with two inputs and two outputs (TITO systems) using relay feedback experiments. By means of this approach multiple points of the Nyquist frequency response can be determined from a single experiment. Identification of more frequency points facilitates parameter estimation of more complex models. The proposed procedure is intended for the identification of TITO systems with a sufficiently strong cross-coupling between inputs and outputs. Frequency domain transfer functions of the second order with a time delay are used for modelling individual links. The proposed procedure is intended for controller autotuning and can be extended for multivariable systems.

Stabilization of an arbitrary order transfer function with time delay H2 Controller

Stabilization of an arbitrary order transfer function with time delay H2 Controller

An optimal washout filter for motion platform using neural network and fuzzy logic

To experience the motion sensation of a real vehicle through a motion simulator, a motion cueing algorithm (MCA) is required to transform the vehicle motions to the driving motion platform (DMP) while respecting the physical limitations of DMP. In this aspect, the optimal washout filter (WF) extracts the optimal motion signals including linear accelerations and angular velocities for the DMP with consideration of the human vestibular model and DMP motion states using the linear quadratic regulator (LQR) technique. The LQR technique is employed to obtain the optimal and pre-defined higher order transfer functions by solving the Riccati equation. However, the Riccati equation is solved using fixed weights, leading to an inconvenient usage of the DMP workspace. In this research, a new optimal WF model is designed and developed using a neural network (NN) and a fuzzy logic controller (FLC). The NN is introduced to solve the Riccati equation online while the FLC model is designed to extract the weighting matrices of the LQR technique. The proposed technique considers the physical DMP limitations online and reproduces accurate motion signals with a high degree of fidelity. The results demonstrate the efficiency of the developed optimal WF model as compared with those of existing optimal WF models.

Design and Virtual Simulation of an Optimal PID/LQRT-PSO Control System for 2WD Mobile Robots

This research paper presents a relevant contribution to optimal control of angular velocities with trajectories tracking for 2WD mobile robots. The dynamic model of each robotic servomechanisms is modelled from experimental data as a second order transfer function. Then, the direct and reverse kinematic equations are analytically developed. Then, the LQRT (Linear Quadratic Regulator with Tracking) gains for angular velocity of servomechanisms, are computed over infinite time horizon from corresponding Riccatti equations, using PSO (Particles Swarm Optimization) values of weighted matrix Q and R. Therefore, the LQRT solution computed from PSO of Q and R is known as LQRT-PSO. In addition, the LQRT-PSO gains computed from the related Riccati equations, are transformed into equivalent PID/LQRT-PSO gains for angular velocities control. Furthermore, a trajectory tracking flowchart is designed to reinforce the robustness of the overall control system. On the other hand, relevant developments conducted in the design step, are organized into an overall Matlab/Simulink PID/LQRT-PSO scheme. Finally, the obtained simulation results are presented in order to show the high performance of the proposed PID/LQRT-PSO control scheme for 2WD mobile robots.