Stability Phase Margin Research Articles

К выбору параметров регулятора непосредственного понижающего преобразователя с одноконтурной системой управления с учетом динамических нелинейностей

The article is devoted to the issues of choosing the parameters of a proportional-integral-differentiating regulator of a single loop control system with a buck converter taking into account dynamic nonlinearities This problem arises when it is necessary to design pulsed voltage conver¬ters with increased performance, when it is necessary to increase the cutoff frequency of an open-loop control loop without the possibility of increasing the carrier frequency of pulse width modulation due to limitations of the element base, which in some cases leads to the appearance of nonlinear effects. This must be taken into account when choosing both the open-loop cutoff frequency and the stability margin. The article proposes a nonlinear dynamic model of a direct buck converter with a proportional-integral-differentiating regulator both in the form of a piecewise smooth system of differential equations and in the form of a Poincaré map. A method for selecting controller parameters is proposed for a given open-loop cutoff frequency, and a given stability margin, as well as for given ranges of input voltage and load resistance based on the use of numerical methods for solving systems of nonlinear equations with given restrictions. The nonlinear dynamics of the system was studied for various sets of controller parameters. It is shown that with an increase in the cutoff frequency and small stability margins, undesirable dynamic modes may arise in the system when the filter capacitance drops within the calculated values, while linear dynamic models show the stability of the system. To eliminate the possibility of the emergence of undesirable modes, it is necessary to increase the stability margin with subsequent monitoring of the results using a nonlinear dynamic model. The proposed method for selecting the cutoff frequency of an open loop and the phase stability margin, based on the analysis of nonlinear dyna¬mics, allows you to design power supplies with increased performance.

An output-capacitor-less flipped voltage follower based low dropout regulator with improved buffer impedance attenuation in 45 nm CMOS technology

A flipped voltage follower (FVF) based low drop out (LDO) with fast transient response is presented here. A simple fast FVF stage is associated with an output impedance enhanced source follower driving gate of pass element for faster recovery during load transients. The proposed LDO is capable of driving 10’s of pF to 1nF capacitive loads while maintaining enough phase margin for stability. This LDO offers stable regulation upto 30 mA producing a regulated voltage of 1.10V with 1.2V dc supply. The LDO is implemented in 45 nm CMOS technology which consumes 72μA of quiescent current under full load of 30 mA. LDO achieves -18-22 dB of PSRR over the band of 1-1MHz, over entire range load current drive of 200A-30 mA. 1% settling time of 32.4 ns is achieved with 1nF capacitive for rising load transition of 30mA-200uA and 47.52 ns settling time for falling load transition of 200μA-30 mA. DC line and load regulations for a typical 100pF load are respectively around 0.018V/V and 1.8mV/30 mA. The regulated voltage of 1.1V is maintained during process corners and wide temperature ranges (-60 °C to 60 °C) for 1.2V supply.

Influence of the switching frequency of the switch and the amplitude of the reference voltage of a pulsed voltage regulator of the lowering type on its stability

On the basis of classical stability criteria, using the expressions of the transfer function, according to the block diagram, the stability of the impulse controller with feedback is estimated. The influence of the switching frequency of the switch and the amplitude of the reference voltage on the stability of a pulsed voltage regulator of a lowering type with deterministic parameters of the system is analyzed. In accordance with the Nyquist criterion for the transfer function of an open-loop system, both stability and phase stability margins for a closed-loop system can be estimated. When simulating the operation of the device, the phase stability margin was obtained, according to the Nyquist criterion, which is с = Н = 7. An increase in the sawtooth voltage is not a desirable phenomenon, which, although it increases the margin of stability, however, reduces stability. Moreover, the dependence of the ripple, affecting the stability of operation, on the amplitude of the sawtooth voltage is not a predictable value and takes on a random value.

High dynamic digital control for a hydraulic cylinder drive

The control of hydraulic cylinders with digital hydraulic valves is often based on modulation principles like pulse-width modulation, pulse-code modulation, or pulse–frequency control. In many cases the dynamic drive performance using such control strategies is far below the natural dynamics of the system, since closed-loop controllers demand a certain phase margin for stability. However, some drive applications require a high dynamic response, which cannot be realized with common closed-loop concepts. In this article the design of a bang–bang feedforward control with regard to the dynamics of a hydraulic cylinder drive in accordance with the theory of optimal control is presented. The control achieves the maximum physical dynamic response and no remaining oscillations after the movement, which forms the basis of a high dynamic three-level position control for hydraulic drives. Furthermore, the influence of valve dynamics and pipe line dynamics with regard to the design of the digital valve control are considered by simulations.

ЧАСТОТНІ ХАРАКТЕРИСТИКИ БЕЗКОНТАКТНИХ МАГНІТО-ЕЛЕКТРИЧНИХ ДВИГУНІВ ЗВОРОТНО-ОБЕРТАЛЬНОГО РУХУ

n this paper, the frequency characteristics of a special brushless magnetoelectric motor of return-rotary motion with sinusoidal and rectangular forms of the carrier signal are investigated. The method of generating a feedback signal on the amplitude of the rotor shaft oscillations angle has been improved by fixing the value of the signal at the moment of reaching its amplitude. The method of calculating the control system of the oscillations angle amplitude is investigated based on the frequency characteristics of the open-loop system by setting the phase stability margin. Examples of the calculation of transient processes of regulation of the oscillations angle amplitude and the effective value of the stator current when starting the motor and changing the mechanical load are given. References 9, figures 6, tables 2.

Frequency response analysis methods for open-loop servo drives and control systems

The paper presents results of development of frequency response analysis methods for open-loop servo drives and control systems, which use frequency response data of closed-loop servo drives and control systems obtained using Fourier and Laplace transforms of transient response calculated using their linear or linearized math models. The methods that have been developed can be used for approximate calculation of frequency response of servo drives and control systems based on their math models with slight non-linearities. Equations are derived for calculating frequency response of open-loop servo drives and control systems for several particular cases of feedback loop transfer function. The paper studies the efficiency of the developed frequency response analysis methods for open-loop servo drives and control systems. The obtained frequency response data for open-loop servo drives and control systems can be used for evaluating the amplitude and phase stability margins for these entities. Key words: frequency response; open-loop servo drive; control systems.

Design of Given Oscillation Index Scalar Controllers: Modal and H∞-Approaches

The algorithms of output controllers design are proposed for linear scalar plants, that ensure the desired or attainable values of oscillation index and of degree of stability, determining the settling time. Both modal control and H∞-approach are used in the design procedurevs. Examples are constructed, demonstrating that striving to provide the degree of stability that is much greater than the distance from the nearest left zero of the plant transfer function to the imaginary axis (even for the minimum phase plants) leads to the quite small gain and phase stability margins, that is unacceptable in practice.

CИНТЕЗ РОБАСТНОГО ПІД-РЕГУЛЯТОРА ДЛЯ НЕВИЗНАЧЕНОЇ НЕЛІНІЙНОЇ МОДЕЛІ БПЛА З ВИКОРИСТАННЯМ ШТУЧНОЇ МОДЕЛІ ПОСИЛЕННЯ І ТИМЧАСОВОЇ ЗАТРИМКИ

Estimations of the flight vehicles aerodynamic coefficients through the theoretical, numerical, wind tunnel and flight-test methods have always errors and uncertainties. Nonlinear dynamics of the unmanned aerial vehicle due to speed variations, as well as variability and uncertainty of the aerodynamic coefficients can be considered as an uncertain model. A robust proportional-integral-derivative controller is designed based on the nonlinear optimization in the time domain for the uncertain nonlinear dynamical model of the unmanned aerial vehicle. Artificial gain and time-delay models are added to achieve required stability margins as system robustness during the robust proportional-integral-derivative control design. The aerodynamic coefficients are divided into two groups on the basis of the output vector's sensitivity to the aerodynamic coefficients. Nonlinear optimization of the criterion is performed in two steps for the robust proportional-integral-derivative controller design. In the first step of the design, nominal values are used for coefficients with low-sensitivity, and upper and lower limits are used only for high sensitive aerodynamic coefficients. In the second step, the upper and lower limits are applied all of the aerodynamic coefficients to evaluate and re-adjust the robust proportional-integral-derivative controller parameters. The robust controller is designed for the uncertain nonlinear roll and lateral dynamic model of the Skywalker X8 flying wing to show the effectiveness of the proposed method to guarantee the stability margins. In the given example during the design of the robust controller, with adding of the artificial gain and time-delay model in the control loop the controller parameters are changed. This regulator increases the phase stability margin by about 10 degrees and the gain stability margin by about two for the family of the equivalent uncertain linear models.

Closing Gaps for Aircraft Attitude Higher Order Sliding Mode Control Certification via Practical Stability Margins Identification

In this paper, the conventional aircraft control system certification approach based on phase margin (PM) and gain margin (GM) is extended to higher order sliding mode (HOSM) controllers. The proposed practical stability PM (PSPM) and the practical stability GM (PSGM) are used to quantify the HOSM control system robustness to unmodeled dynamics. The tools/algorithms for the identification of PSPM and PSGM are developed using describing function-harmonic balance method. A design algorithm of a cascade dynamic compensator for a dynamically perturbed HOSM control system is presented and can be used to satisfy required practical stability margins. The theoretical developments are illustrated and validated on controlling the attitude of an F-16 aircraft.

РЕШЕНИЕ ЗАДАЧИ СТАБИЛИЗАЦИИ ТЕМПЕРАТУРЫ ВОЗДУХА В КАБИНЕ ТРАНСПОРТНОГО СРЕДСТВА

The subject matter of the article is the processes of synthesis of the automatic stabilization system (ASS) of the temperature in the vehicle cabin simulator using the vortex energy separator (VES) as the executive element of the system. The goal is to correct element synthesis of the ASS (CEs), which provides stability and quality of stabilization with the intensive change in the thermal load. The tasks to be solved are: to construct the functional scheme of the ASS which consist of the positioning circuit of the modes of the VES and the air temperature stabilization circuit in the cabin simulator; applying the results of solving the problem of synthesis of the automatic positioning system (APS) of modes of the VES, construct the structural diagram and mathematical model of the ASS of the temperature in the form of interval transfer functions (TF); perform the static calculation of the system to ensure the accuracy in steady-state and transient modes with linearly varying input influences; solve the problem of ensuring stability and dynamic levels of quality of the temperature stabilization using interval logarithmic amplitude-frequency characteristics (LAFC) and indirect levels of quality of the system's functioning in the frequency domain. The applied methods are: LAFC, real frequency characteristics. The following results were obtained: the functional and structural schemes of the ASS of the temperature in the vehicle cabin simulator are constructed, the interval transfer functions of the open-loop and closed-loop system are determined according to the referencing and disturbing influences. The static calculation of the system is performed to determine the required value of the transfer coefficient of the open-loop ASS based on the condition of ensuring the accuracy of the system in the steady-state mode of operation and with the intensive change in the thermal load. The dynamic calculation of the system was performed, as a result of which the structure and parameters of the CEs were determined based on the analysis of the dependence of the phase stability margin and the cut-off frequency on the values of the parameters of the CEs in accordance with the requirements for dynamic levels of quality. Conclusions. The scientific novelty of the results obtained is following: the frequency method of synthesis of the ASS using interval LAFC has been further developed by investigating the behavior of the logarithmic characteristics on the boundaries of the intervals of parameters of the transfer function of close-loop APS of the of the VES

Signal integrity analysis for coupled SWCNT interconnects using stable recursive algorithm

This paper presented a novel stable FDTD algorithm to analyze the crosstalk for coupled metallic single walled carbon nanotube (SWCNT) interconnect based system. This algorithm considers the effect of parameter variation such as: interconnect parasitics, ambient temperature, driver aspect ratios, supply voltages and load capacitance. It has been observed that, the proposed algorithm takes lesser central processing unit (CPU) runtime compared to the conventional FDTD and overcomes the stability problem found in the conventional FDTD and remains stable for all time. Further, we have analyzed the propagation delay of SWCNT interconnect based system for different interconnect parameters. Based on the parameters, minimum delay and crosstalk is obtained. Moreover, the obtained delay and crosstalk is compared with the industry standard HSPICE simulations to check the model accuracy. Additionally, the relative stability of the response obtained from proposed FDTD model is verified using Bode plot and Root locus, the margin of stabilities are noticed as: stability margin for gain is −50 dB and phase stability margin is 40°.

Phase and Gain Stability Margins for a class of Nonlinear Systems

Abstract In this paper, new definitions of Phase and Gain stability margins for a class of Nonlinear (NL) systems (a linear plant with a nonlinear control), specifically, in systems with control saturation, are proposed. The Gain and Phase stability margins are defined as the maximum increase in the gain and the maximum phase shift that can be added to the frequency characteristic of the linear plant such that there are no limit cycles predicted or the sufficient stability condition is satisfied. The algorithms for computing the defined stability margins are developed based on the Circle Criterion (CC) and the Describing-Function-Harmonic-Balance (DF-HB) technique. Both methods that compute practical stability margins are compared and analysed. Case study of the system with control saturation demonstrates the efficacy of the proposed approach.

Design of Modal Control Providing Guaranteed Stability Margin to Continuous Systems

In this paper the problem of modal control design providing required quality indices and guarantied phase stability margin is considered.

On–off and proportional–integral controller for a morphing wing. Part 1: Actuation mechanism and control design

The main objective of this research work is the development of an actuation control concept for a new morphing actuation mechanism made of smart materials, which is built from a shape memory alloy (SMA). Two lines of smart actuators were incorporated to a rectangular wing to modify the upper wing surface, made of a flexible skin, with the intention to move the laminar-to-turbulent transition point closer to the wing trailing edge. After a brief introduction of the morphing wing system architecture and requirements, the actuation lines' design and instrumentation are presented. The integrated controller controls the SMA actuators via an electrical current supply, so that the transducer position can be used to eliminate the deviation between the required values for vertical displacements (corresponding to the optimized airfoils) and their physical values. The final configuration of the integrated controller is a combination of a bi-positional (on–off) controller and a PI (proportional–integral) controller, due to the two heating and cooling phases of the SMA wires' interconnection. This controller must behave like a switch between the cooling and the heating phases, situations where the output current is 0 A, or is controlled by a PI type law. The PI controller for the heating phase is optimally tuned using integral and surface minimum error criteria (Ziegler–Nichols). The controller is numerically tested on the linear identified system in terms of time response, Bode diagram, amplitude and phase stability margins, and root-locus.

Direct Voltage Control for a Stand-Alone Wind-Driven Self-Excited Induction Generator With Improved Power Quality

An improved direct voltage control (DVC) strategy is proposed for the control of terminal voltage and frequency of a stand-alone wind-driven self-excited induction generator with variable loads. The DVC strategy, including a proportional-integral (PI) regulator, lead-lag corrector, and a feed-forward compensator, is designed based on the system transfer function matrix. The PI regulator can eliminate the steady-state tracking errors of the terminal voltage. The lead-lag corrector is employed to enlarge the phase stability margin of the dominant loops while the feed-forward compensator is adopted to mitigate the voltage harmonics resulting from the cross-coupling dynamics. The procedures for capacity design of the excitation capacitors, the voltage source inverter, and the consumer load are also presented. The simulation and experimental results verify that the proposed strategy has a fast dynamic response and can effectively control the generated voltage with low harmonic distortions under different linear or nonlinear loads.

Analyzing stability margins of homogeneous MIMO control systems

Homogeneous MIMO automatic control systems consisting of single-type separate subsystems are considered. Frequency methods of finding modulus and phase stability margins of the MIMO system with respect to amplitude-phase characteristics of open-loop and closed-loop subsystems are proposed. These methods help make constructing stability domains of the MIMO system with the given stability margin easy and visual, which means that one can apply them to solve problems of synthesizing MIMO automatic control systems.

Applications of nonlinear programming for automated multivariable control system design

Conventional control system design, via the classical concepts of gain and phase stability margins and damping ratios, continues to be a principal design approach. This paper discusses the automation of the conventional control system design process using nonlinear programming. Examples are given for three aerospace vehicles. Modern control theory, including the Linear Quadratic Regulator methods, offers advantages when designing multivariable systems. However, conventional control system design can easily include multivariable systems when nonlinear programming techniques are applied. With nonlinear programming, engineering problems can be solved directly; i.e., the problem does not have to be fit into a canonical form.