Analysis and Control of Nonlinear Systems

1993 ◽  
Vol 115 (2B) ◽  
pp. 351-361 ◽  
Author(s):  
J. Karl Hedrick
Keyword(s):  
Nonlinear Analysis ◽  
Flight Control ◽  
Model Error ◽  
Forced Response ◽  
Equivalent Linearization ◽  
Statistical Linearization ◽  
Linearization Methods ◽  
Analysis Tools ◽  
Highly Nonlinear ◽  
And Control

This paper describes my work on nonlinear analysis and control over the last twenty years. The first part of the paper concerns the development of nonlinear analysis tools for predicting stability and forced response characteristics of high speed ground vehicles. The principal motivation was to develop an alternative to “brute force” time domain simulation. The developed tools were extensions of “describing function” or “equivalent linearization” methods for both periodic and stochastic excitation. The “statistical linearization” analysis tools were then extended and applied to design control laws for nonlinear stochastic regulators. The second part of the paper was motivated by control system design for highly nonlinear, multivariable systems, such as automotive powertrain control and aircraft flight control. For these classes of systems, statistical linearization procedures are computationally cumbersome and also provide no stability or robustness guarantees. A method which has proven extremely powerful, both theoretically and experimentally, is “sliding control.” This technique is a form of input/output linearization that directly incorporates model error information with stability and performance measures. My students and I found several difficulties in the direct application of this method to automotive and aircraft control. This paper describes our solutions to the problems of repeated model differentiation, differentiation of model error, undesirable “internal dynamics” and systems with saturating control inputs.

scholarly journals Equivalent Linearization Methods for a Control System with Clutching Inerter Damper

2019 ◽  
Vol 9 (4) ◽  
pp. 688 ◽  
Author(s):  
Luyu Li ◽  
Qigang Liang ◽  
Han Qin
Keyword(s):  
Control System ◽  
Numerical Study ◽  
Integrated Design ◽  
Inertial Mass ◽  
Structural Vibration ◽  
Equivalent Linearization ◽  
Sdof System ◽  
Linearization Methods ◽  
Study Results ◽  
And Control

Inerter-based dampers have gained great popularity in structural vibration control. In this paper, equivalent linearization methods (ELMs) for a single-degree-of-freedom (SDOF) system with a clutching inerter damper (CID) are studied. The comparison of a SDOF system with a CID and an inertial mass damper (IMD) shows the advantage of the CID. Considering that the system with the CID is nonlinear, which is problematic for its performance evaluation and the integrated design of the structure and control system, three equivalent linearization methods based on different principles are proposed and discussed in this paper. The CID is considered to be equal to a combination of an IMD and a viscous damper. The equivalent inertance and damping can be calculated using the obtained formulas for all methods. In addition, all methods are compared in a numerical study. Results show that the ELM based on period and energy is recommended for small inertance-mass ratios.

Nonlinear analysis of stability and control for an F-16 configuration

1997 ◽  
Author(s):  
Zhongjun Wang ◽  
Zhidai He ◽  
C. Lan ◽  
Zhongjun Wang ◽  
Zhidai He ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Stability And Control ◽  
Analysis Of Stability ◽  
And Control

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

scholarly journals Virtual Digital Substation Test System and Interoperability Assessments

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2337
Author(s):  
Linwei Chen ◽  
Haiyu Li ◽  
Thomas Charton ◽  
Ray Zhang
Keyword(s):  
Test System ◽  
Communication Services ◽  
Iec 61850 ◽  
Analysis Tools ◽  
Information Models ◽  
Digital Substation ◽  
Interoperability Testing ◽  
Automation And Control ◽  
And Control ◽  
Intelligent Electronic Devices

Interoperability testing and analysis tools provide a means for achieving and assuring the integrity of multivendor intelligent electronic devices (IEDs) data exchanges. However, the testing and analysis are very time consuming and error prone, and these problems worsen when a substation becomes large and complex during the engineering process, commission, replacement, maintenance, and extension. To address this challenge, this paper presents a virtual digital substation test system (VDSTS) with interoperability analysis tools for assessing and identifying the engineering challenges for the multiple-vendors digital substation. This VDSTS consists of three parts: (i) A virtual digital substation modelling for generating real-time digital substation primary plant operation and fault conditions, (ii) a standard IEC 61850-based substation protection, automation, and control (PAC) system architecture with multivendor IEDs and bay solutions, and (iii) multivendor Substation Configuration description Language (SCL) tools and in-house built data visualisation tool. The study focuses on the interoperability testing of sampled values (SV), generic object-oriented substation events (GOOSE), and manufacturing message specification (MMS) communication services, as defined in IEC 61850. The main issues identified are compatibility issues of SCL tools, protocol implementation issues, different information models, and application limitations. The outcomes will help utilities to reduce the risks associated with the general rollout of digital substations.

A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

Nonlinear Analysis of a Rigid Rotor on Magnetic Bearings

1995 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Stability Criteria ◽  
Safe Operation ◽  
Qualitative And Quantitative ◽  
Quantitative Results ◽  
Nonlinear Equations Of Motion

A simple model of a rigid rotor supported on magnetic bearings is considered. A proportional control architecture is assumed, the nonlinear equations of motion are derived and some essential nondimensional parameters are identified. The free and forced response of the system is analyzed using techniques of nonlinear analysis. Both qualitative and quantitative results are obtained and stability criteria are derived for safe operation of the system.

scholarly journals CONTROL NOVEL MODEL OF KNEE CPM DEVICE

2009 ◽  
Vol 12 (4) ◽  
pp. 18-29
Author(s):  
Thanh Diep Cong Tu
Keyword(s):  
Weight Ratio ◽  
Artificial Muscle ◽  
Network Control ◽  
Continuous Passive Motion ◽  
The Novel ◽  
Highly Nonlinear ◽  
Cord Injury ◽  
And Control ◽  
Novel Model ◽  
Interesting Alternative

In recent years, CPM - Continuous Passive Motion has been proved to be one of the most effective therapeutic methods for patients who have problems with motion such as spinal cord injury, ankle and knee injury, parkinson and so on. Many commercial CPM devices are found in market but all of them use motors as the main actuators. The lack of human compliance of electric actuators, which are commonly used in these machines, makes them potentially harmful to patients. An interesting alternative, to electric actuators for medical purposes, particularly promising for rehabilitation, is a pneumatic artificial muscle (PAM) actuator because of its high power/weight ratio and compliance properties. However, the highly nonlinear and hysteresis of PAM make it the challenging for design and control. In this study, a PID compensation using neural network control is studied to improve the control performance of the novel model of Knee CPM device.

Model Identification and Operating Load Characterization for a Small Horizontal Axis Wind Turbine Rotor Using Integrated Blade Sensors

2010 ◽  
Author(s):  
Scott Dana ◽  
Joseph Yutzy ◽  
Douglas E. Adams
Keyword(s):  
Dynamic Response ◽  
Wind Turbine ◽  
Rotor Blade ◽  
Model Identification ◽  
Turbine Rotor ◽  
Forced Response ◽  
Horizontal Axis ◽  
Horizontal Axis Wind Turbine ◽  
And Control ◽  
Wind Turbine Rotor

One of the primary challenges in diagnostic health monitoring and control of wind turbines is compensating for the variable nature of wind loads. Given the sometimes large variations in wind speed, direction, and other operational variables (like wind shear), this paper proposes a data-driven, online rotor model identification approach. A 2 m diameter horizontal axis wind turbine rotor is first tested using experimental modal analysis techniques. Through the use of the Complex Mode Indication Function, the dominant natural frequencies and mode shapes of dynamic response of the rotor are estimated (including repeated and pseudo-repeated roots). The free dynamic response properties of the stationary rotor are compared to the forced response of the operational rotor while it is being subjected to wind and rotordynamic loads. It is demonstrated that both narrowband (rotordynamic) and broadband (wind driven) responses are amplified near resonant frequencies of the rotor. Blade loads in the flap direction of the rotor are also estimated through matrix inversion for a simulated set of rotor blade input forces and for the operational loading state of the wind turbine in a steady state condition. The analytical estimates are shown to be accurate at frequencies for which the ordinary coherence functions are near unity. The loads in operation are shown to be largest at points mid-way along the span of the blade and on one of the three blades suggesting this method could be used for usage monitoring. Based on these results, it is proposed that a measurement of upstream wind velocity will provide enhanced models for diagnostics and control by providing a leading indicator of disturbances in the loads.

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