A Simplified Robust Circle Criterion Using the Sensitivity-Based Quantitative Feedback Theory Formulation

1999 ◽  
Vol 121 (3) ◽  
pp. 543-547
Author(s):  
David F. Thompson
Keyword(s):  
Complex Plane ◽  
Open Loop ◽  
Specific Class ◽  
Quantitative Feedback Theory ◽  
Single Input Single Output ◽  
Circle Criterion ◽  
Single Output ◽  
Loop Transfer Function ◽  
Plant Uncertainty ◽  
Suspension Model

The circle criterion provides a sufficient condition for global asymptotic stability for a specific class of nonlinear systems, those consisting of the feedback interconnection of a single-input, single-output linear dynamic system and a static, sector-hounded nonlinearity. Previous authors (Wang et al, 1990) have noted the similarity between the graphical circle criterion and design bounds in the complex plane stemming from the Quantitative Feedback Theory (QFT) design methodology. The QFT formulation has specific advantages from the standpoint of controller synthesis. However, the aforementioned approach requires that plant uncertainty sets (i.e., “templates”) be manipulated in the complex plane. Recently, a modified formulation for the QFT linear robust performance and robust stability problem has been put forward in terms of sensitivity function bounds. This formulation admits a parametric inequality which is quadratic in the open loop transfer function magnitude, resulting in a computational simplification over the template-based approach. In addition, the methodology admits mixed parametric and nonparametric plant models. The disk inequality which results represents a much closer analog of the circle criterion, requiring only scaling and a real axis shift. This observation is developed in this paper, and the methodology is demonstrated in this paper via feedback design and parametric analysis of a quarter-car active suspension model with a sector nonlinearity.

A Comparative Study of Single Loop and Multiple Loop Design for Uncertain Single Input Single Output Systems

2004 ◽  
Author(s):  
Mayank Lal ◽  
Suhada Jayasuriya
Keyword(s):  
Casting Process ◽  
Frequency Noise ◽  
Quantitative Feedback Theory ◽  
Low Frequencies ◽  
Single Input Single Output ◽  
Single Loop ◽  
Considerable Uncertainty ◽  
Loop Design ◽  
Single Output ◽  
Performance Specifications

In this paper, studied are the actual advantages offered by SISO cascade loop structures. In Quantitative Feedback Theory it is emphasized that the use of cascaded loops is primarily for the reduction of bandwidth of the controllers. This in turn helps in considerable reduction of the adverse effects of high frequency noise. The question that arises then is whether or not there are any substantial benefits to be gained by cascade loop design in the low frequencies. This issue is the focus of this paper. It is shown using Quantitative Feedback Theory methodology that there aren’t any advantages gained in the low frequencies with the use of cascaded design for meeting performance specifications. In effect it is concluded that if the design is properly executed a single loop controller closed from the output to the input will be sufficient to meet the typical performance specifications. This is shown using an example where the mold level of a continuous casting process is to be controlled. The plant being used has considerable uncertainty so that features of robust control can be highlighted.

Analytic Loop Shaping Methods in Quantitative Feedback Theory

1994 ◽  
Vol 116 (2) ◽  
pp. 169-177 ◽  
Author(s):  
D. F. Thompson ◽  
O. D. I. Nwokah
Keyword(s):  
Uncertain Systems ◽  
Closed Loop ◽  
Design Method ◽  
Control Design ◽  
Quantitative Feedback Theory ◽  
Single Input Single Output ◽  
Single Output ◽  
Direct Design ◽  
Single Input ◽  
Robust Control Design

Quantitative Feedback Theory (QFT), a robust control design method introduced by Horowitz, has been shown to be useful in many cases of multi-input, multi-output (MIMO) parametrically uncertain systems. Prominent is the capability for direct design to closed-loop frequency response specifications. In this paper, the theory and development of optimization-based algorithms for design of minimum-gain controllers is presented, including an illustrative example. Since MIMO QFT design is reduced to a series of equivalent single-input, single-output (SISO) designs, the emphasis is on the SISO case.

scholarly journals A New Scheduling Quantitative Feedback Theory-Based Controller Integrated with Fault Detection for Effective Vibration Control

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
R. Jeyasenthil ◽  
Yang-Sup Lee ◽  
Seung-Bok Choi
Keyword(s):  
Fault Detection ◽  
Control Method ◽  
Point Of View ◽  
Smart Structure ◽  
Time Interval ◽  
Time Varying ◽  
Quantitative Feedback Theory ◽  
Control Effort ◽  
Single Input Single Output ◽  
Single Output

In this work, a new integrated fault detection and control (IFDC) method is presented for single-input/single-output systems (SISOs). The idea is centered on comparing the closed-loop output between the faulty system and fault-free one to schedule/switch the feedback control once the fault occurs. The problem addressed in this work is the output disturbance rejection. The set of feedback controllers are designed using quantitative feedback theory (QFT) for fault-free and faulty systems. In the context of QFT-based IFDC, the proposed active approach is novel, simple, and easy to implement from an engineering point of view. The efficiency of the proposed method is assessed on a flexible smart structure system featuring a piezoelectric actuator. The actuator and sensor faults considered are the multiplicative type with both fixed and time-varying magnitudes. In the fixed magnitude fault case, the actuator/sensor output delivering capability is reduced by 50% (multiplying a factor of 0.5 to its actual output), while in the time-varying magnitude case, it becomes 60% to 50% for a particular time interval. In both cases, the proposed control method identifies the fault and activates the required controller to satisfy the specification with less control effort as opposed to the passive QFT design featured by faulty system design alone.

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.

scholarly journals Design and Implementation of Adaptive PID and Adaptive Fuzzy Controllers for a Level Process Station

2021 ◽  
Author(s):  
Aparna Venkataraman
Keyword(s):  
Real Time ◽  
Fuzzy Logic Controller ◽  
Fuzzy Controller ◽  
Equilibrium Points ◽  
Process Variable ◽  
Open Loop ◽  
Single Input Single Output ◽  
Adaptive Fuzzy ◽  
Single Output ◽  
Adaptive Fuzzy Logic

This proposed work proposes the design and real-time implementation of an adaptive fuzzy logic controller (FLC) and a proportional-integral-derivative (PID) controller for adaptive gain scheduling that can be configured for any complex industrial nonlinear application. Initially, the open-loop test of the single-input single-output (SISO) system, with nonlinearities and disturbances, is conducted to represent the mathematical model of the process around a set of equilibrium points. The adaptive controllers are then developed and deployed by using the national instruments reconfigurable input/output data acquisition device (NI RIO), NI myRIO-1900, and the control parameters are adapted in real-time corresponding to the changes in the process variable. The resulting servo and regulatory performance of the controllers are compared in MATLAB® software. The adaptive fuzzy controller is deduced to be the better controller as it can generate the desired output with quicker settling times, fewer oscillations, and negligible overshoot.

scholarly journals Passivity based Approach for the Level Control of Spherical Tank Process

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Priya C ◽  
Lakshmi Ponnnusamy
Keyword(s):  
Real Time ◽  
Open Loop ◽  
Level Control ◽  
Time Model ◽  
Single Input Single Output ◽  
The Real ◽  
Single Output ◽  
Spherical Tank ◽  
Tank System ◽  
Single Input

The aim of this paper is to obtain the mathematical model and the real time model of the Single Input Single Output (SISO) conical tank system. The experimental model is obtained from the open loop response in real time and the transfer function is obtained using the two point method. For the real time model, two different controllers namely Zeigler Nichols tuned PI controller and passivity based controller are designed and tested in simulation and the performance of both the controllers are tested for servo operation and regulatory operation. The designed controllers are tested in Simulation and the response is recorded. The simulation results shows that the Passivity based Controller works better for the spherical tank process.

Measurement Errors in Closed-Loop Frequency Response Estimates

1980 ◽  
Vol 102 (1) ◽  
pp. 13-20
Author(s):  
P. W. Davall ◽  
P. N. Nikiforuk
Keyword(s):  
Frequency Response ◽  
Measurement Errors ◽  
Closed Loop ◽  
Power Spectra ◽  
Open Loop ◽  
Feedback Signal ◽  
Single Input Single Output ◽  
Closed Loop Systems ◽  
Single Output ◽  
Single Input

The sampling distributions associated with frequency response estimates of single input, single output closed-loop systems are derived for the case where both the output and feedback signal measurements are subject to added noise. This work is an extension of that done by Goodman [1-3] and Akaike [4, 5] on open-loop systems. Conditions for response estimate bias are investigated and approximate distributions for the power spectra estimates of the added noise terms are derived.

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