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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2002; 12:295–302 (DOI: 10.1002 /rnc.649) Horowitz: bridging the gap y Constantine H. Houpis* Air Force Institute of Technology, Wright-Patterson, AFB, OH, USA 1. INTRODUCTION As control theory was being developed in the late 1940 through the 1950s one of the many items of concern was how to design control systems for plants that are strongly nonlinear. Since then, many design methods have been developed for such plants. The principal features of quantitative feedback theory (QFT) appeared in an article by Prof. Isaac Horowitz in 1959 [1]. In developing QFT, Prof. Horowitz felt that there was a need for a control system design technique that control system design engineers could readily understand and apply. Also, for a technique that a control system design engineer would be able to have a ‘handle on the patient’s pulse’ throughout each step of the design process, and be able to handle structured plant parameter uncertainty as well as unstructured plant uncertainty. Thus, along with his graduate students, since 1959, he has developed such a technique: QFT. Through these past many years Horowitz has continually stressed the transparency of QFT; that is, the ability to visually relate the implementation of the design parameters to the real- world problem, from the onset of the design, and throughout the individual design steps. During the 1970s Prof. Horowitz received U.S. Air Force contracts that brought him in contact with the control community at Wright-Patterson Air Force Base. One of these contracts was with the Air Force Wright Laboratory Flight Dynamics Directorate’s Control System Development Branch (AFWL/FIGL). By 1981 the Branch Chief, Mr Evard H. Flinn, and his control system engineers, Mr Duane Rubertus and Mr Phil Chandler, all felt that QFT was a powerful multivariable nonlinear control system design technique for plants having structured parameter uncertainties. As a Senior Research Associate to the Branch and as a Prof. at the Air Force Institute of Technology (AFIT), Mr Flinn asked that I, along with my graduate students, become involved with Prof. Horowitz in applying QFT to flight control problems and to assist him in expanding his technique. 2. THE JOINT AFWL/FIGL-AFIT HOROWITZ YEARS The years of 1982–1992 were a very productive QFT period. The first few years Prof. Horowitz, under AFWL/FIGL contract, annually taught an AFIT course on QFT and was a co-thesis Published in 2002 by John Wiley & Sons, Ltd. *Correspondence to: Constantine H. Houpis, Air Force Institute of Technology, Wright-Patterson AFB, OH, U.S.A y This article is a U.S. Government work and is in the public domain in the U.S.A.

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROLInt. J. Robust Nonlinear Control 2002; 12:295–302 (DOI: 10.1002/rnc.649)

Horowitz: bridging the gapy

Constantine H. Houpis*

Air Force Institute of Technology, Wright-Patterson, AFB, OH, USA

1. INTRODUCTION

As control theory was being developed in the late 1940 through the 1950s one of the many itemsof concern was how to design control systems for plants that are strongly nonlinear. Since then,many design methods have been developed for such plants. The principal features ofquantitative feedback theory (QFT) appeared in an article by Prof. Isaac Horowitz in 1959[1]. In developing QFT, Prof. Horowitz felt that there was a need for a control system designtechnique that control system design engineers could readily understand and apply. Also, for atechnique that a control system design engineer would be able to have a ‘handle on the patient’spulse’ throughout each step of the design process, and be able to handle structured plantparameter uncertainty as well as unstructured plant uncertainty. Thus, along with his graduatestudents, since 1959, he has developed such a technique: QFT.

Through these past many years Horowitz has continually stressed the transparency of QFT;that is, the ability to visually relate the implementation of the design parameters to the real-world problem, from the onset of the design, and throughout the individual design steps.

During the 1970s Prof. Horowitz received U.S. Air Force contracts that brought him in contactwith the control community at Wright-Patterson Air Force Base. One of these contracts was with theAir Force Wright Laboratory Flight Dynamics Directorate’s Control System Development Branch(AFWL/FIGL). By 1981 the Branch Chief, Mr Evard H. Flinn, and his control system engineers, MrDuane Rubertus and Mr Phil Chandler, all felt that QFT was a powerful multivariable nonlinearcontrol system design technique for plants having structured parameter uncertainties. As a SeniorResearch Associate to the Branch and as a Prof. at the Air Force Institute of Technology (AFIT), MrFlinn asked that I, along with my graduate students, become involved with Prof. Horowitz inapplying QFT to flight control problems and to assist him in expanding his technique.

2. THE JOINT AFWL/FIGL-AFIT HOROWITZ YEARS

The years of 1982–1992 were a very productive QFT period. The first few years Prof. Horowitz,under AFWL/FIGL contract, annually taught an AFIT course on QFT and was a co-thesis

Published in 2002 by John Wiley & Sons, Ltd.

*Correspondence to: Constantine H. Houpis, Air Force Institute of Technology, Wright-Patterson AFB, OH, U.S.AyThis article is a U.S. Government work and is in the public domain in the U.S.A.

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advisor to my M.S. Thesis students. During the latter part of this period, with the suggestion tolook into state-of-the-art topics proposed by individuals in the aerospace industry, the QFTtechnique was applied by Horowitz and my theses students to the design of flight controlsystems that utilized thrust vectoring and for high angle-of-attack flight.

During this period Horowitz amazed all those who were closely involved with him with thebreadth and knowledge that he had, not only in control theory but in the field of mathematics.During one of our weekly conferences with a thesis student he said ‘out of the clear blue sky’ tothe student ‘use the Binet–Cauchy theorem’. Nowhere in his QFT publications had he made anyreference to this theorem. In searching through countless linear algebra texts and inquiries, noone was aware of this theorem. After prodding Isaac he finally remembered the text thatdiscussed this theorem.

The European control community is a strong advocate of the frequency-domain approach forcontrol system analysis and synthesis. Thus, they recognized the potential of applying QFT, afrequency-domain technique, to nonlinear control systems containing structured parametricuncertainty. As a consequence, we presented a paper co-authored with Prof. S.H. Wang at theInternational Control Conference 88 at Oxford University, Oxford, England [2].

A heightened awareness of Prof. Horowitz’s contributions to the state-of-the art of controltheory resulted through this association and the presentation of numerous papers by QFTresearchers at technical conferences. With support of AFWL the first QFT symposium was heldat Wright-Patterson AFB, OH. The purpose of this QFT symposium was a testimonial to thefounder of QFT and to the numerous QFT researchers, and many of their results weretransferred to the general public [3]. Throughout this period of association Prof. Horowitzexemplified the essence of the following anonymous quote:

In THEORY (scientist)There is no difference between theory and practice.

In PRACTICE (engineer)There is a difference between practice and theory.

Thus, an engineer who has a firm understanding of the results of the ‘scientific method’ andhas a firm understanding of the nature and characteristics of the plant to be controlled must beable to Bridge the Gap between theory and practice. The essence of Bridging the Gap is broughtout in the following sections and in Chapter 9 of Reference [4].

3. THE UNMANNED RESEARCH VEHICLE (URV)

During the latter part of the 20th century the Control System Development Branch of the AirForce Research Laboratory (AFRL/VACC) was responsible for the design, simulation, andflight testing of digital flight control systems for Uninhabited Research Vehicles (URV). Becauseof the close R&D collaboration of the Branch with AFIT faculty, a number of AFIT M.S.Thesis students were involved in the QFT design of digital flight control systems for the LambdaUAV shown in Figure 1 [3]. The objectives of the project described in this section were asfollows:

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1. To design robust flight control systems using the QFT design technique to satisfy thedesired performance specifications.

2. To flight test these designs.3. To implement an inner loop FCS on the Lambda URV that would be part of an

autonomous flight control system.4. To illustrate some of the real-world problems that are encountered in performing the

control system design process.

Accomplishing this design project required four cycles around the control design processloop. These four design cycles were:

Cycle 1}This cycle involved the satisfaction of only the first two of the project objectives.Cycle 2}Cycle 1 was repeated but involved the design of an improved integrator wind-up

limiter.Cycle 3}A redesign of the FCS was accomplished to satisfy requirements 1–3.Cycle 4}A refinement of the plant model was made in order to take into account a bending

mode that was neglected in the previous designs.

Cycles 1 and 3 were unsuccessful and Cycles 2 and 4 produced successful flight tests.This R&D effort involved the following design steps [3]:

(1) Prescribing the desired flight scenario.(2) Prescribing the desired performance specifications.(3) Obtaining the required number of plant models.(4) The QFT design of the digital flight control system.(5) The linear off-line design simulation.(6) The nonlinear off-line simulation.

Figure 1. Lambda unmanned research vehicle (URV).

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(7) The hardware-in-the-loop simulation/implementation in the laboratory.(8) Flight testing.

Two QFT designs for Cycle 1 were required to satisfy design objectives 1 and 2. The nonlinearand hardware-in-the-loop simulations of the first design revealed that system noise needed to beminimized and the accuracy of the software implementation design needed to be improved.Thus, the second QFT design involved in achieving a lower gain (see Section 9-3:7 in Reference[4]) and the utilization of an improved software algorithm implementation, as suggested inSection 9-3:12 of Reference [4], in order to enhance the controller’s numerical accuracy. Theflight test of the second QFT UAV flight control system design revealed that there existed areversed polarity on an angle sensor and the integrator wind-up limiter design that wasimplemented did not work.

Cycle 2, utilizing the second QFT design of Cycle 1, involved an improved wind-up limiterdesign and the correction to the sensor angle polarity. With these improvements a successfulsecond flight test was achieved.

For Cycle 3 a new QFT design was accomplished that involved the use of a hardware noisefilter and its implementation to minimize system noise and to satisfy design objective 3. Basedupon satisfactory simulations a third flight test was made that revealed that an unmodelledlongitudinal bending mode existed}thus the flight was aborted. Because the bandwidthrequirement of the first two QFT designs was low enough, the bending mode did not affect thesecond flight test.

Based on test data from the third flight test, the bending mode was modelled and incorporatedin the fourth QFT design process of Cycle 4. The fourth flight test of the final UAV flightcontrol system design that was implemented met all requirements. All of these four QFT designcycles demonstrated what Horowitz has continually stressed: the transparency of QFT; that is,the ability to visually relate the implementation of the design parameters to the real-worldproblem, from the onset of the design and throughout the individual design steps.

4. VISTA F-16 SUBSONIC ENVELOPE DESIGN

This QFT design example, as did the previous example, exemplifies two important features:transparency of QFT and Bridging the Gap. Throughout his years of exposing QFT, Horowitzalways stressed the former; that is, the ability to visually relate the implementation of the designparameters to the real-world problem, from the onset of the design and throughout theindividual design steps. Both of these features were involved in the design of a flight controlsystem for the UAV and for the VISTA F-16 shown in Figure 2 [5].

At the onset of the student’s (Major Scott Phillips, an F-16 pilot) VISTA F-16 QFT design, hedetermined from the size of his QFT templates that a robust design with a fixed set of controllerscould not be achieved thanks to the transparency of QFT. As a consequence, he proceeded toachieve a gain scheduling QFT design. This design required the determination of the manner inwhich the gain scheduling was to be accomplished. During the process of achieving this designMajor Phillips told his thesis committee the following:

‘‘I can tell from the feeling at the seat of my pants, as a pilot, when the gain must be changed.’’

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Based upon this feel of the seat of his pants he developed a graph that determined at what pointduring the flight scenario a gain change needed to be done. Thus, he was able to utilize his real-world knowledge of the aircraft and its handling qualities to achieve the desired robust FCS.This situation typifies the second feature Bridging the Gap.

The design of this flight control system involved the six design steps listed in Section 3. Basedupon the successful computer simulations the design was implemented and flown by MajorPhillips on AFRL/VACC Lamars flight test facility. The flight test results verified that theperformance specifications were met and the flying qualities were to Major Phillips’ satisfaction.Based upon the results of this thesis a follow-on full envelope QFT flight control system designwas satisfactorily achieved by another graduate student [6].

5. UNSTRUCTURED PLANT PARAMETER UNCERTAINTY

The previous examples have dealt with QFT designs dealing with structured plant parameteruncertainty. Dr Anthony Bentley illustrated in his article, appearing in Reference [3], howHorowitz’s QFT technique can be applied to nonlinear SISO systems having unstructured plantparameter uncertainty.

6. HOROWITZ’S QFT TRANSPARENCY AND BRIDGING THE GAP

The impetus of the QFT R&D that was achieved through the AFWL/FIGL-AFIT associationwas continued through the association with my AFIT colleague Prof. Meir Pachter (a flightcontrol specialist) with AFRL/VACC since 1992. In one of our student’s QFT flight controlsystem design the student brought to our attention that in his Bode plots of his tii control ratiosspikes occurred which penetrated the upper specified tii control ratio bound in the low frequencyrange of the desired loop bandwidth. Prof. Pachter, because of his aeronautical background,exemplified Horowitz’s exposition of the transparency of QFT. His immediate response was: ‘the

Figure 2. VISTA F-16.

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spikes are due to the phugoid mode of the aircraft and will note effect the aircraft’s desiredresponse’. Naturally, the student was greatly relieved!

As stated in Section 2, an engineer who has a firm understanding of the results of the‘scientific method’ and has a firm understanding of the nature and characteristics of theplant to be controlled must be able to Bridge the Gap between theory and practice. Thisconcept led to the development of QFT Engineering Rules (ERs) in Chapter 9 of Reference [4].This ‘Bridging the Gap’ was also demonstrated by Major Phillips as noted in the previoussection.

7. SUMMARY

The anonymous quotation, given in Section 2, during the 1990s, was best illustrated by thethoughts of control system design engineers and educators throughout the international controlcommunity. They strongly believed that in facing the technological problems of the 21st century,it is necessary that engineers of the future must be able to bridge the gap between the scientificand engineering methods. As indicated in the previous sections, Prof. Horowitz exemplified thisconcept by his development of QFT.

Horowitz’s transparency of QFT and his QFT technique exemplified the concept of ‘Bridgingthe Gap’ which are the essential aspects of the QFT control system design process illustrated inFigure 3. The intent of this figure is to give the control system design engineer an overview ofwhat is involved in achieving a successful and practical control system design. The aspects ofthis figure that present the factors that help in bridging the gap between theory and the realworld. While accomplishing a practical control system design, the designer must keep in mindthat the goal of the design process, besides achieving a satisfactory theoretical robust design, isto implement a control system which meets the functional requirements. In other words, duringthe design process one must keep the real world in mind. For instance, in performing thesimulations, one must be able to interpret the results obtained, based upon a knowledge of whatcan be reasonably expected of the plant that is being controlled. For example, in performing atime simulation of an aircraft’s transient response to a pilot’s maneuvering command to theflight control system, the simulation run time may need to be only 5 s since by that time a pilotwould have instituted a new command signal. If within this 5 s window the performancespecifications are satisfied, then it will be deemed that a successful design has been achieved.However, if the performance of interest is the steady-state response, then the simulation run-time must be considerably longer.

Achieving a satisfactory multivariable robust control system design for a nonlinear system is adifficult problem. There are a number of nonlinear control system design techniques forhandling nonlinear control systems, many of which are highly mathematical. Prof. Horowitzdeveloped a control system QFT design technique that control system design engineers couldreadily understand and apply. Also a technique that a control system design engineer would beable to have a ‘handle on the patient’s pulse’ throughout each step of the design process, and beable to handle structured plant parameter uncertainty.

The contributions [7] of Prof. Horowitz led to the development of the ‘QFT control systemdesign process of bridging the gap’.

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REFERENCES

1. Horowitz IM. Fundamental theory of linear feedback control systems. Transactions of IRE 1959; AC-4.2. Horowitz IM, Wang SH, Houpis CH. Quantitative design for systems with uncertainty and control failures. In:

Proceedings of the International Control Conference 88. Oxford University: Oxford, England, 1988.

Figure 3. The QFT control system design process: bridging the gap.

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3. Houpis CH, Chandler PR. (Eds.), Quantitative Feedback Theory Symposium Proceedings WL-TR-92-3063, WrightLaboratories, Wright-Patterson AFB, OH, 1992.

4. Houpis CH, Rasmusen SJ. Quantitative Feedback Theory Fundamentals and Applications. Marcel Dekker: NY, 1999.5. Phillips S, Pachter M, Houpis CH. A QFT subsonic envelope flight control system design. National Aerospace

Electronics Conference (NAECON), Dayton, OH, May 1995.6. Reynolds O, Houpis CH, Pachter M. Full envelope flight control system design using QFT. AIAA Journal of

Guidance, Control and Dynamics 1996; 19(1).7. Horowitz IM. Survey of quantitative feedback theory (QFT). International Journal of Control 1991; 53(2):255–291.

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