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In a water storage unit consisting of 3 interacting tanks, in its operation there will be problems if manual control is used, because if manual control is not optimal, then when filling water in the three tanks it will cause water overflow, which results in a lot of water being wasted. Two-position control, or "on-off," is a control system that is suitable for use in regulating the water level in the storage unit tank. In a twoposition control system, if the frequency of water up and down (Limit Cycle) is large, it will cause an increase in the number of "switching" and "on-off" operations of the switch and solenoid valve per minute, so that the system becomes unstable and will shorten the life of the component. The Describing Function (DF) method is an analysis method that can determine the Limit Cycle frequency based on the width of the water up and down range (hysteresis) of the twoposition control system, with the aim of determining the hysteresis parameters that cause the system to be stable. [ABSTRACT FROM AUTHOR]

A servo system of automatic loading manipulator arm (ALMA) with backlash nonlinearity is investigated in this paper to suppress the limit cycle oscillation. To provide a more accurate representation of the system response, a two-inertia model method is employed. According to the system response, the influence of variation in backlash width, load inertia, and proportionality factor on the limit cycle is discussed using the frequency domain analysis method. The decrease in transmission torque resulting from backlash nonlinearity as the main cause of limit cycle oscillation is identified. Based on frequency domain analysis, an oscillation suppression method that employs backlash as disturbance compensation is proposed. A novel Third-order Nonlinear Extended State Observer (TNESO) that is more economical and reliable than torque sensors is utilized to estimate the transmission torque. Consequently, the estimated transmission torque as well as the displacement of the motor and load is utilized to obtain the backlash disturbance which can be counteracted by introducing a compensation of current reference value to mitigate the adverse effects of backlash on the system. The comparison of displacement-time curve between compensated and uncompensated experiments reveals that positioning error is reduced from 0.006 to 0.001 rad when displacement is compensated. Besides, the compensated system's position curve is smoother. Thus, the effectiveness of the proposed method is verified. [ABSTRACT FROM AUTHOR]

The fractional-order controllers (FOCs) have recently had a significant impact on control applications. However, they still need further research for feedback systems with hard nonlinearities, such as dead zones. The above compelling evidence motivates the design of a new robust FOC to avoid limit cycles caused by dead zones in the control loops. The proposed FOC consists of the cascade of two shifted in frequency, fractional-order lead networks. They provide high-value and sufficiently flat phase leads in sufficiently large frequency intervals. In this way, the linear part of the control loop can be easily shaped to achieve avoidance of limit cycles. The article applies classical concepts, such as the Nyquist plot and describing function method, to derive guidelines for designing the free parameters of the FOC. Moreover, a realization algorithm and a parameter setting procedure make the new FOC easily implementable in engineering practice.

This work deals with the fundamentally similar dynamic behavior of two apparently different aircraft systems, namely, landing gears and all-movable control surfaces. Both systems typically contain stiffness and damping nonlinearities, leading to shimmy/flutter limit cycle oscillations (LCOs). In a series of earlier papers the authors have developed highly efficient computational methods, based on describing functions, to construct LCO responses for dynamic systems with concentrated nonlinearities in stiffness or damping. These methods are extended in the present paper, and the focus is on the physical insights that can be obtained by using them for systems with multiple nonlinearities. The model parameters are varied to obtain an array of interesting results. For example, each branch of the landing gear response is attributable to a particular nonlinearity. Based on this, a possible reason is advanced for the occurrence of shimmy in the F/A-18 aircraft. On the other hand, the entire flutter response of the all-movable surface can be viewed as being shaped by one nonlinearity and modified by the other. Finally, the well-known Wright Air Development Center wind tunnel flutter test results for an all-movable horizontal tail with freeplay are reinterpreted and explained in the light of the present findings. [ABSTRACT FROM AUTHOR]

The paper proposes a design methodology for the second‐order robust exact differentiator in the presence of small time‐delays characterizing the time of signal processing. With this aim, the describing function is used to provide several sets of the gains ensuring high accuracy in the reconstruction of the first‐order derivative of smooth signals, that is, minimizing the main harmonic of chattering. The proposal fulfills the Loeb's criterion: if self‐excited oscillations appear in the trajectories of the delayed differentiator, they are orbital and asymptotically stable. Besides the global finite‐time stability of the error is proved for the non‐delayed differentiator under such gains settings by using a homogeneous Lyapunov function. Numerical examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

This work represents a new method for robustness analysis of the model reference adaptive controller (MRAC) in the presence of input saturation. Saturation is one of the nonlinear factors affecting the stability of control systems which must be considered in controller design and stability analysis experiments. Various methods are presented for the stability and robustness analysis of adaptive control systems, and employment of describing function (DF) can be attractive and practical, due to the appropriate effectiveness of DF in estimating limit cycles and also the application of quasi-linearization theory. In this work, the stability analysis and a limit cycle estimation of a saturated system in the frequency domain are performed. The controller parameters are adjusted in a way that the system achieves its stable limit cycle in the presence of the initial conditions for the states. Moreover, the efficiency of the proposed method for second-order systems is reported in the presence of symmetric saturation and uncertainty model in Rohrs’s counterexample as the unmodeled dynamics. The results demonstrate the proposed method provides a proper analysis of system stability during the changes in the control parameters and the saturation amplitude. [ABSTRACT FROM AUTHOR]

The paper presents a discussion on the selected nonlinearities existing in sensor and actuator subsystems of the roadheader cutting head speed control system. There have been concerned the most significant nonlinearities - rotational speed encoder and frequency rate limiter in the input of the power electronic converter. There has been presented a detailed analysis of the nonlinear input frequency rate limiter and the frequency-dependent input-output curves have been calculated. They enable qualitative and quantitative evaluation of system performance over a wide range of input signal frequencies and amplitudes. The measurement time of the encoder-based speed sensing should be as short as possible, or continuous measurement (like tachogenerator) should be used. The impact of encoder delay and inertia is much less significant than that of the frequency rate limiter. For better drive system performance, the frequency converter should be overmatched to ensure current overload capability - allowing an increase in the permissible rate of output voltage frequency change. [ABSTRACT FROM AUTHOR]

Based on the describing function (DF) approach, we study how to obtain analytically the synchronization of n identical metronomes on a cart in this paper. To start with, by using the fact that the torque of each metronome is a discontinuous function of its angle and angular velocity, we obtain the formulae of its DF. Next, we present a unified DF solution of the two types of synchronization for which the amplitude of the first harmonic of the angle of each metronome is identical. One type is called the out‐of‐phase synchronization for which all metronomes do not have an identical phase, and the other type is called the in‐phase synchronization for which all metronomes have an identical phase. We reveal some properties of these two types of synchronization. We validate the filter hypothesis and show that it is indeed critical for guaranteeing the success of using the DF approach to analyze the synchronization modes of the metronomes on a cart. Finally, we report in detail our numerical simulations for two and three identical metronomes using the physical parameters of the metronomes in the literature to validate the obtained analytical results and show certain robustness regarding small parameter differences of the synchronization prediction. [ABSTRACT FROM AUTHOR]

The parameters of DC-DC converters in a cascaded converters system are often set up separately, which may cause instability or even breakdown of the whole system. The traditional Middlebrook impedance stability criterion and Nyquist criterion are based on the small-signal model, where the nonlinear links are ignored or linearized, which, however leads to inaccurate modeling, and the difficulty for analytically obtaining stability range. In this paper, the nonlinear links, i.e., pulse width modulation links, of cascaded DC-DC converters system are first modeled by the describing function (DF); then, a novel stability analysis method for the cascaded DC-DC converters system is proposed by combining the impedance analysis method, Nyquist criterion and DF to accurately determine the stability range of the cascaded converters system. Since the DF method is only used into single converter so far for stability analysis, a source/load converter equivalent method is proposed in this paper to apply DF method into the cascaded converters. To this end, the two-stage cascaded boost converters systems with and without considering the parasitic parameters are taken as examples to conduct the simulation and experiment for verifying the correctness and the accuracy of the proposed DF-based stability analysis method. This work provides an analytical method to determine not only the stable and unstable ranges but also the critical stability range of the cascaded system, as well as provides a reference to quantificationally design the control parameters.

Microgrids relying on cooperative control are supported by communications, which are highly vulnerable to cyberattacks. A significant amount of research is already carried out on the detection and mitigation of cyberattacks to secure the operation of dc microgrids. Although cyberattacks are fully capable of causing cascaded converter outages leading to full/partial system blackouts, disturbing the system stability can also be a viable target by the adversaries, which has been overlooked so far. Hence, this article focuses on addressing the instability caused by stealth cyberattacks, which can easily bypass the well-defined observability tests. In addition, this article also introduces a novel adaptive stabilization method to eliminate the unstable modes due to cyberattacks, which has been designed considering a previously defined cyberattack detection metric as an input. To investigate its feasibility, a detailed model of a stable dc microgrid is first developed. Then, considering stealth cyberattack as a nonlinear element, the describing function-based method is used to investigate system stability under attack conditions. Finally, theoretical analysis, simulation, and experimental results under various scenarios are presented to verify the effectiveness of the proposed stabilization scheme. [ABSTRACT FROM AUTHOR]

In this article, a frequency-domain approach is developed to deal with the global consensus problem for a class of general second-order multiagent systems (MASs) subject to actuator saturations. By employing the describing function and the generalized Nyquist criterion, the global consensus problem is thoroughly investigated for both undirected and directed topologies. First, the describing function is introduced to characterize the actuator saturations in the $s$ -plane, and the inherent representation error is quantitatively analyzed from a frequency-domain perspective. Then, by means of the Kronecker product, the addressed consensus problem of the MAS is transformed into a corresponding stability analysis problem for a certain multi-input–multi-output (MIMO) system and, consequently, the generalized Nyquist criterion for MIMO systems is exploited to derive the condition for the global consensus of the MAS where the impact from the actuator saturation is explicitly reflected. Finally, numerical simulations are provided to illustrate the validity of the proposed theoretical result. [ABSTRACT FROM AUTHOR]

Polyvinyl chloride (PVC) gels represent a novel type of electroactive polymer actuators with a number of appealing characteristics, including low cost, high compliance, large strain, medium-to-high stress output, fast response, and thermal stability. Despite their vast potential in a variety of applications, modeling and control of nonlinear dynamics of PVC actuators has received little attention. In this article, we first present a data-driven approach to modeling nonlinear dynamics of PVC gel actuators. A Hammerstein model, consisting of a nonlinear module cascaded with linear dynamics, is proposed to capture the pronounced dependence of the voltage input–displacement output frequency response on the input amplitude and bias. A control scheme is then designed based on the model, where an inverse compensator for the nonlinear element is combined with a PID feedback controller. A disturbance observer is further introduced for the estimation and rejection of the influences from imperfect inverse compensation and model uncertainties. Experimental results are presented to support the efficacy of the proposed modeling and control approach. In particular, for a number of reference trajectories, the proposed control scheme results in over 80% reduction of tracking error in comparison with a well-tuned PID controller. [ABSTRACT FROM AUTHOR]

Dynamic systems with self-excited periodic motion have a wide range of applications in mechanical systems. For instance, a class of non-minimum phase underactuated and nonprehensile systems require self-oscillations instead of tracking an external reference signal. To solve this problem, we proposed a two fuzzy inference system, which is based on fuzzy logic theory, in order to generate a periodic output. The idea is to enforce the conditions that ensure the orbital asymptotic stability of the periodic solution of the closed-loop system. In this study, we considered Euler-Lagrange systems, with emphasis in underactuated systems. The describing function method was used to design the fuzzy controller and set the desired frequency and amplitude of the periodic output. Moreover, in accordance with Loeb's criteria, we established sufficient conditions for orbital stability. Finally, we tested and validated our proposal, via simulation and experiments on two laboratory platforms: a single-link pendulum and an underactuated non-minimum-phase rotational inverted pendulum. [ABSTRACT FROM AUTHOR]

Oscillations of grid-connected voltage source converter (VSC) usually reaches sustained state because of the limiters in controller. Describing function has been adopted to analyze the amplitude and frequency of the sustained oscillations, but high-order oscillation components caused by the limiter are ignored in previous literatures. This letter proposes an analysis method for sustained oscillations which considers high-order oscillation components. This method could obtain a more precise oscillation frequency and the amplitude of 1st, 2nd, and 3rd order components. The proposed method is verified by case studies and simulations in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

High proportion of renewable energy generation, especially wind power generation, has changed the dynamic behavior of power systems and leads to emerging stability issues such as oscillation accidents. The commonly used stability analysis methods based on linear system theory cannot tackle the influence of nonlinear elements in the control loop. To fill this gap, the describing function method is used to analyze the stability and power oscillations of a grid-connected permanent magnet synchronous generator (PMSG) wind power generation system in this paper. A complete PMSG system model is taken into consideration, including a wind turbine, a generator, a machine-side converter, a grid-side converter, and a weak grid. Particularly, the nonlinear element introduced by maximum power point tracking control in the power control loop is modeled and analyzed, and the influences of critical system parameters are studied. With the high accuracy of the describing function method, it is revealed that the machine-side converter mainly influences the oscillation amplitude, while the grid-side converter mainly influences the oscillation frequency. Furthermore, the following results can be obtained: 1) High bandwidth of maximum power point tracking control and rotation speed control may enlarge the oscillation amplitude, while a fast current loop of the machine-side converter is beneficial to the stability; 2) Grid-side voltage loop can significantly affect the frequency of the oscillation, and improper high bandwidth of a phase-locked loop (PLL) is harmful to system stability; 3) A stronger grid is not always beneficial to the system stability, and the influence of grid strength should be carefully analyzed and examined when nonlinear elements are considered. All analyses are verified by simulations based on MATLAB/Simulink.

Recently, with the fast development of renewable energy, various power-electronic-based devices have been widely incorporated in power systems, and controller saturation limiters have been broadly utilized, such as in voltage-source converter. It has been well recognized that these saturation limiters make sustained oscillations possible. To study the impact of saturation limiters, by considering the dynamical response of double saturation limiters in both the d-axis and q-axis of the alternating current control, this paper establishes single-input-single-output models for two novel phenomena including the double-clipped oscillation and single-clipped oscillation, based on the describing function. Then the describing-function-based Nyquist criterion is used to obtain the amplitude and frequency of the sustained oscillations. The model accuracy is verified by the electromagnetic transient simulation, and the influences of control parameters are extensively studied. All these findings clearly demonstrate that the saturation limiters play an active role in sustained oscillations in power-electronic-based power systems.

Non-singular terminal sliding mode control (NTSMC) is widely popular due to its various industrial applications. In many practical circuit systems, the control input is actually given to an actuator rather than directly to the plant. Therefore, it is important to study the effect of actuators on NTSMC performance. In this brief, frequency-domain characteristics of NTSMC are analyzed using the describing function method. It is shown that in the presence of actuator dynamics, the system exhibits a self-sustained periodic oscillation known as chattering. The relationship between the fundamental frequency, the amplitude of this periodic motion and the NTSMC parameters is explored. The effectiveness of the theoretical analysis is verified via a practical example based on an industrial emulator system. [ABSTRACT FROM AUTHOR]

The present paper aims to analyze the stability of dynamic Interval Type‐2 fuzzy control systems (IT2 FCSs) with adjustable parameters by investigating the existence of limit cycles based on the describing function (DF) method. To simplify the stability analysis, the following structured procedure is described. First, to avoid complex computation, a simple architecture of the IT2 FCS using two embedded Type‐1 fuzzy control systems (T1 FCSs) is proposed. Then, the DF of IT2 FCS is obtained based on the DFs of embedded T1FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stability regions. Moreover, particle swarm optimization (PSO) technique is utilized to minimize the limit cycle region. Other focus of this paper is on the stability margins analysis for robust design. For this purpose, a gain‐phase margin tester is applied to determine the minimum Gain Margin (GMmin) and Phase Margin (PMmin) when limit cycles can arise. Finally, two simulation examples are given to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In an empirical context, a method to use nonlinear control theory in the dynamic analysis of supply chain resilience is developed and tested. The method utilises block diagram development, transfer function formulation, describing function representation of nonlinearities and simulation. Using both ‘shock’ or step response and ‘filter’ or frequency response lenses, a system dynamics model is created to analyse the resilience performance of a distribution centre replenishment system at a large grocery retailer. Potential risks for the retailer’s resilience performance include the possibility of a mismatch between supply and demand, as well as serving the store inefficiently and causing on-shelf stock-outs. Thus, resilience is determined by investigating the dynamic behaviour of stock and shipment responses. The method allows insights into the nonlinear system control structures that would not be evident using simulation alone, including a better understanding of the influence of control parameters on dynamic behaviour, the identification of inventory offsets potentially leading to ‘drift’, the impact of nonlinearities on supply chain performance and the minimisation of simulation experiments. [ABSTRACT FROM PUBLISHER]

In data center networks, quantized congestion notification (QCN) has been ratified as the standard layer 2 congestion control mechanism. Since the congestion control algorithm of QCN conducts nonlinear switching between the rate increasing and decreasing stages, it is very difficult to analyze QCN theoretically. Previous works derive the stability condition of QCN using tools from linear control theory. However, the tools cannot reveal the reason why the queue at a congested link oscillates persistently when QCN is enabled. In this paper, we use the describing function method from nonlinear control theory to analyze queue oscillation. We show that unsuitable network configurations like more flows, a higher link capacity and a larger link delay will cause more severe oscillation of the queue. In particular, the impacts of the QCN parameters, such as the sampling probability and the constant in the active increase phase in QCN, on the oscillation magnitude of the queue are also analyzed. The simulation results validate the conclusion from our theoretical analysis well.

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, this brief shows that the Egan conjecture is not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for which an infinite hold-in range implies an infinite pull-in range. Using the direct Lyapunov method for the cylindrical phase space we suggest a sufficient condition of the pull-in range infiniteness, which provides a solution to the Egan problem. [ABSTRACT FROM AUTHOR]

To study the electric actuator, a model is established with backlash nonlinearity and equivalent rigidity considered. Applying the describing function, the limit cycle of the actuator system is analyzed, and the characteristics of the limit cycle's frequency and amplitude are also analyzed. A method adding negative feedback moment to the load is proposed. The feedback moment can suppress the limit cycle of the actuator by changing the motion state of the load. The effect of the feedback moment to the servo system is analyzed and the principle of the feedback coefficient is given. The simulation results show the effectiveness of the describing function in predicting the limit cycle in the nonlinear system, and the proposed method does not affect the servo performance of the system and the negative feedback moment is valid in suppressing the limit cycle of the electric actuator with the backlash nonlinearity. [ABSTRACT FROM AUTHOR]

Actuator rate limiting is the primary course of aircraft pilot coupling(APC) for fly-by-wire(FBW) aircraft. The actuator rate limiting is modeled by describing function. The relationships between actuator rate limiting, APC onset frequency and PVS closed-loop stability are analyzed. On the basis of this, an actuator rate limiting boundary determining method is proposed. A relaxed static stability(RSS) aircraft is taken as an example, based on the optimized McRuer pilot model, the longitudinal actuator rate limiting boundary that can ensure the closed-loop stability is determined. The open loop onset point(OLOP) criterion evaluating results shows that the method can avoid APC with minimum cost and the determined actuator rate limiting boundary coincides with the actuator rate corresponds to OLOP criterion boundary, indicating that the proposed rate limiting boundary determining method is reasonable.

This paper focuses on the limit cycles prediction problem to discuss the stability analysis of dynamic nonlinear interval type-2 Takagi–Sugeno–Kang fuzzy control systems (NIT2 TSK FCSs) with adjustable parameters. First, in order to alleviate computational burden, a simple architecture of NIT2 TSK FCS using two embedded nonlinear type-1 TSK fuzzy control systems (NT1 TSK FCSs) is proposed. Then, describing function (DF) of NIT2 TSK FCS is obtained based on the DFs of embedded NT1 TSK FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stable regions. Moreover, particle swarm optimization technique is applied to minimize the limit cycle region. Furthermore, for robust design, a gain-phase margin tester is utilized to specify the minimum gain margin ( GM min ) and phase margin ( PM min ) when limit cycles can arise. Finally, two simulation examples are considered to validate the advantages of the presented method. [ABSTRACT FROM AUTHOR]

This article presents a novel stability analysis of plunge centerless grinding. The analysis considers the nonlinearity associated to wheel-workpiece detachment under large waviness. The loss of contact is approximated by a harmonic linearization, in the frequency domain, by a double input describing function (DIDF). The stability analysis shows the effects of clipping and structural compliance: both clearly produce a waviness with a quasi-integer number of lobes. Our approach removes the need of additional hypotheses, sometime found in the literature. Under increasing lobes amplitude, clipping reduces waviness growth rate until a limit cycle is reached. Numerical and experimental verifications are provided. [ABSTRACT FROM AUTHOR]

Rate limit of system actuators is one of the major restrictions in the physical world. However, in classical and modern control design, the actuator rate limit has always been neglected. The rate limit generates amplitude attenuation and phase delay of the control signal, which will deteriorate closed-loop system performance, and may even lead to system instability. In this study, the Bode step control method was applied to the first-order plus time-delay system to achieve a better tolerance of smaller rate limit value. A rate limit compensation strategy is proposed based on the describing function and the onset frequency of the rate limiter. Both illustrative example and hardware-in-the-loop experiments are given to show the effectiveness of Bode step controller and the proposed rate limit compensation method. [ABSTRACT FROM AUTHOR]

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Multi-jump resonance indicates the behaviour of a nonlinear, non-autonomous system whose frequency response is characterised by several hysteresis regions. This paper faces the problem of the design of a nonlinear dynamical system such that it exhibits multi-jump resonance. Analytic aspects of the problem as well as electronic implementation issues of multi-jump resonance circuits are discussed, providing criteria for the design of systems with given hysteresis regions and guidelines for circuit realisation. [ABSTRACT FROM AUTHOR]

The nonlinearity of the switching process in DC-DC converters can result in the inaccuracy and invalidation of traditional stability criterion based on linear modeling, which is very harmful in practice, especially for the DC-DC converters with high stability requirements. In this paper, the describing function method is adopted for the modeling of switching process, namely, pulse width modulation (PWM), in DC- DC converters, and the describing function of the PWM is derived in detail. Considering the nonlinear items in the obtained describing function of PWM, the selection of the parameters in these nonlinear items are first provided and proved in this paper. With the obtained describing function, the stability of the PWM DC-DC converter can be analyzed exactly. Taken a PWM boost converter as an example, the nonlinear model based on describing function and the linear model are established, respectively; furthermore, the stability analysis based on these two kinds of models are carried out. Comparing with the traditional linear stability criterion, the simulation and experimental results validate the effectiveness and accuracy of the stability analysis based on describing function method. Furthermore, the transition interval of the PWM DC-DC converter from a stable region to an unstable region can be determined exactly by the proposed stability analysis method, which is helpful to determine the stability margin in real engineering applications. Therefore, this paper provides a practical stability analysis method for PWM DC-DC converters.

Present-day mechanical manipulators reveal limited performances when compared with the human arm. Joint-driven manipulators are sub-optimal due to the high actuator requirements imposed by the transients of the operational space tasks. Muscle-actuated arms are superior because the anatomic structures adapt the task requirements to the driving linear actuators. However, the advantages of muscle actuation are difficult to unravel using the standard integer-order kinematics based on the integer derivatives, namely the positions, velocities and accelerations. This paper investigates the human arm and evaluates the influence of biomechanics upon the driving actuators by means of a new method of kinematic analysis and visualisation. The proposed method uses the tools of fractional calculus for computing the continuous propagation of the signals between positions and accelerations. The behaviour of the variables is compared in the joint and muscle spaces, using both the kinematics in the time domain and the describing function method. In this line of thought, the classical integer-order kinematics, with three discrete levels of visualisation, is generalised to a continuous description represented by the fractional-order kinematics. [ABSTRACT FROM AUTHOR]

This research describes an adaptation-based control strategy to deal with the pulse-width pulse-frequency modulator. The subject behind the research is to control the above-referenced modulators the hard limiter block via closed-loop describing function representation. In a word, this modulator has a set of parameters, which are all in need of adjusting, accurately, in order to guarantee its high performance, in the entire areas of overall systems under control. The investigated results indicate that parameter’s adjustment of the aforementioned pulse-width pulse-frequency modulator can be recognized as the state-of-the-art outcomes via adaptation rules. [ABSTRACT FROM AUTHOR]

In mobile machinery, the existing load sensing system is featured by low response and oscillation tendency. As a promising alternative, the Electrohydraulic Flow Matching (EFM) system has the controllability advantages of fast response and good damping, but suffers from the flow mismatch problem leading to pressure impacts and low efficiency. To retain the controllability advantages and reduce flow mismatches of the EFM system, this paper proposes an Electrohydraulic Load Sensing (ELS) system via flow/pressure switched control, in which the pump displacement is controlled by the smaller output of the flow controller and the pressure controller. The actual flow requirement is calculated by the flow feedforward controller, while the pressure margin is kept as a desired value by the pressure feedback controller. The system linearization model is firstly established, and then the theoretical analysis was carried out to investigate the stability performance in the flow or pressure control mode. More importantly, the stability is analyzed under the condition of switching between flow/pressure controls. Using a converted hydraulic excavator, a test rig was constructed to verify the effectiveness of the switched controller. The performance of the existing EFM controller is studied as a comparison The result indicates that the pressure impacts caused by flow mismatches were avoided, and then the energy consumption was reduced. Meanwhile, the velocity performance is consistent with the EFM controller without loss of controllability. • A new electrohydraulic load sensing system is proposed for mobile machinery. • The proposed system is based on a switched flow/pressure control method. • The system is featured by high energy efficiency and good controllability. • The proposed controller is validated on a test rig with a 2-ton hydraulic excavator. [ABSTRACT FROM AUTHOR]

• A method is proposed to analyze frequency oscillations with governor deadbands. • Stability criteria based on eigenvalue locus with frequency amplitudes are given. • Effect of a deadband on frequency oscillations is analyzed using damping torque. Frequency oscillations are observed in several power systems. Governor deadband introduces nonlinearity to the system and affects frequency oscillations. A method using describing functions is proposed to analyze frequency oscillations with multiple intentional governor deadbands, including nonstep and step implementations. The deadbands are represented as gains of their describing functions dependent on frequency amplitudes, and the locus of eigenvalues with frequency amplitudes is computed to study the behavior of frequency oscillations. The stability criteria based on the eigenvalue locus are given. The relative location of the locus of damping ratios to the horizontal axis determines the behavior of frequency oscillation. The effect of a deadband on frequency oscillations is analyzed using the damping torque. Whether a deadband is beneficial or detrimental to frequency oscillations is affected by the damping torque of the prime mover. Time-domain simulation results validate the proposed methods and conclusions. [ABSTRACT FROM AUTHOR]

• The actual test shows a windup problem of the electrohydraulic load sensing pump. • A switched flow/pressure control scheme is proposed to achieve anti-windup. • The advantages are simper structure and stability property of the overall system. • The proposed controller has been successfully validated with a hydraulic excavator. The electronization demand of hydraulic systems is more and more urgent to improve the automation level of mobile machinery. The hydro-mechanical variable displacement pumps are being replaced increasingly by electronically controlled pumps to integrate flow control, power limitation and other functions flexibly. However, this paper discloses that the flow/power control requirements bring about an integral windup problem for the existing PID pump controller. Accordingly, an anti-windup switched flow/power controller is proposed to address this problem. The switched controller introduces a flow matching method to replace the electronic load sensing (ELS) controller, while a power controller with dynamic compensation is utilized to achieve power limitation. The mathematical model of the control system is established. The stability of the switched control system is discussed through the linearization model. Especially, the system stability when switching between the flow/power modes is proven by the describing function method. Boom motion tests with a 2-ton hydraulic excavator are implemented to validate the proposed controller. The test results indicated that the proper pump flow was supplied to achieve desired load velocity, and also the system power was limited within the setting range. Moreover, performance deterioration caused by integral windup is avoided thoroughly compared with the existing ELS controller. The comparison tests also show the limitation of traditional anti-windup methods. [ABSTRACT FROM AUTHOR]

This paper devotes to the robust stability problem for an uncertain linear time invariant (LTI) feedback system with actuator saturation nonlinearity. Based on a three degree of freedom (DOF) non-interfering control structure, the robust stability is enforced with the describing function (DF) approach for an uncertain LTI system to avoid the limit cycle. A new type of anti-windup (AW) compensator is designed using the quantitative feedback theory (QFT) graphical method, which results in a simple design procedure and low-order AW control system. One of the most significant benefits of the proposed method is free of the non-convexity (intractable) drawback of the linear matrix inequality (LMI)-based approach. The analysis conducted on the benchmark problem clearly reveals that the proposed QFT-based anti-windup design is able to handle both saturation and uncertainty in a very effective manner. [ABSTRACT FROM AUTHOR]

Highlights • The paper analyzes the flapper-nozzle type pneumatic valve with two ports in the frequency domain. • The valve is a part of the pneumatically driven parallel robot platform. • The system is observed as a parallel connection between the fixed orifice, the nozzle and the chamber. • The describing function is reduced to the unit gain and does not depend on the amplitude of the input signal. • The system becomes linear and is described only by means of the frequency response. Abstract This paper addresses the mass flow rate characteristic of a pneumatic valve set in the frequency domain. The valve set consists of a flapper-nozzle type valve and a constant isothermal volume chamber. It represents a part of the control system of the pneumatic parallel robot platform. Different flow regimes are analyzed because of air compressibility. The nonlinearity originating from the mass flow rate characteristic is approximated by the sinusoidal input describing function. Analytical determination of the describing function in a general case is not possible. However, the equivalent nonlinearity and the corresponding Hammerstein model can be introduced for a certain flow regime. In that case, the describing function of nonlinearity can be determined analytically. Amplitude and frequency responses show that the nonlinearity becomes more prominent at smaller frequencies and higher amplitudes of the exogenous signal. Analytical results show good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

The describing function approach is a powerful tool for characterizing nonlinear dynamical systems in the frequency domain. In this paper, we extend the describing function approach to detect and localize the damage in initially healthy nonlinear systems with limited measurements. The requirement of complete FRF of the underlying linear system by describing function approach is overcome by using a newly developed nonparametric principal component analysis-based model. Numerical simulation studies have been carried out by considering a cantilever beam with multiple local nonlinear attachments to demonstrate the localization process of the improved describing function approach with limited instrumentation. Parametric estimation of a shear building model is considered as a second numerical example to demonstrate the capability of the proposed approach in identifying the different types of nonlinearities and as well as combined types of nonlinearities (i.e. more than one type of nonlinearity). These combined nonlinearities can exist either in the same or different spatial locations. Experimental investigations have also been presented in this paper to complement the numerical investigations to demonstrate the practical applicability. [ABSTRACT FROM AUTHOR]