Showing papers on "Describing function published in 1998"

System identification for limit cycling systems: a case study for combustion instabilities

Abstract: Presents a case study in system identification for limit cycling systems. The focus of the paper is on (a) the use of a model structure derived from physical considerations and (b) the use of algorithms for the identification of component subsystems of this model structure. The physical process used in this case study is that of a reduced order model for combustion instabilities for lean premixed systems. The identification techniques applied in this paper are the use of linear system identification tools, time delay estimation and qualitative validation of model properties using harmonic balance and describing function methods. The novelty of the paper, apart from its practical application, is that closed loop limit cycle data is used together with a priori process structural knowledge to identify both linear dynamic forward and nonlinear feedback paths.

Power Control in Cellular Radio Systems

Abstract: The primary goal of cellular radio systems, is to provide communication services to a large number of mobile users. Due to the rapid expansion of the market in this area, the available resources have to be used efficiently. The main issue in this thesis is methods to assign appropriate transmission powers, given coarsely quantized measurements, in order to meet the quality requirements from the users despite various disturbances.We propose a concept of a power regulator comprising the steps of estimating relevant quantities, handling quality specications, and controlling the powers. With this setting, the power controlling component relates directly to the mainstream of the algorithms proposed to date.For practical reasons, it is necessary to control the powers in a distributed fashion, and these distributed algorithms can be seen as local control loops. The effects of time delays and power output constraints in these loops are analyzed with respect to stability, using root locus techniques and describing functions. We emphasize the importance of identifying these time delays and constraints in order to choose the appropriate controller parameters for stable operation. The relevance of the local stability results on the overall system level is discussed, and further analyzed in a simulation environment, which has been developed.The literature is surveyed, and the contributions are classified with respect to a common framework in order to stress their similarities and differences. We show that an integrating controller forms the basis for the most popular algorithms. Methods for convergence analysis are investigated and related to the theory of linear systems. These methods are applied when proving global convergence of the integrating controller.The power control strategies are evaluated under more realistic circumstances in an environment simulating the operation of a GSM system. Comparing the results when using different power control algorithms we note that the proposed concept performs better than the algorithms proposed to date, both in terms of transmission quality of service and capacity.

A general class of sliding surface for sliding mode control

Abstract: In the conventional sliding mode control, the relative degree of the chosen sliding surface is usually one. This paper addresses a general class of sliding surface whose relative degree is no longer restricted to one. We show that when the relative degree is more than two, it is inevitable that there will exist a limit cycle for the nonlinear sign function. And for the case of relative degree two the system possesses poor phase margin. However, these disadvantages can be remedied remarkably by smoothing out the control nonlinearity in a suitable boundary layer with a saturation function that ensures asymptotic stability of the overall system.

Pilot-Induced Oscillations Involving Multiple Nonlinearities

Abstract: A pilot-induced oscillation is a type of instability caused by dynamic couplingbetween the pilot and the aircraft. Linear system analysis reveals that the pilot/aircraft system is unstable during the oscillation event. However, nonlinearities in the feedback system can limit the response variables so that a sustained, constant amplitude limit cycle results. A method is presented to analyze the limit cycle behavior of pilot/aircraft systems as a means of understanding pilot-inducedoscillations and their causes. A new computationaltechnique is considered and a new methodof testing limit cycle stability is presented. An analysisof the YF-12 pilot-inducedoscillation characteristics is used to demonstrate the method.

Power control in cellular systems subject to constraints and time delays

Abstract: Stability is a fundamental property desirable for any controlled system. We briefly review the root locus and describing function techniques, which are tools for stability analysis, and show how they can be applied to power control algorithms in cellular radio networks. The root locus method is used to find stability limits on controller parameters, and describing functions for predicting the presence of oscillations in the system. Thus these methods can be used to support the design phase, when deciding upon the appropriate controller parameters. These tools are demonstrated for various control algorithms and when different smoothing filters are applied. The analysis reveals that the distributed power control (DPC) algorithm, which works fine under ideal circumstances, yields an unstable system when subject to a small time delay. Furthermore, it is concluded that the performance with respect to stability is better when the measurements are averaged by an exponential forgetting filter than by the moving average filter.

A bifurcation-based procedure for designing and analysing robustly stable non-linear hydraulic servo systems:

Abstract: A critical evaluation of current hydraulic servo system analysis methods indicates a need for alternative methods better able to quantify robust stability One promising method recently developed for analysing large-scale power systems determines stability robustness in a high-dimensional parameter space by computing the distance to the ‘closest’ Hopf bifurcation (which corresponds to the birth of a limit cycle oscillation) In this paper a procedure is developed for applying closest Hopf bifurcation theory in the design and analysis of robustly stable hydraulic servo systems The procedure addresses practical implementation issues such as the impact of an inhomogeneous parameter space and the choice of a metric that yields a meaningful quantitative measure of stability robustness Results from the new procedure applied to a common position control system compare favourably with published describing function results and new simulation results Additionally, the new procedure is easier to apply and

Describing function analysis of nonlinear systems with parametric uncertainties

Abstract: Periodic phenomena, such as limit cycles, are among the most prominent features of nonlinear control systems. Predictions as to whether or not oscillations of this kind are likely to exist can be made using the describing function approach. Here, some of the now well established robustness results regarding linear systems are combined with the describing function method to analyze the stability of autonomous uncertain systems with separable nonlinearities. An example is provided to substantiate the mathematical derivations and theoretical conclusions.

Automatic tuning of systems with one or two unstable poles

Abstract: Stabilizability and identification of systems with one or two unstable poles is addressed. Two limit points of conditional stability are characterized using closed-loop dynamics with a relay and a novel nonlinear element. An algorithm is developed to analyze information from the resultant stable limit cycles in the process input and output. An easily tuned cascade PID control structure is then proposed to stabilize the system and achieve desirable performance. The proposed autotuning technique is tested with good results on a wide variety of unstable systems.

Stability analysis of neurocontrol systems using a describing function

Abstract: This paper presents the stability analysis of closed loop systems with a linear plant and a neural network as controller (neurocontroller). The describing function of the neural network is used to determine the bounds for the network weights in order to predict the limit cycles and stable system response.

Phase compensation: a means of preventing aircraft-pilot coupling caused by rate limitation

Abstract: The non-linear behaviour of rate limiting elements in flight control systems could lead to severe Pilot-Induced Oscillation (PIO) or Aircraft-Pilot Coupling problems (APC) The additional phase lag created in rate saturated conditions is the primary cause for aircraft-pilot instabilities This problem could be reduced by compensating the phase lag via specific signal filtering The paper describes a simple phase compensation algorithm for a rate limiting element which is derived directly from rate limiter describing function relationships The proposed compensator uses no feedback or logic and gives adequate results for all types of inputs The development of this new algorithm will be discussed and the performance evaluated Further, PIO protection capability will be demonstrated on a simulated pilot-in-the-loop bank angle control task Finally, this new phase compensator, connected to rate-limited actuators, was flight tested on DLR's In-Flight Simulator ATTAS in order to prove the capability under fly-by-wire system operations and under real flight conditions Flight test results are presented and discussed

Limit cycles in neurocontrolled minirobots

Abstract: This paper presents the stability analysis of the movement of a small robot controlled with a feedforward neural network, the minirobot is assumed to have one position sensor and one motor. A describing function of the neural network is used to determine the bounds for the network weights in order to predict limit cycles and to avoid oscillations of the minirobot when it is close to obstacles.

Robust nonlinear control based on describing function methods

Abstract: The robust control problem for nonlinear sys-tems is discussed from the standpoint of the amplitudesensitivity of the nonlinear plant and final control system.Failure to recognize and accommodate this factor may giverise to nonlinear control systems that behave differently forsmall versus large input excitation, or perhaps exhibit limitcycles or instability. Sinusoidal-input describing functions(sidfs) are shown to be effective in dealing with amplitudesensitivity in two areas: modeling (providing plant mod-els that achieve an excellent trade-off between conservatismand robustness) and nonlinear control synthesis. In ad-dition, sidf-based modeling and synthesis approaches arebroadly applicable. Several practical SIDF-based nonlinearcompensator synthesis approaches are presented and illus-trated via application to a position control problem.Keywords: Nonlinear control systems; describingfunctions; frequency-domain modeling; fourier analysis;frequency-domain design; robust control; synthesis meth-ods; pid control; fuzzy logic; position control.

On the limit cycle of the underwater vehicle control system

Abstract: Underwater vehicle control systems usually experience the limit cycle due to inherent nonlinear properties. Two major nonlinearities existing in such a system are the fluid drag force and the thruster dynamics. Solution of the limit cycle for the underwater vehicle control system using the describing function approach is presented in this paper. It appears that the proportional controller gain to excite the limit cycle has a lower bound. Simulation study is conducted to investigate characteristics of the limit cycle for an underwater vehicle position control system. Prediction performance of the limit cycle using the proposed method is evaluated by comparing with actual amplitude and frequency of the limit cycle measured from step responses of a complete dynamics model. Simulation results demonstrate excellent performance of prediction. Effect of model linearization on the limit cycle will also be examined.

Application of the Describing Function Method to Motion Generation Using a Neuro Oscillator

Abstract: As a central pattern generator, a neuro-oscillator with four neurons was used for the motion generation of a biped locomotive robot. There is a problem to determine unknown parameters in nonlinear differential equations of the neuro-oscillator so that it generates joint trajectories which yields reasonable biped locomotion. For this problem, we apply the describing function method for the neuro-oscillators, then we obtain equations which should be satisfied for the existence of a periodic solution. Adding a walking pattern which is represented by a trajectories of swinging leg, we can determine the unknown parameters from the equations obtained above. The effectiveness of the proposed method as a design procedure of the biped locomotion was assured by simulation study and experiments with a small biped robot.

The dynamic calibration of a high performance motion system

Abstract: The dynamic calibration of a high-performance flight simulator motion system is presented in this paper. The results were obtained through experimental measurements of the SIMONA Research Simulator motion-base and controller. This motion-base must be able to guarantee a high level of performance throughout its workspace. To do this, first a test procedure and a framework was defined whereby the dynamic characteristics could be quantified. A basis for the procedure is the long existing AGARD Advisory Report AR-144, which quantifies several independent tests including the measurement of describing functions, dynamic thresholds, noise levels and the hysteresis. This set of tests gives insight into several linear and non-linear properties of a controlled motion system in both the time and frequency domains. The AGARD tests had to be modified to include the high-frequency dynamics, and extended to enable characterisation of the system throughout its operating area. In order to arrive at a standardised approach, it is proposed that the latter be achieved by performing a set of path tracking tests. Furthermore, it was noticed that in order to enable an accurate characterisation of a high-performance motion system, both the experimental set up and test method have to be critically observed.

Robust stability of nonlinear hydraulic servo systems using closest Hopf bifurcation techniques

Abstract: A critical evaluation of current methods for analyzing hydraulic servo systems indicates a need for alternative methods that are better able to quantify robust stability, especially with respect to the existence of nonlinear oscillations. This paper addresses that need by examining a new analysis method that is capable of predicting stability robustness for nonlinear systems with high-dimensional parameter spaces. The method is based on the computation of "closest" Hopf bifurcations which correspond to the birth of limit cycle oscillations. A formal procedure that makes use of closest Hopf bifurcations for analyzing the robust stability of nonlinear systems is presented and applied. Practical implementation issues are addressed, with emphasis on interpretation of results to yield a meaningful quantitative measure of stability robustness. The new analysis method is validated via comparisons with previously published describing function results and new simulation results.

NARMAX modeling and robust controller design of internal combustion engines

Abstract: Presented in this paper is robust controller design procedure utilizing a discrete nonlinear model. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. For the engine idle speed control of this study, a SISO NARMAX model of the engine is given between the by-pass idle air valve (BPAV) and engine speed. From this model, a describing function representation is obtained for controller design subject to the time domain tolerance |/spl Delta/ rpm|/spl les/100 rpm on idle speed perturbations despite nonmeasurable 20 Nm external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.

Power control algorithms and stability analysis for radio network control

Abstract: Power control algorithms in cellular radio networks are analyzed. This is basically a MIMO problem where the controlled input is the powers used by the transmitters, and the measurements consist of signal to interference ratios for each receiver. These algorithms can, for each single connection and neglecting the cross couplings, be interpreted as a feedback system. The main contribution here is to analyze a generic control algorithm, which covers some important suggested classical control theory methods such as the root locus and describing function. The results include the important conclusion that unavoidable time delays and nonlinearities (saturation and quantization) in the feedback loop can cause a considerable loss in the stability margin. The results are supported by simulations.

Recursive optimization procedure for fuzzy-logic controller synthesis

Abstract: We present a method for the synthesis of fuzzy-logic controllers (FLCS) for amplitude-sensitive nonlinear plants based on sinusoidal-input describing-function (SIDF) methods plus step response optimization. This method involves a two-step process wherein an initial controller is obtained via the direct generation of the membership functions and output levels based on the "frequency response" of the nonlinear plant in the describing-function sense, then the FLC is perfected via recursive optimization of the step responses for a specified set of input amplitudes. By "recursive" we mean that the average step response obtained from step k is used as the objective for the k+1 optimization problem, and the process iterates until convergence, with the objective of achieving closed-loop system j performance that is as insensitive to reference-input amplitude as possible for the selected controller configuration. An illustration of the method and its effectiveness is provided, based on a prototypical position control problem where a servo motor plus mechanical load are characterized by torque saturation and nonlinear friction (stiction).

Analysis of Nonlinear Sustained Oscillations in Discrete Systems with Backlash and Resolution by Using a Discretization-Oriented Describing Function

Abstract: In this paper, a discretization-oriented describing function is derived for nonlinear devices combining backlash and quantization (resolution) while being subject to discretization through a sampler and zeroorder hold. Such a describing function is frequency-dependent so that the overall nonlinearity, which includes both resolution and backlash, is interpreted as possessing nonlinear inertia. That nonlinear inertia is generated by the sampling process, since it does not appear if the system is continuous. The presence of nonlinear sustained oscillations (limit cycles) is investigated through simulations.