Second-order Transfer Function Research Articles

Separate Guidance and Control Design for Autonomous Path-following

This paper addresses the separate guidance and control design for an unmanned aerial vehicle (UAV) to follow the desired path with arbitrary curvature. The proposed design is appealing since it neither requires the information about the path curvature to be implemented nor necessitates tracking a moving virtual target. Such a feature makes our design simple and elegant. We first show that it is sufficient to nullify the UAV's perpendicular distance with respect to the path in order for it to track and follow the desired path and that there is no restriction on the UAV's initial configuration. This makes the proposed design globally valid. Next, we augment the UAV's guidance system with an autopilot obtained by approximating its higher-order dynamics as a second-order transfer function. We demonstrate the efficacy of the proposed design through simulations for various scenarios.

A 12.1bit-ENOB noise shaping SAR ADC for biosensor applications

This paper proposes a low power fully-passive noise shaping successive approximation register analog-to-digital converter (SAR ADC) for biosensor applications. The proposed ADC includes a second-order fully-passive integrator achieves a second-order noise transfer function. With an independent residue voltage generator to adjust common voltage between the main and residue path, the power efficiency of three differential inputs comparator is improved. The 0.18μm CMOS prototype chip occupies a total area of 1.37 mm2 with a core area of 0.58 mm2 and consumes 131 μW from a 1.3 V supply. The proposed SAR ADC achieves a peak signal-to-noise-and-distortion ratio (SNDR) of 74.8 dB and a peak spurious-free dynamic range (SFDR) of 89.7 dB at a sampling rate of 8 MSPS and oversampling rate of 16, leading to the Schreier figure of merit (FoMs) of the proposed ADC of 167.4 dB.

Integral-Square-Error Based Normalized Relative Gain Array for the Input-Output Pairing and Equivalent Transfer Function Design of MIMO Processes

Input-output pairing effectively minimizes the loop interaction in MIMO processes and avoids integral instability. In this article, a modified Relative Normalized Gain Array is proposed for the Input-Output Pairing and design of the First-order and Second-order Equivalent Transfer function. The proposed modified Relative Gain Array (mRNGA) matrix is derived by Normalizing the Relative Gain Array matrix with a normalization factor, which is calculated by minimizing the Integral Square Error of the given MIMO process. After that, the first order and second order Equivalent Transfer function is design by the derived mRNGA matrix, which offers an improved estimation of the Effective open-loop transfer function of the given MIMO process. The proposed method is corroborated with the help of the Input-Output pairing examples up to the 5 × 5 MIMO processes and three ETF design example.

Control of electric machines using flower pollination algorithm based fractional order PID controller

In this work, fractional order proportional integral derivative controller (FOPIDC) is proposed and implemented for speed control of electric machines using nature-inspired metaheuristic optimization algorithm (MOA) named as flower pollination algorithm (FPA). Investigations are performed by considering the second-order transfer function of D.C Motor. FOPIDC constants KP, KI, KD, λ, and μ are optimized by considering FPA. The desired response of the electric machine is obtained by using tuned parameters of FOPIDC. After that, FOPIDC response using FPA is compared with PIDC response using FPA in the sense of time-domain specifications and performance indices (PI) like ‘integral of square error (ISE), integral of time-weighted square error (ITSE), integral of absolute error (IAE) and integral of time-weighted absolute error (ITAE)’. Finally, the desired response of electric machine using FPA based FOPIDC is compared with desired response of electric machine using firefly algorithm (FA) and particle swarm optimization (PSO) algorithm based FOPIDC.

Validation and application of nonlinear hydrodynamics from CFD in an engineering model of a semi-submersible floating wind turbine

Nonlinear hydrodynamics play a significant role in accurate prediction of the dynamic responses of floating wind turbines (FWTs), especially near the resonance frequencies. This study investigates the use of computational fluid dynamics (CFD) simulations to improve an engineering model (based on potential flow theory with Morison-type drag) by modifying the second-order difference-frequency quadratic transfer functions (QTFs) and frequency-dependent added mass and damping for a semi-submersible FWT. The results from the original and modified engineering models are compared to experimental data from decay tests and irregular wave tests. In general, the CFD results based on forced oscillation tests suggest increasing the frequency-depending added mass and damping at low frequencies compared to first order potential flow theory. The modified engineering model predicts natural periods close to the experimental results in decay tests (within 5%), and the underprediction of the damping is reduced compared to the original engineering model. The motions, mooring line tensions and tower-base loads in the low-frequency response to an irregular wave are underestimated using the original engineering model. The additional linear damping increases this underestimation, while the modified QTFs based on CFD simulations of a fixed floater in bichromatic waves result in larger difference-frequency wave loads. The combined modifications give improved agreement with experimental data in terms of damage equivalent loads for the mooring lines and tower base.

Estimation of Transfer Function Coefficients for Second-Order Systems via Metaheuristic Algorithms.

The present research develops the parametric estimation of a second-order transfer function in its standard form, employing metaheuristic algorithms. For the estimation, the step response with a known amplitude is used. The main contribution of this research is a general method for obtaining a second-order transfer function for any order stable systems via metaheuristic algorithms. Additionally, the Final Value Theorem is used as a restriction to improve the velocity search. The tests show three advantages in using the method proposed in this work concerning similar research and the exact estimation method. The first advantage is that using the Final Value Theorem accelerates the convergence of the metaheuristic algorithms, reducing the error by up to 10 times in the first iterations. The second advantage is that, unlike the analytical method, it is unnecessary to estimate the type of damping that the system has. Finally, the proposed method is adapted to systems of different orders, managing to calculate second-order transfer functions equivalent to higher and lower orders. Response signals to the step of systems of an electrical, mechanical and electromechanical nature were used. In addition, tests were carried out with simulated signals and real signals to observe the behavior of the proposed method. In all cases, transfer functions were obtained to estimate the behavior of the system in a precise way before changes in the input. In all tests, it was shown that the use of the Final Value Theorem presents advantages compared to the use of algorithms without restrictions. Finally, it was revealed that the Gray Wolf Algorithm has a better performance for parametric estimation compared to the Jaya algorithm with an error up to 50% lower.

Pole-based analysis of coupled modes in metal–insulator–metal plasmonic structures

A second-order transfer function analysis is performed on plasmonic modes with disparate quality factors. This generalized analysis technique is applied to the coupling of modes in metal–insulator–metal structures in the mid-wave infrared, which are systematically studied, both experimentally and with computational modeling. Coupling between these disparate modes is observed from the asymmetric Fano-like lineshape at the resonant crossings in both finite element method simulations and angle dependent spectra. The pole analysis method applied to both experimental and numerical data allows for extraction of the coupling coefficient for this system and is applicable to other plasmonic and photonic coupled resonances.

Analysis of the influence of control parameters on the interaction between direct-driven wind turbines

In order to study the influence of control parameters on the interaction between direct-driven wind turbines, this paper presents the interaction model and analysis method of direct-driven wind turbines. Firstly, the harmonic linearization method is used to establish the interaction model of two direct-driven wind turbines, and the interaction mechanism between the two units is studied; secondly, the influence of phase-locked loop and DC voltage loop on the interaction between the two units is analyzed from the perspective of bandwidth and damping ratio of second-order closed-loop transfer function, and the interaction law of phase-locked loop and DC voltage loop on the interaction between the two units is studied and summarized; finally, the time-domain simulation of the two units grid-connected system is carried out, and the results are compared with the frequency domain analysis results to verify the rationality of the theoretical analysis.

Simulation of response characteristic of VTVL system with hybrid rocket engine

To determine the suitability of the control performance of the VTVL system with hybrid rocket engine, simulations were done for the vertical and horizontal motion using various engine data. In the simulation, the thrust modulation characteristics of each engine were modeled with the same second-order transfer function in all cases. The results showed that the VTVL system with HRE showed better performance in terms of vertical motion error and touch down speed. In addition, this confirms the possibility for successful VTVL flight missions using HRE. In the next step, a better control algorithm and an efficient control technique will be attempted for developing the VTVL demonstrator.

Effects of second-order hydrodynamics on an ultra-large semi-submersible floating offshore wind turbine

Second-order wave loads on floating offshore wind turbine (FOWT) may excite severe resonance at the eigenfrequencies of the floating system and cause fatigue damage. The hydrodynamic coefficients including first- and second-order wave force transfer functions are calculated, and fully coupled time-domain simulation by FAST is conducted for selected environmental conditions. Each load case is simulated without second-order loads, and with difference-frequency full quadratic transfer functions (QTFs), sum-frequency full QTFs, and complete second-order solution. The effect of second-order difference- and sum-frequency wave loads on the dynamic behaviors of the 10 MW semi-submersible FOWT is discussed. Subsequently, the effect of second-order wave loads on the structural fatigue behavior of the 10 MW and 5 MW semi-submersible FOWTs is investigated and compared by computing ultimate and damage-equivalent loads (DELs). The results show that ignoring second-order difference-frequency wave loads may underestimate the low-frequency responses, and second-order sum-frequency wave loads significantly affect the structural dynamics of the 10 MW FOWT. In addition, the effect of second-order wave loads on the fatigue damage of the 5 MW and 10 MW semi-submersible FOWTs are significantly different.

Optimal fractional‐order controller design using direct synthesis method

In this study, an optimal fractional-order controller is proposed for a type of fractional-order model utilising the direct synthesis method. In that respect, the fractional counterpart of the second-order integer transfer function is selected as a closed-loop reference transfer function. The stability region of the fractional-order closed-loop reference transfer function is given via a theorem and related lemmas. Considering that a unity feedback loop is used, the parameters of the fractional-order closed-loop reference transfer function are specified based on the integral square error performance index within the specified stability region using a genetic algorithm. The time-domain characteristics of the optimal fractional-order closed-loop reference transfer function are compared with those of the optimal second-order integer closed-loop reference transfer function. The fractional- and integer-order controllers that are designed based on optimal closed-loop reference transfer functions are implemented on a real-time system. The performance of the fractional-order controller outperforms that of the integer counterpart on the integral square error criterion. Moreover, the simulation and practical results are consistent with each other.

A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model

A feedback control method with consideration of the next-nearest-neighbor interactions is investigated in the lattice hydrodynamic traffic model. The stability condition is obtained by discussing the first-order transfer function G1 and the second-order transfer function G2. The solution of mKdV equation which describe the density wave are yielded by nonlinear analysis. Theoretical analysis result indicates that the feedback gain λ, the weight coefficient of the nearest-neighbor interaction and the next-nearest-neighbor interaction have a great impact on the improvement of the stability of traffic flow. Numerical simulations by analyzing the short-term, long-term behaviors and hysteresis loop of traffic flow verify that the impacts of the feedback gain λ, the nearest-neighbor weight and the next-nearest-neighbor weight on traffic control. The feedback control method considering the next-nearest-neighbor interactions displays the nonlocal characteristics in the implementation of local control process.

Dynamic Rollover Prediction of Heavy Vehicles Considering Critical Frequency

Rollover of commercial heavy vehicles can cause enormous economic losses and fatalities. It is easier for such vehicles to rollover if the driver’s steering frequency is close to the critical frequency of the vehicle’s roll motion; however, the critical roll frequency has rarely been investigated. In this study, the second-order transfer function between the steering input and roll angle was developed to calculate the critical frequency of the vehicle’s roll motion. The simulated spectrum and transfer function were then used to dynamically predict the peak lateral load transfer ratio. Laboratory experiments were conducted using a scaled vehicle to verify the critical roll frequency. The results suggest that the peak value of the lateral load transfer ratio during steering can be accurately determined from the driver’s input, and the critical roll frequency has a dominant effect on the dynamic rollover of heavy vehicles.

FAPI Controller for Frequency Support in Low-Inertia Power Systems

This paper presents different forms of Fast Active Power Injection (FAPI) control schemes for the analysis and development of different mitigation measures to address the frequency stability problem due to the growth of the penetration level of the Power Electronic Interfaced Generation (PEIG) in sustainable interconnected energy systems. Among the studied FAPI control schemes, two different approaches in the form of a derivative-based control and a virtual synchronous power (VSP) based control for wind turbine applications are also proposed. All schemes are attached to the PEIG represented by a generic model of wind turbines type 4. The derivative-based FAPI control is applied as an extension of the droop based control scheme, which is dependent on the measurement of the network frequency. By contrast, the proposed VSP-based FAPI is fed by the measurement of the active power deviation. Additionally, unlike existing approaches for virtual synchronous machines, which are characterized by high-order transfer functions, the proposed VSP-based FAPI is defined by a second-order transfer function, which can contribute to fast mitigation of the system primary frequency deviations during containment period. The Great Britain (GB) test system, for the Gone-Green planning scenario for the year 2030 (GG2030), is used to evaluate the effects of the proposed FAPI controllers on the dynamics of the system frequency within the frequency containment period. Thanks to proposed FAPI controllers, it is possible to reach up to 70% for the share of wind power generation without violating the threshold limits for frequency stability. For verification purposes, a full-scale wind turbine facilitated with each FAPI controller is tested in EMT real-time simulation environment.

The Dynamic Performance Study of Six-Dimensional Dynamic Force Generator

A six-dimensional dynamic force generating device is developed based on the dynamic performance calibration requirement of a six-dimensional force test platform based on the exciter force generating unit. The finite element software is used to perform modal analysis on the dynamic force generating device to obtain the natural frequency response of the device. Based on the finite element analysis results, the second-order transfer function at the sixth-order natural frequency point of the device is obtained, and the amplitude-phase frequency characteristic curve is obtained. Combined with the characteristic parameters of the exciter, the relationship curve between the excitation frequency and the excitation force under the influence of the natural frequency of the device is obtained. The comprehensive of finite element method and calculation results show that the designed dynamic force generating device can meet the requirements of use. According to the analysis results, it is found that the excitation capability can be maintained at a low frequency state to achieve high amplitude fixed frequency excitation, and low amplitude fixed frequency excitation is realized at a high frequency state.

Application of reliability-based robust optimization in spacecraft attitude control with PWPF modulator under uncertainties

The main objective of this paper is to enhance the robustness of an on–off attitude control under uncertainties while limiting the probability of failure in attitude control. To do this, the concept of system optimization is utilized for detailed engineering of spacecraft control using reliability-based robust design optimization (RBRDO). The probability of failure of the attitude control is chosen by the system designer as the input of the RBRDO algorithm. The single-axis spacecraft attitude is controlled using a combination of the observer-based anti-windup modified PI-D with pulse-width pulse-frequency modulator in the presence of external disturbance. The on–off thruster is modeled with a delay followed by a second-order transfer function. The input frequency of the thruster is limited to 50 Hz. The uncertain parameters are given as the spacecraft moment of inertia, thrust level, and thruster delay. The controller gains are determined by using traditional, robust, and reliability-based robust design optimizations under uncertainties and disturbance. The simulations are carried out using quasi-normalized equations, along with reducing problem variables and computational burden, to obtain more applicable results for a preliminary design. The traditional optimization gives the highest pointing accuracy without uncertainty, whereas the robust optimization obtains an approximately flat behavior for the mean of absolute pointing error under uncertainties. Under this situation, RBRDO could satisfy the prescribed reliability with a small loss in accuracy for the on–off attitude control of spacecraft, but under system limitations.

Design and implementation of second-order microwave integrator

ABSTRACTIn this paper, a new design methodology is developed for the implementation of a second-order microwave integrator on microstrip circuit. Firstly, an existing digital first-order integrator with best magnitude and phase performance is adopted as a prototype to give digital second-order integrator transfer function. Then, by using the autoregressive process and a least mean square based error function, coefficients of the formulated second-order digital integrator are transformed into the impedance values of transmission line elements. Different sets of impedance values are obtained through the optimization process, and design with a highly accurate frequency response having maximum relative error value not more than 7.2% over the angular frequency range 0.18pi to 0.94pi is selected for implementation purpose. RT/Duroid 5880 is used to fabricate the proposed second-order microwave integrator design. Measured results for transmission coefficient S21(f) are found to follow theoretical values over the frequency range of 1.8 GHz to 8.6 GHz.

Model identification of critically damped second order plus time delay systems

ABSTRACTIn the present work, a simple method is proposed to calculate the parameters of a critically damped second-order transfer function model from the fractional step response of higher order systems. Five simulation examples are given to show the simplicity of the proposed method. The method makes use of a unique property of a critically damped second order plus time delay system (Harriott, Process Control, McGraw Hill, New Delhi), that, a time of 2.58τ is required to reach a fractional step response of 0.73. The time required to reach 0.35 (or any value) of fractional step response is also required. The derivation of the equations for the model parameters is simpler than that proposed by Rangaiah and Krishnaswamy (Ind. Engg. Chemistry Research, V 33, 1994, 1867–1871). The ISE and IAE values for the present method are compared with that of Rangaiah and Krishnaswamy. The method is also modified to get the model parameters of a FOPTD system: .

RF Reflectionless Filtering Power Dividers

A new class of Wilkinson-type power dividers with co-integrated bandpass-filter (BPF) functionality and input-reflectionless behavior is presented. They make use of a resistively terminated bandstop-filter (BSF) branch that is connected at their input terminal and exhibits a quasi-complementary transfer function with regard to the ones of the BPF-type power-divider arms. Thus, the RF-input-signal energy that is not transmitted by this triple-function reflectionless filtering power divider (FPD) to its output ports is dissipated by the loading resistor of its input BSF-type branch. Design formulas and theoretical synthesis examples for first-to-fourth-order FPD schemes and arbitrary power-division ratios are given. Furthermore, the extension of this concept to FPD realizations with multi-passband response and reflectionless capabilities at both the input and output accesses is shown. Theoretical design guidelines and limitations of center-frequency-tunable reflectionless FPD implementations are also provided. For experimental-demonstration purposes, a frequency-tunable 3-dB microstrip prototype with second-order transfer function is also manufactured and tested.

Parameter Identification and Model-Based Nonlinear Robust Control of Fluidic Soft Bending Actuators

Soft actuators are of great interests in recent years due to inherent compliance and adaptability. However, most of current studies focus on the physical actuation phenomenon and their fabrication, few results can be found on the modeling and closed-loop control due to their complicated elastic deformation. This paper studies physical modeling, parameter identification, and model-based nonlinear robust control for fluidic soft bending actuators governed by high-speed on–off solenoid valves. With the dynamic complexity and characteristics of fluidic soft actuators, the system has been described by two parts: motion dynamics and air dynamics. A second-order transfer function is used for the motion dynamics which describes the behavior from driving pneumatic pressure to soft actuator bending angle, and the model parameters are identified by with different operating frequencies. The nonlinear physical modeling of air dynamics which describes the behavior from control voltage to driving pneumatic pressure is also built and its parameters are identified by using the least square method. Based on the identified high-order model, a nonlinear robust control algorithm is developed for soft actuator by backstepping design to deal with nonlinearities and uncertainties. Experimental results show that the closed-loop stability is guaranteed and the good tracking performance is achieved by the proposed method.