Integrated design of an aircraft guidance system

using feed-back linearization

G.Bertoni, N.Bertozzi, P.Castaldi, M.E.Penati

University of Bologna, Aerospace Engineering Faculty

Italy

M.Bonfè, S.Simani

ENDIF, University of Ferrara

Italy

An innovative technique for integrated design of aircraft guidance system using Feed-back Linearization technique is discussed. Numerical results using a Piper PA-30 nonlinear mathematical model are given in a various range of flight situations. The integrated approach is expected to be characterized by a good flexibility about trajectories, aircrafts and autopilots used, significant precise performances, and capability of rejection atmosphere disturbances and faults on command surfaces.

1. Introduction

To day, in almost every field of engineering technology, a great development of automatic procedures and capabilities is observed. A great boost to the development of fully automated flights, have come, since the last 10 years, from the diffusion of Unmanned Aerial Vehicle (UAV) in military operations and some civil ones. The aim of this effort is to enable a precise trajectory tracking in a complex and full of disturbances ambient such as the free atmosphere. The great freedom about available trajectories granted by free airspace contrast with the strict request of accuracy in the positioning system and precise tracking due to safety procedures, so that both the guidance and the control system requests should be, at the same time, characterized by good flexibility and high performances, which implies a deep level of specialization. Therefore there is a higher request of interaction between the definition of the guidance calculations and the mathematical model of the aircraft dynamics, in order to accomplish the requirements. In this paper we want to investigate the possibility of using the Feed-back Linearization (FL) technique (see Isidori, 1995) in order to design an integrated guidance system for an aircraft flying on a desired trajectory. The application of FL to nonlinear systems requires the design of a nonlinear control law such that the closed loop of the original nonlinear plant with the controller becomes exactly equivalent to a linear system. The nonlinear control law will be named hereafter dynamic compensator. This block calculates a control action that applied to the nonlinear plant will make it produce an output in linear relationship with the reference input that we may call pseudo-input, of the dynamic compensator itself. The results obtained by the use of FL to design a guidance system are twofold: first, dynamic compensator automatically generates the correct kinematic input in order to perform the desired trajectory; second, it makes the global system linear, thus much simpler to control. On the other hand, the FL technique is difficult to apply directly on the full mathematical model of an aircraft; since there are several mathematical constrains that may not be satisfied by a detailed dynamic model of such a complex system. Moreover, even if FL may be applied to a slightly simplified model, the dynamic compensator may result any way computationally costly for on-board computer control systems, especially considering small UAVs. To avoid these problems and also to reduce costs and computational efforts, the proposed linearization procedure done on a simple kinematic model, this is actually valid, under some assumptions, for any possible aircraft. It must be denoted that the resulting dynamic compensator can be successfully applied to the real airplane model thanks the interactive role of autopilots, as will be described with more details in the rest of the paper (Section 3). This paper presents thus an approach for the application of Feed-back Linearization on a six degrees of freedom nonlinear aircraft model and analyses the performances of the interaction on a complex three-dimensional trajectory. It is important to remark that numerical results have been obtained considering a full nonlinear mathematical model, complete with measurements noise and wind gusts, during the simulation, even if the FL linearization technique has been applied, as will be described in next section, to a simple kinematic model. Therefore, the results demonstrate the feasibility of the proposed approach even for practical application on real aircrafts.

5. Conclusions

The results obtained during the four numerical tests shown in the paper confirm the capabilities of the guidance system proposed. The integration of Feed-back Linearization technique on a six-degree of freedom aircraft has been managed through the trick of using autopilots in order to make the airplane close to a unicycle model. The combination of basic mathematical tools leads however to a system characterized by high-level features: flexibility in trajectories and performances requests, rejection of atmospheric disturbances and command surface faults and good tracking accuracy; all together in a low cost architecture.

References

1.          Isidori. Nonlinear Control Systems, 3rd Edition, 1995, Springer-Verlag.

2.          De Luca, G.Oriolo. Modelling and Control of Non-holonomic Mechanical Systems. In Kinematics and Dynamics of Multi-Body Systems, J. Angeles, A.Kecskemethy Eds., CISM Courses and Lectures No. 360, 1995, Springer-Verlag, Wien, pp. 277-342.

3.          G.Oriolo, A.De Luca, M.Vendittelli. WMR control via dynamic feed-back linearization: Design, implementation and experimental validation. IEEE Transactions on Control Systems Technology, vol. 10, No. 6, 2002, pp. 835-852.

4.          d'Andrea-Novel, G.Bastin, G.Campion. Control of nonholonomic wheeled mobile robots by state feed-back linearization. Int. J.Robot. Res., vol. 14, No. 6, 1995, pp. 543-559.

5.          M.Bonfè, P.Castaldi, V.Geri, S.Simani. Fault detection and isolation for on-board sensor of a general aviatiom aircraft. International journal of adaptive control and signal processing, No. 20 issue 8, 2006, pp. 381-408.

6.          S.Sastry. Non linear systems: analysis, stability and control. Chap 8-9, Springer Verlag, 1999.

 

 

Gianni Bertoni, Dr., Prof. He graduated in electronic engineering at the University of Bologna in 1961 and at present is full professor of Automatic control at the Faculty of Aerospace Engineering of the same University. In 1971 he was visiting professor at the Department of Aeronautics and Astronautics of Stanford University (California). He has been consultant of a number of Companies for the study of automation problems and control process. In particular during the period 1978÷1983 he worked for Aeritalia and C.N.R. (National Research Council) for the special project Aids for navigation and air traffic control. At present, his professional interests are on Manufacturing flexible systems and Computer Integrated Manufacturing and his research interests are on the automatic flight control and on satellite-based navigation, approach and landing systems. He is author of a large number of scientific publications and books on control theory and industrial automation. He has been Chairman of automatic control related sessions of many international Congresses and Symposia. Since 1980 he has been a member of IFAC Committee on Automatic control in aerospace.

Paolo Castaldi, Dr., Prof. He received the "Laurea'' degree (cum laude) in Electronic Engineering in 1990 from the University of Bologna and the Ph.D degree in System Engineering in 1994 from the University of Bologna, Padova and Firenze. Since 1995 he has been Associate Researcher at the Department of Electronics, Computer Science and Systems of the University of Bologna. Since 2008 he has been a member of IFAC Committee on Automatic Control in Aerospace. His research interests include: the theoretical development and implementation of linear and non-linear methodologies for the FDI of the navigation, guidance and control systems of general aviation aircraft and UAVs; adaptive filtering, system identification and their applications to mechanical and aerospace systems. He is author of more than 90 refereed journals and conference papers as well as a books on these topics. He has been Chairman of automatic control related sessions of many international Congresses and Symposia and he is reviewer of many international journals. In particular he was awarded as ``outstanding reviewer'' of "Automatica" in 2004 and 2005.

Marcello Bonfe', Dr. He received the M.Sc. in Electronic Engineering from the University of Ferrara (Italy) in 1998 and the Ph.D. in Information Engineering in 2003 from the University of Modena and Reggio Emilia (Italy). He is currently Assistant Professor in Automatic Control, at the Department of Engineering of University of Ferrara, and IEEE Member since 2002. His main research interests are formal methods for manufacturing systems control, automatic fault diagnosis, modeling and control of mechatronic systems, on which he has published more than 15 international journal papers and more than 50 international conference papers.

Nicola Bertozzi, Dipl. Eng. He received the "Laurea" degree in Aerospace Engineering in December 2008 at the University of Bologna (Italy). Since then he had researched in non linear guidance and control systems, as his best scientific interest, in cooperation with the University of Bologna coming off with some articles in international congress and journals.

Maria Elisabetta Penati, Dr. Maria Elisabetta Penati graduated magna cum laude in electronic engineering at the University of Bologna in 1978. In 1983 she became assistant professor and ever since she has been working at the teaching activities and scientific projects at the Electronic, Computer Science and System Department of the University of Bologna. Since 2002, E. Penati has been working at the development of an autonomous management system for Unmanned Aerial Vehicles of small dimensions, that can be hand-piloted from ground and that can fly automatically. At present, she teaches Automatic Control at the Faculty of Managerial Engineering of the University of Bologna. She is the author of scientific publications and books on control theory and industrial automation.

Silvio Simani, Dr., Prof. He received the "Laurea" degree (cum laude) in Electrical Engineering in June 1996 from the Department of Engineering at the University of Ferrara (Italy). In February 2000 he was awarded the Ph.D. in "Information Science: Automatic Control" at the Department of Engineering of the University of Ferrara and Modena (Italy). Since 1999 Dr. Simani has been Research Associate at the Department of Engineering of the University of Ferrara. Since July 2000 he is a member of the SAFEPROCESS Technical Committee, and since February 2002 Dr. Simani is Assistant Professor at the Department of Engineering of the University of Ferrara. He received the nomination of IEEE Senior Member in December 2006. Dr. Simani's research interests include fault diagnosis and fault tolerant control of dynamic processes, system modelling and identification, and the interaction issues between identification and fault diagnosis. He is reviewer of many international journals, and author of more than 100 international journal, and conference papers, as well as two books on these topics.