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.

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.

A Frequency-Domain INS/GPS Dynamic Response Method for Bridging GPS Outages

2010 ◽  
Vol 63 (4) ◽  
pp. 627-643 ◽  
Author(s):  
Mohammed El-Diasty ◽  
Spiros Pagiatakis
Keyword(s):  
Neural Network ◽  
Transfer Function ◽  
Dynamic Response ◽  
Dynamic System ◽  
Least Squares ◽  
Frequency Domain ◽  
Impulse Response ◽  
Time Domain ◽  
Response Model ◽  
Response Method

We develop a new frequency-domain dynamic response method to model integrated Inertial Navigation System (INS) and Global Positioning System (GPS) architectures and provide an accurate impulse-response-based INS-only navigation solution when GPS signals are denied (GPS outages). The input to such a dynamic system is the INS-only solution and the output is the INS/GPS integration solution; both are used to derive the transfer function of the dynamic system using Least Squares Frequency Transform (LSFT). The discrete Inverse Least Squares Frequency Transform (ILSFT) of the transfer function is applied to estimate the impulse response of the INS/GPS system in the time domain. It is shown that the long-term motion dynamics of a DQI-100 IMU/Trimble BD950 integrated system are recovered by 72%, 42%, 75%, and 40% for north and east velocities, and north and east positions respectively, when compared with the INS-only solution (prediction mode of the INS/GPS filter). A comparison between our impulse response model and the current state-of-the-art time-domain feed-forward neural network shows that the proposed frequency-dependent INS/GPS response model is superior to the neural network model by about 26% for 2D velocities and positions during GPS outages.

Selecting the Performance Weights for the μ and H∞ Synthesis Methods for SISO Regulating Systems

1996 ◽  
Vol 118 (1) ◽  
pp. 126-131 ◽  
Author(s):  
M. A. Franchek
Keyword(s):  
Time Domain ◽  
Synthesis Methods ◽  
Single Input Single Output ◽  
Hard Time ◽  
Single Output ◽  
Single Input ◽  
Performance Problem ◽  
Plant Uncertainty ◽  
Step Disturbance ◽  
Domain Constraints

Presented in this paper is a method in which the performance weights W1(s) and W2(s) of the robust performance problem and the H∞ optimization problem can be chosen to directly enforce hard time domain constraints. The class of systems addressed are single-input-single-output (SISO) regulating systems required to maintain the output within a prespecified time domain tolerance despite (i) plant uncertainty, (ii) an external step disturbance, and (iii) actuator output saturation. The performance weights are extracted from the feedback configuration and facilitate performance maximization.

Incorporating Right Half-Plane Poles and Zeros in a Frequency Domain Design Technique

1994 ◽  
Vol 116 (4) ◽  
pp. 593-601 ◽  
Author(s):  
Massoud Sobhani ◽  
Suhada Jayasuriya
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Design Methodology ◽  
Minimum Phase ◽  
Phase Problem ◽  
Nonminimum Phase ◽  
Phase Loop ◽  
Poles And Zeros ◽  
Bounded Disturbance ◽  
Domain Constraints

The frequency domain design methodology developed in Jayasuriya and Franchek (1988) for the synthesis of controllers that maximize the allowable size of an unknown-but-bounded disturbance in the presence of several time domain constraints is revisited. It is shown that (i) the basic ingredients of the methodology stays essentially the same for systems with nonminimum phase zeros and/or unstable poles, and (ii) two modifications can facilitate the loop shaping step. In particular, a nonminimum phase problem may be converted to one of frequency shaping a minimum phase loop; and a prestabilization scheme may be used for unstable systems. Two examples illustrate the proposed modifications with one compared to results obtained by the so called Set-Theoretic (ST) approach.

Small-Signal Admittance of Forward-Biased a-Si:H p+-i-n+ Diodes by Time Domain Analysis

1998 ◽  
Vol 507 ◽  
Author(s):  
F. Lemmi ◽  
N. M. Johnson
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Forward Bias ◽  
Transient Current ◽  
Frequency Variation ◽  
Displacement Current ◽  
Current Response ◽  
Small Signal ◽  
Low Frequencies ◽  
Dc Bias

ABSTRACTIn order to study the observed frequency variation of small-signal admittance of forward- biased amorphous silicon (a-Si:H) p-i-n diodes, we performed time-resolved measurements of currents induced by application of a small voltage step superimposed on a constant DC bias. The small amplitude ensures a linear behavior of the system under study. The transient current response includes all the details necessary to explain the stationary response to small sine-wave excitation. Details are obtained through a Fourier transform of the transient current. The real and imaginary parts of the resulting complex current are related to the capacitance and conductance spectra. This approach can explain phenomena taking place in the stationary regime such as negative capacitance values measured at low frequencies.In the frequency domain, measured capacitances do show negative values, as well as a clear dependence on the applied forward bias voltage. Namely, higher voltages extend the region in which the phenomenon occurs to higher frequencies of the probe signal. In the time domain, all measured transient currents exhibit common features such as an initial decay after the displacement current and, for higher DC biases, a gradual increase. A physical explanation of the current transient is proposed which accounts for the dependence on applied DC bias. A mathematical model is used to show how a delayed increase in the current leads to a modulation of the capacitance and conductance in the frequency domain, the two being related to each other. This finally allows the comprehension of the observed frequency domain behavior.

A Frequency Domain Identification Scheme for Flexible Structure Control

1990 ◽  
Vol 112 (3) ◽  
pp. 427-434 ◽  
Author(s):  
A. P. Tzes ◽  
S. Yurkovich
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Time Domain ◽  
Flexible Manipulator ◽  
Flexible Structure ◽  
Structure Control ◽  
Identification Schemes ◽  
Domain Identification ◽  
Frequency Domain Methods ◽  
Self Tuning

Transfer function identification schemes for use in self-tuning control applications are considered. Frequency domain methods generally require less computational load than time domain methods, and for certain classes of systems may be more accurate. For control purposes, however, a time domain parameterization of the system transfer function is often preferred, because of the direct relationship to controller parameters. In this paper we present a new method called Time-varying Transfer Function Estimation (TTFE) in which system parameters are computed through identification in the frequency domain. The method is particularly well suited for flexible structure control problems, and a self-tuning control law with frequency shaping is derived and demonstrated on a flexible manipulator system.

scholarly journals Numerical Convolution Method in Time Domain and Its Application to Nonrigid Earth Nutation Theory

2000 ◽  
Vol 178 ◽  
pp. 595-605 ◽  
Author(s):  
Toshio Fukushima ◽  
Toshimichi Shirai
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Time Domain ◽  
Least Squares Method ◽  
Numerical Differentiation ◽  
Linear Response Theory ◽  
Central Difference ◽  
Numerical Theory ◽  
Rigid Earth ◽  
The Time Domain

AbstractWe developed a numerical method to incorporate nonrigid effects into a nutation theory of the rigid Earth. Here we assume that the nonrigid effects are based on a linear response theory and its transfer function is expressed as a rational function of frequency. The method replaces the convolution of the transfer function in the frequency domain by the corresponding integro-differential operations in the time domain numerically; namely multiplying the polynomial in the frequency domain by the numerical differentiations in the time domain and multiplying the fractions in the frequency domain by the numerical integrations with a suitable kernel in the time domain. In replacing by the integrations, the method requires the determination of the coefficients of free oscillation. This is done by a least-squares method to fit the theory incorporated with the nonrigid effects to the observational data, whose availability is also assumed. The numerical differentiation and integration are effectively computed by means of the symmetric formulas of differentiation and integration. Numerical tests showed that the method is sufficiently precise to reproduce the analytically convolved nutation at the level of 10 nano arcseconds by using the 9-point central difference formulas and the 8-point symmetric integration formula to cover the period of 15 years with 1.5-hour stepsize. Since we only require the rigid Earth nutation theory to be expressed as a numerical table of time, this method enables one to create a purely numerical theory of nutation of the nonrigid Earth.

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