Describing Function Model Research Articles

Joint use of DSRC and C‐V2X for V2X communications in the 5.9 GHz ITS band

Vehicular communications networks form the backbone of cooperative intelligent transport systems to support road safety and infotainment applications amongst users. IEEE 802.11p of the Dedicated Short-Range Communications protocol stack has been the technology of choice for Vehicle-to-Everything communications within the United States and Japan and has been extensively trailed in other countries such as Australia. With the advent of cellular technologies, a new, competing cellular-based Device-to-Device technology, known as Cellular Vehicle-to-Everything Sidelink, has emerged. Considering both technologies suffer from performance limitations, there is a current debate as to which of these technologies will eventually dominate the cooperative intelligent transport systems landscape if they cannot coexist. To investigate mechanisms of spectrum sharing between Dedicated Short-Range Communications and Cellular Vehicle-to-Everything for deployment in a common region, this paper initially reviews the background and technicalities of both technologies. The paper subsequently sets forth Vehicle-to-Everything platform models that allow not only spectrum sharing at the ITS band but also concurrent and simultaneous propagations of Dedicated Short-Range Communications and Cellular Vehicle-to-Everything messages. The transmission and reception mechanisms of hybrid Vehicle-to-Everything platforms are verified through a describing function model.

Fluid-Elastic Lock-in of a Cavity Shear Layer Instability With the Modes of a Submerged Cantilevered Beam

AbstractLock-in flow tones can occur for many different types of flow instabilities and structural-acoustic resonators at low Mach number. This paper examines the interaction between a shear layer instability generated by flow over a shallow cavity and the modes of an elastic cantilevered beam containing the cavity. A describing function model indicates that a cavity shear layer instability capable of producing lock-in with acoustic pipe resonances cannot achieve lock-in with equivalent structural beam resonances, particularly resonances of submerged structures. Fluid-elastic cavity lock-in is unlikely to occur due to the high level of damping that exists for a submerged structure, the high fluid-loaded modal mass, and the relatively weak source strength a cavity generates. Limited experimentation using pressure, acceleration, and particle image velocimetry (PIV) measurements has been performed which are consistent with the describing function model. A stronger source produced by a larger scale flow instability—separated flow over a bluff body—was able to lock-in with modes of the same submerged structure, further demonstrating that the concern for lock-in from a cavity shear layer instability is isolated to systems capable of stronger coupling or those dominated by fluid-acoustic resonances.

Adaptive control of tonal disturbance in mechanical systems with nonlinear damping

This paper describes an adaptive system for controlling the tonal vibration of a single-degree-of-freedom system with nonlinear damping. The adaptive control system consists of a force actuator in parallel with the suspension, which includes the nonlinear damper, and a velocity sensor mounted on the mass. The adaptation of the controller is done once every period of the excitation. Because the response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a linear model of the plant, can be slow to converge and may not achieve the desired performance. An on-line observer is used to obtain a describing function model of the plant, which can vary with the excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.

Adaptive vibration control of a mechanical system with nonlinear damping excited by a tonal disturbance

In this study, an adaptive control system to reduce the tonal vibration of a mechanical system characterized by nonlinear damping is considered. Since the response of the system to a sinusoidal excitation is however mainly sinusoidal, nonlinear controllers are not required for the control of a tone in such a mechanical system. The adaptation and stability of an adaptive control algorithm, however, depends on the accuracy of the plant model. Since the tonal response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a fix linear model of the plant, can be slow to converge and may not achieve the desired performance. The use of an online observer is proposed, to estimate the describing function model of the plant, which will vary with excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.

Nonlinear Proportional and Rate Feedback Controller Design Synthesis with Experimental Verification

AbstractA new procedure for synthesis of nonlinear proportional and nonlinear rate-feedback controllers for use with unstable nonlinear systems with application to a direct drive inverted pendulum is presented. The approach is to stabilize the nonlinear system followed by generation of the corresponding describing function models at various operating regimes of interest. With the known stabilizing controller and the stabilized frequency domain models, the frequency domain models of the unstable plant are algebraically extracted. A computer-aided design technique is used, and a set of proportional plus rate feedback controllers for the set of obtained open-loop frequency domain models is designed. The table of rate feedback gains as a function of rate feedback block input amplitudes is treated as the describing function model of the unknown nonlinear rate feedback gain; describing function inversion is used to obtain the nonlinear rate feedback gain. One linear proportional controller at an arbitrary opera...

Describing function model of series resonant inverter with current limiting diode-clamp

An equivalent circuit model for predicting the steady-state behaviour of the series resonant inverter with a current limiting diode-clamp is derived using describing function techniques. An iterative procedure is employed to determine the conduction point of the diode-clamp. Experimental results taken from a prototype inverter are presented to validate the model.

Idle speed control using a describing-function approach

A new systematic method for idle speed control of uncertain automobile engines with a time delay is developed. The method is based on obtaining a describing-function model of the internal combustion engine. This is followed by designing a classical controller via an algebraic approach. The design method and the associated software are applied to a specific automobile engine, and it is shown that the results compete with the observer-based design of Bengea et al. Stability is demonstrated by successful generation of describing-function models of the final non-linear closed-loop system.

Single‐range controller design for a cruise missile

PurposeThe purpose of this paper is to describe the application of a systematic single‐range controller design procedure to control a cruise missile.Design/methodology/approachThe controller design approach is based on one describing function model of the missile followed by linear system identification. The missile includes discontinuous nonlinear terms, and therefore, a small signal model is not obtainable by straight linearization. Once a linear approximation to the quasilinear model of the missile is obtained, a H∞ controller is designed to achieve a robust nonlinear closed‐loop system.FindingsIt is found that performance of the closed‐loop system with the applied simple controller design approach competes with one other complicated describing function‐based controller design technique.Research limitations/implicationsAt present, the research is limited to design of linear H∞ controllers.Practical implicationsThe major outcome of this paper is the verification that the applied simple describing function‐based H∞ controller design procedure may be used to design high‐performance controllers for cruise missiles.Originality/valueThis is the first paper that adopts an existing single‐range H∞ controller design procedure to design high‐performance controllers for cruise missiles.

Matlab software for inversion of describing functions

New Matlab functions for inversion of describing function models are developed. These functions are based on a newly developed computer-aided procedure. The procedure starts by guessing the initial values for the independent variables of an assumed nonlinear function. Then, the describing function model of the nonlinearity is numerically generated. This is followed by minimizing an objective function that yields the desired parameters of the nonlinear function. Such software has applications in synthesizing nonlinear gains of a controller. The printout of the software is given, and three demonstration problems are presented.

Combustion chamber pressure control based on mixed H∞-describing function approach

A new single range controller design approach for use with nonlinear liquid propellant engines (LPE) is developed. The approach is based on a describing function model of the nonlinear LPE coupled with the application of the H ∞ control theory. The approach is applicable to nonlinear LPEs of a general nature without any restrictions on nonlinearity type, number of nonlinear terms, nonlinearity arrangement, or system order. The approach is applied to an existing nonlinear LPE, and the results are compared with those obtained with an alternative method that was previously reported in the open literature.

A systematic single-range controller synthesis procedure for nonlinear and multivariable liquid propellant engines

A new systematic single-range controller synthesis procedure for use with nonlinear, multivariable, and time-varying liquid propellant engines is developed. The developed procedure is based on one describing function model of the nonlinear plant coupled with two different linear algebraic controller design procedures; one of the algebraic procedures is to achieve decoupling, and the second one is to achieve command following. The developed procedure is demonstrated by solving an example problem comparing the results using a H ∞ controller design procedure.

Robust Nonlinear H2/H.INF. Control for a Parallel Inverted Pendulum with Dry Friction.

A robust nonlinear H2/H∞ control method is presented for a parallel inverted pendulum system with uncertain parameters and dry friction. The dry friction is quasi-linearized into a describing function model by the random input describing function technique, and the uncertain system under consideration is described by state equations that depend on time invariant, unknown-but-bounded, uncertain parameters. Then, the robust nonlinear H2/H∞ control system that establishes the stability of the closed loop system in face of the nonlinear dry friction and uncertain parameters was constructed. However, it is difficult to solve coupled Riccati equations due to the nonlinear correction term contained in the Riccati equations. Thus, it is shown that the Riccati equations can be solved by some algebraic transformations of the coupled Riccati equations. This result enables robust nonlinear controllers to be designed easily. Hence, if the parameters of the parallel inverted pendulum vary as certain bounds, the proposed control has the robustness to both the system parameter variations and the nonlinear dry friction.

H∞ Control of a Nonlinear System using Simplicial Algorithms

This paper presents a new method for designing H∞ optimal or suboptimal controllers for nonlinear systems. A stability analysis is conducted using simplicial algorithms. In this example gains are used as the H∞ weighting functions. The system is a unstable first order plant, driven by a Bang-Bang actuator. A describing function model of the actuator is used in this analysis.

Adaptive Perturbation Control of an Unstable Plant using Simplicial Stability Analysis

This paper discusses a new method for the stability analysis of a nonlinear system using simplicial algorithms. The system analyzed is a unstable first order plant, driven by a Bang-Bang actuator, stabilized by a nonlinear adaptive perturbation filter. A describing function model of the actuator is used in this analysis. This system is implemented on a digital computer, and in analog circuit form, to demonstrate the practicality of the method.

Non-linear modelling of an electro-rheological vibration damper

Mechanical vibration dampers which employ electro-rheological (ER) fluids are capable of providing continuously variable damping forces in response to a suitable electrical stimulus. Such devices are potentially valuable for implementing “optimum” vibration control schemes such as those described by Sevin and Pilkey [1]. However, before serious design studies can begin, more information is required on the kind of forces which are developed by an ER fluid in vibration. This paper describes experiments in which digital processing of experimental records is used to determine viscous and Coulomb friction terms associated with a prototype ER damper. The models are verified through the use of a describing function model which is used to predict the approximate frequency response functions of the vibrating system.

W-domain design of single- and double-valued relay control systems

The design of relay control systems is presented having ideal, dead zone and rectangular hysteresis transfer characteristics. The choice of the appropriate describing function model is considered and examples are given of limit cycle prediction and digital compensation in the w-domain. The method described is particularly useful for the analysis of slowly sampled systems.

Invariants in loaded goal directed movements.

Goal directed movements, executed by means of a manipulator with various dynamics, were investigated in order to establish to what extent the loading affects the executed movement. The desired movement concept, together with a describing function model for goal directed movements, was applied to parameterize the movements. Analysis of the results showed that the position trajectories, when scaled by means of a fundamental scale property, with respect to the maximum velocity of the desired movements, were invariant under variation of the manipulator dynamics. From this invariance in the phasing of the movements, it was concluded that the subjects fully adapted to the applied loads.

Influence of combined visual and vestibular cues on human perception and control of horizontal rotation.

Measurements are made of manual control performance in the closed-loop task of nulling perceived self-rotation velocity about an earth-vertical axis. Self-velocity estimation is modeled as a function of the simultaneous presentation of vestibular and peripheral visual field motion cues. Based on measured low-frequency operator behavior in three visual field environments, a parallel channel linear model is proposed which has separate visual and vestibular pathways summing in a complementary manner. A dual-input describing function analysis supports the complementary model; vestibular cues dominate sensation at higher frequencies. The describing function model is extended by the proposal of a non-linear cue conflict model, in which cue weighting depends on the level of agreement between visual and vestibular cues.

Anticipation, Stability and the Transfer Function of the Human Pursuit System

Investigation into the 'predictive' properties of the human oculomotor pursuit system revealed that most of the anticipatory behaviour can be explained in tarns of an adaptive control system. A generalised 2 parameter describing function model has been derived which showed an excellent agreement with the experimentally obtained frequency response data.

On the Limits of Manual Control

Theoretical predictions and experimental data for the limits of manual control of unstable oscillatory second-order controlled elements are presented. At the limits of manual control, amplitude distributions of the system error and operator output were nearly Gaussian. The quasi-linear describing function model of the human operator implied from analysis of the experimental measurements indicates that the operator was capable of generating equalization equivalent to a double lead and that, for certain controlled elements, he adopted a response behavior analogous to quasiprecognitive tracking with a compensatory display.