Frequency Domain Design for Maximal Rejection of Persistent Bounded Disturbances

1991 ◽  
Vol 113 (2) ◽  
pp. 195-205 ◽  
Author(s):  
S. Jayasuriya ◽  
M. A. Franchek
Keyword(s):  
Frequency Domain ◽  
Transfer Functions ◽  
Design Method ◽  
Design Procedure ◽  
Loop Shaping ◽  
Trade Offs ◽  
Control Objective ◽  
Bounded Disturbances ◽  
The Time Domain ◽  
Domain Constraints

A frequency domain methodology for synthesizing controllers for SISO systems under persistent bounded disturbances is presented. The control objective is to maximize the disturbance magnitude without violating prespecified state, control and bandwidth constraints. These constraints are treated explicitly in the design process. State and control constraints expressed in the time domain are first mapped into a set of equivalent frequency domain design specifications. The latter specifications define a set of frequency domain constraints on admissible loop transfer functions. These constraints are then displayed on a Nichols chart highlighting the dependency of the loop gains on phase and frequency. The final step in the process is to follow a loop shaping procedure to satisfy the frequency domain constraints. In the proposed methodology, the structure of the controller emerges naturally as a consequence of loop shaping and is not preconceived. The design procedure is semi-graphical and clearly demonstrates the design trade-offs at each frequency of interest. The effectiveness of the design method is illustrated by synthesizing a controller for a third order boiler-turbine set.

Frequency Domain Design for Maximizing the Allowable Size of a Step Disturbance in Linear Uncertain Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 635-642
Author(s):  
Suhada Jayasuriya ◽  
Massoud Sobhani
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Time Domain ◽  
Design Procedure ◽  
Control Input ◽  
Low Frequencies ◽  
Loop Shaping ◽  
Loop Transfer Function ◽  
Step Disturbance ◽  
Domain Constraints

A design methodology is developed for a linear, uncertain, SISO system for maximizing the size of a step disturbance in the presence of hard time domain constraints on system states, control input, output and the bandwidth. It is assumed that the system dynamics can be represented by a combination of structured uncertainty in the low frequencies and unstructured uncertainty in the high frequencies. The design procedure is based on mapping the time domain constraints into an equivalent set of frequency domain constraints which are then used to determine an allowed design region for the nominal loop transfer function in the plane of amplitude-phase. Once such a region is found, classical loop shaping determines a suitable nominal loop transfer function. The pole-zero structure of the compensator is a natural consequence of loop shaping and is not preconceived. An illustrative example demonstrates the trade-off between controller bandwidth, or the cost of feedback, and the tolerable size of step disturbance.

scholarly journals Bond graph based frequency domain sensitivity analysis of multidisciplinary systems

2002 ◽  
Vol 216 (1) ◽  
pp. 85-99 ◽  
Author(s):  
W Borutzky ◽  
J Granda
Keyword(s):  
Frequency Domain ◽  
Transfer Functions ◽  
Linear Time ◽  
Graph Model ◽  
Bond Graph ◽  
Sensitivity Matrix ◽  
Symbolic Form ◽  
Multidisciplinary Systems ◽  
Set Up ◽  
The Time Domain

Multidisciplinary systems are described most suitably by bond graphs. In order to determine unnormalized frequency domain sensitivities in symbolic form, this paper proposes to construct in a systematic manner a bond graph from another bond graph, which is called the associated incremental bond graph in this paper. Contrary to other approaches reported in the literature the variables at the bonds of the incremental bond graph are not sensitivities but variations (incremental changes) in the power variables from their nominal values due to parameter changes. Thus their product is power. For linear elements their corresponding model in the incremental bond graph also has a linear characteristic. By deriving the system equations in symbolic state space form from the incremental bond graph in the same way as they are derived from the initial bond graph, the sensitivity matrix of the system can be set up in symbolic form. Its entries are transfer functions depending on the nominal parameter values and on the nominal states and the inputs of the original model. The sensitivities can be determined automatically by the bond graph preprocessor CAMP-G and the widely used program MATLAB together with the Symbolic Toolbox for symbolic mathematical calculation. No particular program is needed for the approach proposed. The initial bond graph model may be non-linear and may contain controlled sources and multiport elements. In that case the sensitivity model is linear time variant and must be solved in the time domain. The rationale and the generality of the proposed approach are presented. For illustration purposes a mechatronic example system, a load positioned by a constant-excitation d.c. motor, is presented and sensitivities are determined in symbolic form by means of CAMP-G/MATLAB.

Repetitive Controller Design in Parameter Space

2003 ◽  
Vol 125 (1) ◽  
pp. 134-138 ◽  
Author(s):  
Levent Gu¨venc¸
Keyword(s):  
Frequency Domain ◽  
Parameter Space ◽  
Controller Design ◽  
Design Method ◽  
Testing Machine ◽  
Design Procedure ◽  
Controller Parameter ◽  
Performance Specifications ◽  
Material Testing Machine ◽  
Repetitive Controller

A new and simple repetitive controller design procedure in controller parameter space, where the structure of the filters in the repetitive controller are fixed from the start and parameters within these filters are tuned, is presented here. This approach results in simple and physically meaningful controllers that are easily implementable. The design method is based on mapping frequency domain performance specifications into a chosen plane of controller parameters. Sensitivity function magnitude bounds and a relative stability measure are chosen as the frequency domain specifications to be mapped into controller parameter space here. The design method is illustrated numerically in the context of a servohydraulic material testing machine application available in the literature.

Vehicle Vibration Analysis Using Frequency Domain Techniques

1969 ◽  
Vol 91 (4) ◽  
pp. 1075-1080 ◽  
Author(s):  
W. F. Lins
Keyword(s):  
Frequency Domain ◽  
Transfer Functions ◽  
Frequency Domain Analysis ◽  
Test Case ◽  
Response Functions ◽  
Vehicle Simulation ◽  
Absorbed Power ◽  
The Time Domain ◽  
Comparison Of The Results ◽  
Frequency Domain Techniques

This paper describes a method of determining and evaluating vehicle vibration through frequency-response functions. Human transfer functions and absorbed power are used to investigate the effects of vibration on the human being. The advantages and limitations of frequency domain analysis in contrast to vehicle simulation in the time domain are discussed. A test case showing a series of computer simulations using both techniques is presented, and a comparison of the results is made.

Adaptive Frequency Shaped Linear Quadratic Control of Mechanical Systems: Theory and Experiment

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
An-Chyau Huang ◽  
Ting-Kai Jhuang
Keyword(s):  
Frequency Domain ◽  
Function Approximation ◽  
Design Procedure ◽  
Adaptive Controller ◽  
Optimal Performance ◽  
Approximation Technique ◽  
Linear Quadratic ◽  
System Output ◽  
Dual Stage ◽  
The Time Domain

The traditional linear quadratic (LQ) controller can give optimal performance to a known linear system with weightings in the time domain, while the frequency shaped LQ (FSLQ) controller is able to provide optimal performance to the same class of systems with weightings in the frequency domain. When the system contains uncertainties, both of these two approaches fail. In this paper, an adaptive controller is proposed to an uncertain mechanical system such that LQ performance can be achieved with weightings in the frequency domain. The function approximation technique is applied to represent the uncertainties into a finite combination of a set of known basis functions. This allows the system to be with various nonlinearities and uncertainties without significant impact on the design procedure. The Lyapunovlike analysis is used to ensure convergence of the system output and boundedness of the internal signals. A dual stage is built to evaluate the performance of the proposed scheme experimentally.

A Conceptual Design Method for Parametric Study of Blades for Offshore Wind Turbines

2011 ◽  
Author(s):  
Lars Fro̸yd ◽  
Ole G. Dahlhaug
Keyword(s):  
Wind Turbines ◽  
Design Method ◽  
Design Procedure ◽  
Rotor Blades ◽  
Offshore Wind ◽  
Offshore Wind Turbines ◽  
Integrated Method ◽  
Horizontal Axis Wind Turbines ◽  
Parametric Studies ◽  
The Time Domain

This article presents a simplified, integrated method for design studies of blades for offshore wind turbines. The method applies to variable speed horizontal axis wind turbines with pitch control, and allows designing the rotor blades based on a very limited set of input parameters. The purpose of the method is to allow parametric studies of different design configurations of the rotor at a reasonable effort. The resulting wind turbine models are at a level of detail suitable for preliminary design considerations using e.g. aero-elastic simulations in the time domain. The aerodynamic design is based on blade element momentum (BEM) considerations using a distribution of 2D airfoil characteristics. The structural design of the blades is based on aerodynamic forces calculated from a small number of load cases. The design procedure is facilitated by using simplified cross-section definitions and iterative approaches. The resulting blade designs are shown to compare well with data from available turbine models.

scholarly journals FAST: An extension of the Wavelet Synchrosqueezed Transform

2021 ◽  
Author(s):  
Samit Chakrabarty ◽  
Amey Desai ◽  
Thomas Richards
Keyword(s):  
Frequency Domain ◽  
Wavelet Transforms ◽  
Sources Of Information ◽  
Multiple Sources ◽  
Complex Signals ◽  
Hilbert Transforms ◽  
Critical Areas ◽  
Trade Offs ◽  
The Time Domain ◽  
Heisenberg's Uncertainty Principle

<p>Extracting frequency domain information from signals usually requires conversion from the time domain using methods such as Fourier, wavelet, or Hilbert transforms. Each method of transformation is subject to a theoretical limit on resolution due to Heisenberg’s uncertainty principle. Different methods of transformation approach this limit through different trade-offs in resolution along the frequency and time axes in the frequency domain representation. One of the better and more versatile methods of transformation is the wavelet transform, which makes a closer approach to the limit of resolution using a technique called synchrosqueezing. While this produces clearer results than the conventional wavelet transforms, it does not address a few critical areas. In complex signals that are com-posed of multiple independent components, frequency domain representation via synchrosqueezed wavelet transformation may show artifacts at the instants where components are not well separated in frequency. These artifacts significantly obscure the frequency distribution. In this paper, we present a technique that improves upon this aspect of the wavelet synchrosqueezed transform and improves resolution of the transformation. This is achieved through bypassing the limit on resolution using multiple sources of information as opposed to a single transform.</p>

scholarly journals The Analysis of Controllability and Stability of an Approximate Model of Heat Transfer in an Autoclave

2018 ◽  
Vol 28 (3) ◽  
pp. 416-428 ◽  
Author(s):  
Sergey A. Mokrushin ◽  
Valeri S. Khoroshavin ◽  
Sergey I. Ohapkin ◽  
Alexander V. Zotov ◽  
Victor S. Grudinin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Transfer Functions ◽  
Structural Transformations ◽  
Space Representation ◽  
Proportional Integral ◽  
State Space Representation ◽  
The Matrix ◽  
The Stability ◽  
The Time Domain

Introduction.Ensuring the safety of country food industry in terms of the duration of storage and the quality of products is impossible without sterilizing products in autoclaves. The effectiveness of the sterilization processes depends on the degree of their automation. In the last twenty years, the improvement of automatic and automated control systems was primarily based on the development of technical means for automation without theoretical justification of decision-making. The proposed work is aimed at identifying the links between the parameters and connections of the sterilization process and the choice of structural and parametric features of the control system. Materials and Methods. A qualitative analysis is carried out based on the modern theory of automatic control for an approximative model of the thermal process of steam heating in an autoclave, taking into account the laws of heat transfer and the sufficiency of using a twodimensional model depending upon the structural and functional features of the model, which have regard to the parameters and relationships of the process, namely, the Kalman’s controllability properties of the model in the time domain in the state-space representation (the transition from the transfer function with zeros in the numerator to the normal differential system differential equations is also described). There were also analized the stability properties of the model in the frequency domain by means of transfer functions and structural transformations and the relationship of parameters in the form of inequalities with the subsequent choice of proportional-integral-differential configuration components for a real autoclave using the matrix of expert estimates. Results. It is shown that to make a qualitatively study of the issues of controllability and stability of the approximative model of the thermal process of water heating by steam in an autoclave, depending on the process parameters, it is necessary to represent the model the time domain (in the state-space representation) and in the frequency domain (in the form of transfer functions). The analysis of the controllability of the process is based on three approaches: the first (formalized) approach is based on the representation of the model in the form of a normal system of ordinary differential equations in the Cauchy form with the development of a method of decreasing the order of the higher derivatives of coordinates and introducing additional control signals taking into account the control derivatives; the second (unformalized) is based on the exclusion of management derivatives through structural transformation; the third (direct) approach uses the first-order heat balance and heat conduction equations derived from physical considerations. Under the conditions of Kalman’s controllability, dependencies between the parameters of the process and the degree of its controllability have been obtained.The analysis of the stability of the process is based on studying the poles of the transfer functions in the frequency domain and the characteristic roots of the equations of state in the time domain. On the basis of structural transformations, a closed canister heating loop with water with inertia, depending on the autoclave charging parameters, is isolated. Transient processes in this circuit take an amplifying, aperiodic or integral character, which affects the nature of the transient processes of the control system as a whole. The formalized choice of the components of the proportional-integral-differential regulation law is carried out depending on the frequency of application of the degree of loading and the need for the components of the proportional-integral-differential regulator using the matrix of expert estimates. Conclusions. The results of the research will serve as the material for the development of a real model of the autoclaving process, taking into account the static and dynamic characteristics of measuring, conversion and actuating elements, investigating the influence and compensation of inertia and nonlinearities of real elements, followed by the development of an automated system for controlling the sterilization process in autoclaves. The results of the work can be used to study general and applied problems of optimal control in both food and other industries, for example, in the production of building materials and the production of rubber products.

Robust Repetitive Controller Design in Parameter Space

2005 ◽  
Vol 128 (2) ◽  
pp. 406-413 ◽  
Author(s):  
Bilin Aksun Güvenç ◽  
Levent Güvenç
Keyword(s):  
Frequency Domain ◽  
Parameter Space ◽  
Controller Design ◽  
Design Method ◽  
Testing Machine ◽  
Design Procedure ◽  
Controller Parameter ◽  
Performance Specifications ◽  
Nominal Performance ◽  
Repetitive Controller

A new and simple robust repetitive controller design procedure in controller parameter space is presented here. The structure of the repetitive controller filters are fixed, thus, simplifying the design procedure to tuning of the fixed structure filters’ parameters. This approach results in simple and physically meaningful robust controllers that are easily implementable. The design method is based on mapping frequency domain performance specifications into a chosen controller parameter plane. Weighted sensitivity (nominal performance) and weighted complementary sensitivity (robust stability) function magnitude bounds are chosen as the frequency domain specifications to be mapped into controller parameter space here. The design method is illustrated numerically in the context of a servohydraulic material testing machine application available in the literature.

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