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 D-Optimal Design for Information Driven Identification of Static Nonlinear Elements

2021 ◽  
Author(s):  
Nalika Ulapane ◽  
Karthick Thiyagarajan ◽  
sarath kodagoda ◽  
Linh Nguyen
Keyword(s):  
Optimal Design ◽  
Model Calibration ◽  
Design Method ◽  
Single Input Single Output ◽  
Single Output ◽  
Order Polynomial ◽  
Information Maximization ◽  
Pros And Cons ◽  
Single Input ◽  
Optimal Design Method

<div>Identification of static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) is crucial for the success of system identification tasks. Identification of static nonlinear elements though can pose several challenges. Two of the main challenges are: (1) mathematical models describing the elements being unknown and thus requiring black-box identification; and (2) collection of sufficiently informative measurements. With the aim of addressing the two challenges, we propose in this paper a method of predetermining informative measurement points offline (i.e., prior to conducting experiments or seeing any measured data), and using those measurements for online model calibration. Since we deal with an unknown model structure scenario, a high order polynomial model is assumed. Over fit and under fit avoidance are achieved via checking model convergence via an iterative means. Model dependent information maximization is done via a D-optimal design of experiments strategy. Due to experiments being designed offline and being designed prior to conducting measurements, this method eases off the computation burden at the point of conducting measurements. The need for in-the-loop information maximization while conducting measurements is avoided. We conclude by comparing the proposed D-optimal design method with a method of in-the-loop information maximization and point out the pros and cons. The method is demonstrated for the single-input-single-output (SISO) static nonlinear element case. The method can be extended to MISO systems as well.</div>

Robust Control Design of a Single Degree-of-Freedom Magnetic Levitation System by Quantitative Feedback Theory

2012 ◽  
Author(s):  
Feng Tian ◽  
Mark Nagurka
Keyword(s):  
Robust Control ◽  
Magnetic Levitation ◽  
Design Method ◽  
Control Design ◽  
Open Loop ◽  
Quantitative Feedback Theory ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Maglev System ◽  
Robust Control Design

A magnetic levitation (maglev) system is inherently nonlinear and open-loop unstable because of the nature of magnetic force. Most controllers for maglev systems are designed based on a nominal linearized model. System variations and uncertainties are not accommodated. The controllers are generally designed to satisfy gain and phase margin specifications, which may not guarantee a bound on the sensitivity. To address these issues, this paper proposes a robust control design method based on Quantitative Feedback Theory (QFT) applied to a single degree-of-freedom (DOF) maglev system. The controller is designed to successfully meet the stability requirement, robustness specifications, and bounds on the sensitivity. Experiments verify that the controller maintains stable levitation even with 100% load variation. Experiments prove that it guarantees the transient response design requirements even with 100% load change and 39% model uncertainties. The QFT control design method discussed in this paper can be applied to other open-loop unstable systems as well as systems with large uncertainties and variations to improve system robustness.

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.

scholarly journals D-Optimal Design for Information Driven Identification of Static Nonlinear Elements

2021 ◽  
Author(s):  
Nalika Ulapane ◽  
Karthick Thiyagarajan ◽  
sarath kodagoda ◽  
Linh Nguyen
Keyword(s):  
Optimal Design ◽  
Model Calibration ◽  
Design Method ◽  
Single Input Single Output ◽  
Single Output ◽  
Order Polynomial ◽  
Information Maximization ◽  
Pros And Cons ◽  
Single Input ◽  
Optimal Design Method

<div>Identification of static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) is crucial for the success of system identification tasks. Identification of static nonlinear elements though can pose several challenges. Two of the main challenges are: (1) mathematical models describing the elements being unknown and thus requiring black-box identification; and (2) collection of sufficiently informative measurements. With the aim of addressing the two challenges, we propose in this paper a method of predetermining informative measurement points offline (i.e., prior to conducting experiments or seeing any measured data), and using those measurements for online model calibration. Since we deal with an unknown model structure scenario, a high order polynomial model is assumed. Over fit and under fit avoidance are achieved via checking model convergence via an iterative means. Model dependent information maximization is done via a D-optimal design of experiments strategy. Due to experiments being designed offline and being designed prior to conducting measurements, this method eases off the computation burden at the point of conducting measurements. The need for in-the-loop information maximization while conducting measurements is avoided. We conclude by comparing the proposed D-optimal design method with a method of in-the-loop information maximization and point out the pros and cons. The method is demonstrated for the single-input-single-output (SISO) static nonlinear element case. The method can be extended to MISO systems as well.</div>

Robust Disturbance Rejection for a Class of Nonlinear Systems Using Disturbance Observers

2013 ◽  
Author(s):  
Ahmed H. El-Shaer ◽  
Abdulrahman H. Bajodah
Keyword(s):  
Nonlinear Systems ◽  
Disturbance Rejection ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Single Input Single Output ◽  
Luenberger Observer ◽  
Single Output ◽  
Single Input ◽  
Bounded Disturbance

This paper is concerned with disturbance rejection performance in single-input single-output (SISO) nonlinear systems that are described by uncertain linear dynamics and bounded nonlinearities. First, the nonlinear terms are transformed into an equivalent bounded disturbance at the output of a linear system. Then, a disturbance observer (DOB) is added to the closed loop to achieve robust disturbance rejection. The DOB design is formulated as an extended Luenberger observer having internal dynamics with at least an eigenvalue at the origin. The synthesis of a (sub)optimal DOB is carried out by solving multi-objective H∞ sensitivity optimization. The design approach is applied to an inverted pendulum with actuator backlash. Closed loop response shows that tracking performance is indeed greatly enhanced with the DOB.

A Control Design Approach for TITO Systems Using Measured Data

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Sofiane Khadraoui ◽  
Raouf Fareh ◽  
Hazem N. Nounou ◽  
Mohamed N. Nounou
Keyword(s):  
Frequency Domain ◽  
Closed Loop ◽  
Controller Design ◽  
Control Design ◽  
Intermediate Step ◽  
Single Input Single Output ◽  
Plant Modeling ◽  
Single Output ◽  
Performance Specifications ◽  
Tito Systems

This paper deals with the design of fixed-structure controllers for two-input two-output (TITO) systems using frequency-domain data. In standard control approaches, a plant model is first derived, then a suitable controller is designed to meet some user-specified performance specifications. Basically, there are two common ways for obtaining mathematical models: white-box modeling and black-box modeling. In both approaches, it is difficult to obtain a simple and accurate model that completely describes the system dynamics. As a result, errors associated with the plant modeling may result in degradation of the desired closed-loop performance. Moreover, the intermediate step of plant modeling introduced for the controller design is a time-consuming task. Hence, the concept of data-based control design is introduced as a possible alternative to model-based approaches. This promising methodology allows us to avoid the under-modeling problem and to significantly reduce the time and workload for the user. Most existing data-based control approaches are developed for single-input single-output (SISO) systems. Nevertheless, a large class of real systems involve several manipulated and output variables. To this end, we attempt here to develop an approach to design controllers for TITO systems using frequency-domain data. In such a method, a set of frequency-domain data is utilized to find an adequate decoupler and to tune a diagonal controller that meets some desired closed-loop performance measures. Two simulation examples are presented to illustrate and demonstrate the efficacy of the proposed method.

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