- Email: [email protected]
CONTROL THEORY AND FLIGHT CONTROL EDUCATION AT A CIVIL AVIATION ENGINEERING SCHOOL
CONTROL THEORY AND FLIGHT CONTROL EDUCATION AT A CIVIL AVIATION ENGINEERING SCHOOL
F€lix Mora-Camino* and Karim Acha•bou#
*Ecole Nationale de l’Aviation Civile - ENAC, Laboratoire d’Automatique et Recherche Op•rationnelle - LARA 7 Av. Edouard Belin, 31055 Toulouse, France, [email protected] #
Institut National Polytechnique de Toulouse et LARA/ENAC, [email protected]
Abstract: In this communication, the teaching of Control Theory in a civil aviation engineering school, ENAC, is considered. After describing the evolution of flight control systems along the last decades and pointing out the new challenges faced in this area, teaching objectives with respect to Control Theory are discussed. The constraints involved with this multidisciplinary area are analyzed and the current teaching practice is described and assessed. Copyright € 2006 IFAC
Keywords: aerospace, flight control, control theory, control education, teaching.
1. INTRODUCTION
Control theory has played a central role in the development of modern air transport aircraft, starting from the development of autopilots and auto land systems in the late fifties and early sixties to automatic separation and avoidance systems at the beginning of the new century. Control Theory has become an unavoidable discipline in the curriculum of aeronautical engineering schools. ENAC, the French civil aviation institute, which provides professional training for many activities related with Civil Aviation (air traffic control, airport operations and management, airline management, etc) houses also an engineering school which belongs to the French “grandes •coles” group. Many difficulties arise at the time of defining the contents of the teaching in Control Theory as well as its relative position within its curriculum. Some of them are listed here:
-Aeronautical schools are involved with a specific field of application not with Control Theory per se. -Atmospheric flight dynamics present many complicating factors which are often tackled in practical ways by other aeronautical disciplines. -Human factors involving pilots and passengers take an important place in flight operations. -What should be the connections with purely aeronautics disciplines?
-How to attract the interest of student for such a theoretical discipline while operations and practice are emphasized by many other disciplines ? In this paper first the evolution during the last fifty years of flight control systems for air transportation aircraft is analyzed briefly, then the challenge of teaching Control Theory in an aeronautical engineering school is considered. Actual solutions and practices are displayed and discussed. Finally, two illustrations of the way Control Theory concepts are connected with flight control applications, are displayed in annex.
2. EVOLUTION OF AIRCRAFT FLIGHT AUTOMATION
2.1 First steps towards safety and efficiency In the late fifties, with the development of jet aircraft presenting higher speed and range, safety issues have led to the development of autopilots whose functions where devoted to the enhancement of natural stability (mainly along the yaw axis) , to basic auto modes (control of pitch and bank attitude angle) and to superior modes with the objective of tracking guidance parameters such as heading angle, speed and flight level parameters. At that time only analogue computers were available while control theory was mainly concerned with SISO feedback control. However, through different treatments such as
decoupling of longitudinal and lateral dynamics around an equilibrium situation and frequency decoupling of the fast dynamics (rotating dynamics) from the slow dynamics (translational dynamics), it was possible to design quite efficient control laws with a rather high degree of robustness since with gain scheduling schemes around few reference points, it was possible to cover the whole flight envelope. One of the main success of this generation of flight control systems was the realization of auto land systems which helped to improve notably the regularity of flights and the safety level of the sector. Using high levels of redundancy (up to four parallel auto land systems in some aircraft), reliability levels (probability of a catastrophic event less than 10-9 per flight hour, a probability of less than 10-7 for a catastrophic landing) were met. It is useful to observe that in the case of “auto” land, the aircraft needed the help of external signals (ILS) to achieve the maneuver. At that time, most aeronautical engineering schools had access to flying laboratories to make demonstration of the flight dynamics characteristics, either natural or acquired through automation. What remain from this today? When digital computers were introduced to achieve flight control functions, for economics reasons and also airworthiness requirements, the first practice was to merely digitalize the previous control laws, while already the main results of modern control theory were already available. So, some aging aircraft equipped with this generation of flight control systems are still in operation. However, SISO feedback control theory remains of actuality since many control channels, even when fly by wire technology is used, are still designed using the formalism of transfer functions and servo control.
2.2 Modern control theory and flight control In the seventies, with the adoption of state space representations of longitudinal and lateral flight dynamics, modal control and state estimation techniques allowed the design of more efficient multidimensional control structures insuring stability, accuracy and reliability. At that time appeared a number of valuable textbooks (Nelson, 1989), (McLean, 1990) and (Blakelock, 1991). Also, issues related with structural modes of larger and more flexible aircraft where better tackled with the state space formalism.
Later, with the development of robust control theory, many studies have been performed to get robust flight control laws, however with little success in the case of air transportation aircraft. Note that the same happened with adaptive control techniques. More recently, publication series promoted by AIAA have allowed a continuous updating of applied knowledge in this area (for instance Pratt, 2000). It was the time when many Kalman filter applications have been developed not only to design new airborne control functions, such as anti turbulence systems, but also to improve navigation systems performances with the introduction of hybridization between the current available data channels (for instance: baro-inertial
hybridization to get better current flight level estimates, Doppler-inertial hybridization to get better estimates of current ground speed). With the increasing price of fuel and the fierce competition between airlines, they asked for more efficiency with respect to flight costs and optimal control techniques were used to tackle the flight plan optimization problem: while Hamiltonian related optimality conditions helped to characterize in practical terms optimal flight conditions, techniques such as dynamic programming were used to compute effectively optimal flight plans. This function was the pivot of the new Flight Management Systems introduced in the mid eighties and which have become mandatory today not only for wide body aircraft but also for regional aircraft. With the increasing performances of on board computers, new functions such as navigation and monitoring where integrated in Flight Management Systems. 2.3 Increased air traffic and new challenges With the sustained growth of air transportation new control problems related with traffic saturation either at airports or in airways have been considered. At the level of airports with longer and larger taxiing networks, improved taxiing guidance capabilities are required to ensure ground traffic safety and efficiency. This leads to the consideration of complex non linear control and supervision problems for ground guidance involving engine, brakes and wheel orientation.
Air Traffic Control has remained until recently human-based for decisions taken mainly from the ground with no aircraft autonomy for reactivity to traffic conditions. New on board concepts such as Communication, Navigation and Surveillance (CNS) systems are now introduced to improve the efficiency of Air Traffic Management systems. This implies more autonomy for the aircraft to predict and solve air traffic conflicts and to maintain safe separations with other surrounding traffic. Also, the organization of traffic flows supposes the implementation of new flight control modes such as merge modes, 4D trajectory tracking and relative guidance modes. It appears that these functions should lead to the consideration of advanced control issues such as hybrid control and multi agent control systems which are still in they early development. 3. AIRCRAFT CENTRED CONTROL THEORY EDUCATION 3.1 Control Theory versus Flight Control In many aeronautical engineering schools, control theory takes a large place in the curricula, however this teaching has in general very little connections with the pure aeronautical disciplines such as aerodynamics, flight mechanics and flight qualities, propulsion, navigation, human factors (pilot related) , airworthiness and safety requirements and finally, air traffic and airlines economics. This cannot be the case at ENAC, since his graduated students are not generalists, but are specialized engineers in air transportation issues with particular emphasis in
aircraft operations, traffic operations and civil aviation support systems.
from one year to the next by different students until completion.
From section 2, it appears that not every topics in Control Theory are today useful for air transportation applications. Some of them, such as on line identification and adaptive control techniques are very questionable from the certification point of view and airworthiness regulations and practice. Once, when Control Theory was taught at ENAC by external teachers having an Electrical Engineering background, to few adaptations to its particular needs were performed and a common and depressing reflection among students was ”encore des maths!”(“more math!”). This was characteristic of the wrong perception of the control disciplines by students coming from the French preparatory school systems where Algebra and Analysis where overwhelming disciplines. On the other side, teaching about airborne flight automation systems had at that time a pure descriptive and practical nature and was performed by instructors having a very basic background in Control Theory. It was up to the students to eventually connect the control theory with airborne applications. So, aeronautical firms (aircraft manufacturers, airborne systems firms,...) were hiring in one side generalists from other schools with good knowledge in Control Theory and on the other side aeronautical engineers with a practical and descriptive knowledge about airborne flight control systems and environment with communication difficulties between them in many situations. 3.2 Enforcing Control Theory teaching In general the students at ENAC are enthusiastic with aircraft issues and an efficient way to make them get interest in Control Theory has been to integrate in many ways this teaching with other aeronautical disciplines. For that, different steps and actions have been taken: -Today at ENAC, all Control Theory teachers have some aeronautical background. -Every taught topic in Control Theory is systematically illustrated by several applications in the aeronautical field. - Connections between Control Theory notions and aeronautical issues (for instance between “asymptotic stability” and “dynamic stability”, “controllability” and “handling qualities”) are always emphasized. -The usefulness in the aeronautical field of special Algebra or analytic developments performed in the context of Control Theory can be easily evidenced by pointing out direct applications. -Numerical flight simulators for different aircraft and with growing complexity are used to support directed studies in the field of Control Theory. -Matlab/Simulink which has been a standard at ENAC for many years displays a lot of aeronautical case studies (Simulink, 1994) which are motivating and ready to . -Small personal projects with multidisciplinary characteristics, including Control Theory issues, are proposed to the students by the end of the fourth and the fifth semesters. These projects can be continued
4. AIRCRAFT CENTRED CONTROL THEORY EDUCATION The curriculum at ENAC being organized in a semester basis, to each semester a goal has been assigned with respect to Control Theory and aeronautical applications. The first two semesters close the three years training at BSc level as defined by the Bologna declaration, while the four following semesters correspond to the MSc training level. 4.1 Curriculum at BSc level in Control Theory First semester: Transfer function modeling and feedback control of SISO linear systems is introduced. Since many students have a previous knowledge in this area, taught in general in a very theoretical way, a large importance is given to the systems engineering approach of real physical systems through mathematical modeling. Different applications are considered in the field of sensors and actuators modeling: for instance, study of the performances of a vario-meter with a complementary filter structure, modeling and PID control of an electro hydraulic servo actuator for an aileron of a wide body aircraft. Second semester: Modeling and feedback control of SISO non linear systems with for instance application to the study of pilot induced oscillations (PIO) when the rate limitation of an elevator is active. Numerical flight simulations are also used to display the non linear nature of flight dynamics, mainly when considering energy aspects. 4.2 Curriculum at MSc level in Control Theory Third semester: -State representation of linear MIMO systems, where modal analysis (eigen values and eigen vectors of the state matrix) provides a systematic way to identify the aircraft natural dynamic modes (phugoƒd, short oscillation, Dutch roll, roll and spiral mode) as well as the main couplings between modes and flight variables. A valuable side product of the classical controllability study of aircraft lateral motion is a justification of the choice of the yaw axis to install a mechanical back up for lateral control. In annex 1 the text of a possible directed study is presented. - Linear control theory (state feedback control with model following control and mainly modal control, Luenberger state estimator) with application to the design of flight augmentation and basic flight control functions. It is shown that in general, the direct application of state feedback control to the design of control laws for guidance are not acceptable (aircraft structure, flight safety, passenger comfort) and that basic modes sequencing must be used to perform acceptable guidance maneuvers. This is where pilot’s flight deck organization can be discussed. - Optimal control with application to flight plan optimization issues: analysis of optimality conditions and comparison with actual airline practice (in flight
cost index tuning) for vertical profile optimization, minimum time solutions for lateral flight plan optimization. Practical work with an FMS emulator is also performed where realistic flight control conditions are reproduced for a full flight. Fourth semester: - Stochastic processes with for instance application to the modeling of processes such as atmospheric turbulence and error propagation in inertial reference systems. - Kalman filtering with flight control, fault detection and hybridization of navigation sensors applications. (see annex 2). Here the accent is given to the understanding of the way Kalman filtering works so that the students are able to develop news applications with possibly extended Kalman filters. - A specific teaching about Airborne Flight Control Systems is performed where the emphasis is given to the different functions which are performed , their integration and the distribution of flight control authority between the auto flight systems and the pilot. A simulation software, ICARE, developed at ENAC with full flight mechanics and with a reconfigurable set of built-in auto flight functions, is used to illustrate this teaching. Fifth semester: - Advanced control topics are considered to conclude the Control Theory Education. They are divided into model based (Non Linear Inverse control, Flatness) and non model based (fuzzy control and neural control) topics. - A sequence of conferences about airborne flight control systems are performed by engineers from the aeronautical industry (Airbus, Thales, Dassault, Smith, etc). Auto flight systems and interfaces are mainly described and development and evaluation methods and tools are displayed and discussed. Sixth semester: This semester is devoted to the realization of a final personal project. This project is performed within industry and depending of the subject, the acquired Control Theory knowledge can be applied in a real industrial environment. 4.3 Towards PhD in Control Theory and Aeronautics ENAC has been associated in Toulouse to the “Systems” doctoral school and more recently to the new multidisciplinary doctoral school in “Aeronautics and Aerospace”. So during the fifth semester, selected students can complete the Control Theory education with lectures provided by the Systems doctoral school. Then, during the sixth semester, these students perform a study which has been agreed both by ENAC as a final personal project and by the Systems doctoral school as an initial research project. These studies can be performed either in a research laboratory such as LAAS/CNRS, CERT/ONERA or LARA/ENAC in Toulouse, in other French or European research laboratories or even in industry. Then, if successful, the students are able to apply to a three years PhD research project. Subjects such as flight plan optimization, 3D and 4D trajectory tracking, trajectory generation, aircraft ground guidance, auto land control law design and
relative guidance, have been tackled at the PhD level with advanced control concepts. 5. CONTROL THEORY EDUCATION AND RESEARCH ACTIVITIES Research activities in the field of Control Theory and applications to Flight Control have started at ENAC in the early nineties (Mora-Camino, et a.l, 1993; MoraCamino, et al., 1995) and been pursued (Hagelauer , et al., 1997; Miquel, et al., 2003; Lu, et al., 2005) with a strong collaboration of a large research laboratory, LAAS/CNRS, located in the immediate vicinity. More recently, research activities have been structured at ENAC and the LARA has been created to perform studies and research activities in the field of Control Theory and applications in air transportation. Research activities have been chosen taking into account at the same time the new research fields considered by the control community (robust control, fault detection and identification, fault tolerant control, fuzzy and neural control, non linear inverse control and differentially flat systems, etc) and new needs in the field of air transportation automation (flight control law scheduling, normal load factor control, flight plan optimization, ground guidance, automatic separation, formation flight, relative guidance, etc). The active participation to specialized conferences such as IFAC Aerospace Conference, Guidance Navigation and Control-GNC from AIAA and to Digital Avionics Systems Conference-DASC from IEEE, have been a large source of inspiration and of bibliography for students and researchers. Students at ENAC can be, as early as during their fourth semester, with small personal projects, be associated to research activities performed by the LARA laboratory. They can pursue this research activity during the fifth semester and during the personal final project. Examples of topics considered have been: non linear control techniques applied to the steering of the front wheel of a grounded aircraft, neural inversion of flight guidance dynamics for trajectory tracking, design of virtual airborne sensors for fault tolerant data acquisition, aircraft attitude estimation from GPS data, etc. In different cases, this activity has been completed by a PhD research within the aeronautical industry. This has been the opportunity to strengthen the ties between ENAC and industry and to better understand the real needs in Control Theory education directed to this field of industrial activity. 6. CONCLUSION AND PERSPECTIVES Aircraft flight dynamics appears as a wide field of application for the most various approaches developed by Control Theory to design efficient and safe control systems. Then, the teaching of Control Theory in a civil aviation engineering school is a very challenging activity with constantly renewed problems as new auto flight control functions are needed to face the continuously changing reality of air transportation. Often, advanced concepts from Control Theory are necessary to solve these problems and it is naturally
that these topics should find their place in the curriculum of a civil aviation engineering school. A good start for that appears to be through early association of students to research activities while tight connections with industry remain essential to catch better its present and future needs.
REFERENCES
Nelson, R.C. (1989).Smith, S.E. (1991). Flight Stability and Automatic Control, McGraw-Hill, New York. McLean, D. (1990), Automatic Flight Control Systems, Prentice Hall International, Cambridge. Blakelock, J.H. (1991), Automatic Control of Aircraft and Missiles, John Wiley & Sons, New York. Pratt, R.W., editor (2000), Flight Control Systems, Progress in Astronautics and Aeronautics, Volume 184, Paul Zarchan Editor-in-Chief , copublished by AIAA and IEEE, Cambridge. SIMULINK, Simulink User’s Guide (1994), The MathWorks,Inc. Mora-Camino, F. and Achaibou, K. (1993), Design of guaranteed performance controllers for systems with varying parameters, AIAA Journal of Guidance ,Control and Dynamics, Vol.16, n…6, nov.1993. Mora-Camino, F. and Achaibou, K. (1995), From flight qualities to flight control law design, 2nd International Conference on Simulation in Engineering Education, SCS, Las Vegas, USA, January. Hagelauer, P. and Mora-Camino, F. (1997), Evaluation of practical solutions for on-board aircraft 4D guidance, Journal of Guidance, Control and Dynamics, Vol.20, n…5, September. Miquel,T., Mora-Camino, F., Loscos J.M., and Achaibou,K. (2003), Design of a supervised flight control system for aircraft relative Guidance, 22nd Digital Avionics Systems Conference (DASC), Indianapolis. Lu, W.C., Mora-Camino, F. and Achaibou, K., (2005), New approaches for flight guidance based on neural networks, SICPRO, Moscow, 25-28 January 2005, 987-997,11p. 7. ANNEX 1: CONTROL LAW DESIGN FOR AIRCRAFT LATERAL DYNAMICS The lateral motion of a wide body aircraft (mass of 130 t, centering :18%) in cruise condition at FL310 with a Mach number of 0.8 (TAS=241.23 m/s), is given by the linearized state space model: dx/dt = A x + B u
(1)
with x = (,p,r,)' and u = (p ,r)' 0.13
A = 6.77 2.35 0
0.01 0.99 0.041 1.38 0.412 0 , 0.026 0.32 0 1 0.01 0
B=
0 0.82 0.06 0
(2) 0.030 0.940 1.51 0
(3)
7.1 Design of an augmentation system for lateral dynamic modes : Identify and analyze the natural modes of this aircraft for these flight conditions. Can the system be stabilized using feedback state control laws applied to the rudder ? If affirmative, find a control law such that the closed loop lateral mode eigen values become -1 j and -2 j. Explain the choice of these values. Do the same with the ailerons deflection as input and compare solutions. What can be the practical applications of this result? Find the state feedback control gain G for a law applied simultaneously to the ailerons and the rudder which produces the same result. Compare the solution obtained with the previous ones. Simulate the response of the system with and without this control law when initial conditions are x0 = (/180, 0, 0 , 0)’. 7.2 Design of a bank angle control law. Here, the objective is to control the bank angle while maintaining near zero the side slip angle . The feedback control law designed before is supposed to be active. Find the direct gain H such that there is no position error for the bank angle. What is the resulting response time? When the reference value of the bank angle is such that c = 0.1 rad, identify the flight situation obtained in permanent regime. Starting from a straight level equilibrium state, study the evolutions of the bank and side slip angles when c = 0.1 radians. 7.3 Design of heading control law Here, the objective is to control the heading angle while maintaining near zero the side slip angle . Complete the lateral dynamics state representation. Complete the lateral stabilizer law such that a new stable mode, associated to an eigen value of -0.5, is added to the others. Find the direct gain F which provides perfect position accuracy. Starting from a straight level equilibrium state at =0, study the evolutions of heading, bank and side slip angles when c = /4. Is this acceptable? Then, justify the operational practice adopted for air transport systems to perform heading acquisition and maintain maneuvers. 7.4 Design of decoupling law for manual lateral control To ease the manual control of lateral dynamics , a decoupling control law between roll rate (input : control wheel) and sideslip angle (input : pedals) is considered . Try to find a solution from multidimensional modal control techniques, then try to find a solution from linear inverse control techniques. Compare the two approaches. 8. ANNEX 2: HYBRIDIZATION FOR NAVIGATION BY KALMAN FILTERING
The inertial navigation system (INS) is for an aircraft an autonomous mean to obtain position, speed and attitude information. In this study we consider a simplified position computation channel composed of an accelerometer and two integrators, with: (4) x i ai a w where a is the true acceleration, ai is the inertial acceleration, vi is the inertial speed and xi is the inertial position. The accelerometer noise w is supposed to be a centered Gaussian white noise of covariance W =2 10-4 (m/s2 )2 . 8.1 Absolute position estimation The initial position and speed are supposed exactly known, study the evolution of the errors in the inertial speed and position channel. Write: x = xi -x and v= vi –v (5) Matlab simulations will be performed for periods of time of one and three hours. The GPS provides another estimation of the position of the aircraft. A simplified mono dimensional functional view of this system can be such as: (6) x gps x v where the measurement error is supposed to be a centered Gaussian white noise of covariance V = 104 m2 . Find the expression of the position observation equation. Find the expression of the Kalman filter which allows the estimation of the position error. The Kalman filter will be supposed to be placed in cascade with the measurement devices (INS and GPS). Starting from a perfectly known position, simulate the evolution of the estimation error x* resulting from the use of the Kalman filter.. Find the following transfer functions: x*(p)/x(p), x*(p)/(p) et x*(p)/w(p), where x*(t) = xi(t) - x*(t) and p is the Laplace variable. Draw and analyze the corresponding Bode locus . Now, the computation channel is supposed to include the Kalman filter estimates of the aircraft speed and position errors. Propose a graphical view of the system and find the new expression of the estimates of speed and position. Find the expression of the transfer function linking x to x*. What are the advantages of this solution over the former? 8.2 Speed estimation A Doppler radar is used to measure the inertial speed of the aircraft. A simplified expression of the error model is: (7) V dr V z where V is the true ground speed, Vdr is the Doppler radar speed, z is supposed to be a stationary noise with a zero mean and a covariance given by: Ez22 exp(-) with = 0.01 m h-1 et = 0.1 h-1 .
(8)
Show that z can be obtained from a centered gaussian white noise of covariance 2 2 which is applied to a generator filter of transfer function: F(p) = 1/(p+) (9) Propose an architecture for the speed estimator based on the use of a Kalman filter. Find the expression of the corresponding Kalman filter and evaluate its performances through a simulation study. 8.3 Relative position estimation The TCAS is a device which generates alert and advisory messages to the pilot when "intruders" fly into the neighborhood of the reference aircraft. The detection channel of the TCAS provides then information about the position of other aircraft within range. Data links to perform the direct exchange this kind of information between aircraft are today under development. Now we consider the situation in which two aircraft fly within the same area (the separation rules are supposed to be respected at least initially). Aircraft number 1 and aircraft number 2 are equipped with INS and GPS and exchange data through a numerical communication system. We want to design a device to estimate at best the relative position of aircraft number 2 with respect to aircraft number 1 by making use of all available information (measurement data and statistical data about noises).Two cases are considered: In the first case aircraft number 2 sends to aircraft number 1 its already hybridized inertial-GPS position and speed (see part 8.1). In the second case, aircraft number 2 sends separately to aircraft number 1 its inertial situation (position and speed) and its GPS position. In this case it is considered that the error in the difference between the two raw GPS positions is a centered white noise of covariance DV= 400 m2. Answer, for these two cases, to the following questions: -Find the expression of the Kalman filter which allows a best estimation of the error of the relative position. -Starting from a known situation, simulate the evolution of x* , the Kalman filter estimation error for the relative position. Starting from a situation characterized by inertial position and speed errors for each aircraft, simulate the evolution of x* , the Kalman filter estimation error for the relative position. Finally, compare the performances of the solutions obtained through these two designs.
CONTROL THEORY AND FLIGHT CONTROL EDUCATION AT A CIVIL AVIATION ENGINEERING SCHOOL
F€lix Mora-Camino* and Karim Acha•bou#
*Ecole Nationale de l’Aviation Civile - ENAC, Laboratoire d’Automatique et Recherche Op•rationnelle - LARA 7 Av. Edouard Belin, 31055 Toulouse, France, [email protected] #
Institut National Polytechnique de Toulouse et LARA/ENAC, [email protected]
Abstract: In this communication, the teaching of Control Theory in a civil aviation engineering school, ENAC, is considered. After describing the evolution of flight control systems along the last decades and pointing out the new challenges faced in this area, teaching objectives with respect to Control Theory are discussed. The constraints involved with this multidisciplinary area are analyzed and the current teaching practice is described and assessed. Copyright € 2006 IFAC
Keywords: aerospace, flight control, control theory, control education, teaching.
1. INTRODUCTION
Control theory has played a central role in the development of modern air transport aircraft, starting from the development of autopilots and auto land systems in the late fifties and early sixties to automatic separation and avoidance systems at the beginning of the new century. Control Theory has become an unavoidable discipline in the curriculum of aeronautical engineering schools. ENAC, the French civil aviation institute, which provides professional training for many activities related with Civil Aviation (air traffic control, airport operations and management, airline management, etc) houses also an engineering school which belongs to the French “grandes •coles” group. Many difficulties arise at the time of defining the contents of the teaching in Control Theory as well as its relative position within its curriculum. Some of them are listed here:
-Aeronautical schools are involved with a specific field of application not with Control Theory per se. -Atmospheric flight dynamics present many complicating factors which are often tackled in practical ways by other aeronautical disciplines. -Human factors involving pilots and passengers take an important place in flight operations. -What should be the connections with purely aeronautics disciplines?
-How to attract the interest of student for such a theoretical discipline while operations and practice are emphasized by many other disciplines ? In this paper first the evolution during the last fifty years of flight control systems for air transportation aircraft is analyzed briefly, then the challenge of teaching Control Theory in an aeronautical engineering school is considered. Actual solutions and practices are displayed and discussed. Finally, two illustrations of the way Control Theory concepts are connected with flight control applications, are displayed in annex.
2. EVOLUTION OF AIRCRAFT FLIGHT AUTOMATION
2.1 First steps towards safety and efficiency In the late fifties, with the development of jet aircraft presenting higher speed and range, safety issues have led to the development of autopilots whose functions where devoted to the enhancement of natural stability (mainly along the yaw axis) , to basic auto modes (control of pitch and bank attitude angle) and to superior modes with the objective of tracking guidance parameters such as heading angle, speed and flight level parameters. At that time only analogue computers were available while control theory was mainly concerned with SISO feedback control. However, through different treatments such as
decoupling of longitudinal and lateral dynamics around an equilibrium situation and frequency decoupling of the fast dynamics (rotating dynamics) from the slow dynamics (translational dynamics), it was possible to design quite efficient control laws with a rather high degree of robustness since with gain scheduling schemes around few reference points, it was possible to cover the whole flight envelope. One of the main success of this generation of flight control systems was the realization of auto land systems which helped to improve notably the regularity of flights and the safety level of the sector. Using high levels of redundancy (up to four parallel auto land systems in some aircraft), reliability levels (probability of a catastrophic event less than 10-9 per flight hour, a probability of less than 10-7 for a catastrophic landing) were met. It is useful to observe that in the case of “auto” land, the aircraft needed the help of external signals (ILS) to achieve the maneuver. At that time, most aeronautical engineering schools had access to flying laboratories to make demonstration of the flight dynamics characteristics, either natural or acquired through automation. What remain from this today? When digital computers were introduced to achieve flight control functions, for economics reasons and also airworthiness requirements, the first practice was to merely digitalize the previous control laws, while already the main results of modern control theory were already available. So, some aging aircraft equipped with this generation of flight control systems are still in operation. However, SISO feedback control theory remains of actuality since many control channels, even when fly by wire technology is used, are still designed using the formalism of transfer functions and servo control.
2.2 Modern control theory and flight control In the seventies, with the adoption of state space representations of longitudinal and lateral flight dynamics, modal control and state estimation techniques allowed the design of more efficient multidimensional control structures insuring stability, accuracy and reliability. At that time appeared a number of valuable textbooks (Nelson, 1989), (McLean, 1990) and (Blakelock, 1991). Also, issues related with structural modes of larger and more flexible aircraft where better tackled with the state space formalism.
Later, with the development of robust control theory, many studies have been performed to get robust flight control laws, however with little success in the case of air transportation aircraft. Note that the same happened with adaptive control techniques. More recently, publication series promoted by AIAA have allowed a continuous updating of applied knowledge in this area (for instance Pratt, 2000). It was the time when many Kalman filter applications have been developed not only to design new airborne control functions, such as anti turbulence systems, but also to improve navigation systems performances with the introduction of hybridization between the current available data channels (for instance: baro-inertial
hybridization to get better current flight level estimates, Doppler-inertial hybridization to get better estimates of current ground speed). With the increasing price of fuel and the fierce competition between airlines, they asked for more efficiency with respect to flight costs and optimal control techniques were used to tackle the flight plan optimization problem: while Hamiltonian related optimality conditions helped to characterize in practical terms optimal flight conditions, techniques such as dynamic programming were used to compute effectively optimal flight plans. This function was the pivot of the new Flight Management Systems introduced in the mid eighties and which have become mandatory today not only for wide body aircraft but also for regional aircraft. With the increasing performances of on board computers, new functions such as navigation and monitoring where integrated in Flight Management Systems. 2.3 Increased air traffic and new challenges With the sustained growth of air transportation new control problems related with traffic saturation either at airports or in airways have been considered. At the level of airports with longer and larger taxiing networks, improved taxiing guidance capabilities are required to ensure ground traffic safety and efficiency. This leads to the consideration of complex non linear control and supervision problems for ground guidance involving engine, brakes and wheel orientation.
Air Traffic Control has remained until recently human-based for decisions taken mainly from the ground with no aircraft autonomy for reactivity to traffic conditions. New on board concepts such as Communication, Navigation and Surveillance (CNS) systems are now introduced to improve the efficiency of Air Traffic Management systems. This implies more autonomy for the aircraft to predict and solve air traffic conflicts and to maintain safe separations with other surrounding traffic. Also, the organization of traffic flows supposes the implementation of new flight control modes such as merge modes, 4D trajectory tracking and relative guidance modes. It appears that these functions should lead to the consideration of advanced control issues such as hybrid control and multi agent control systems which are still in they early development. 3. AIRCRAFT CENTRED CONTROL THEORY EDUCATION 3.1 Control Theory versus Flight Control In many aeronautical engineering schools, control theory takes a large place in the curricula, however this teaching has in general very little connections with the pure aeronautical disciplines such as aerodynamics, flight mechanics and flight qualities, propulsion, navigation, human factors (pilot related) , airworthiness and safety requirements and finally, air traffic and airlines economics. This cannot be the case at ENAC, since his graduated students are not generalists, but are specialized engineers in air transportation issues with particular emphasis in
aircraft operations, traffic operations and civil aviation support systems.
from one year to the next by different students until completion.
From section 2, it appears that not every topics in Control Theory are today useful for air transportation applications. Some of them, such as on line identification and adaptive control techniques are very questionable from the certification point of view and airworthiness regulations and practice. Once, when Control Theory was taught at ENAC by external teachers having an Electrical Engineering background, to few adaptations to its particular needs were performed and a common and depressing reflection among students was ”encore des maths!”(“more math!”). This was characteristic of the wrong perception of the control disciplines by students coming from the French preparatory school systems where Algebra and Analysis where overwhelming disciplines. On the other side, teaching about airborne flight automation systems had at that time a pure descriptive and practical nature and was performed by instructors having a very basic background in Control Theory. It was up to the students to eventually connect the control theory with airborne applications. So, aeronautical firms (aircraft manufacturers, airborne systems firms,...) were hiring in one side generalists from other schools with good knowledge in Control Theory and on the other side aeronautical engineers with a practical and descriptive knowledge about airborne flight control systems and environment with communication difficulties between them in many situations. 3.2 Enforcing Control Theory teaching In general the students at ENAC are enthusiastic with aircraft issues and an efficient way to make them get interest in Control Theory has been to integrate in many ways this teaching with other aeronautical disciplines. For that, different steps and actions have been taken: -Today at ENAC, all Control Theory teachers have some aeronautical background. -Every taught topic in Control Theory is systematically illustrated by several applications in the aeronautical field. - Connections between Control Theory notions and aeronautical issues (for instance between “asymptotic stability” and “dynamic stability”, “controllability” and “handling qualities”) are always emphasized. -The usefulness in the aeronautical field of special Algebra or analytic developments performed in the context of Control Theory can be easily evidenced by pointing out direct applications. -Numerical flight simulators for different aircraft and with growing complexity are used to support directed studies in the field of Control Theory. -Matlab/Simulink which has been a standard at ENAC for many years displays a lot of aeronautical case studies (Simulink, 1994) which are motivating and ready to . -Small personal projects with multidisciplinary characteristics, including Control Theory issues, are proposed to the students by the end of the fourth and the fifth semesters. These projects can be continued
4. AIRCRAFT CENTRED CONTROL THEORY EDUCATION The curriculum at ENAC being organized in a semester basis, to each semester a goal has been assigned with respect to Control Theory and aeronautical applications. The first two semesters close the three years training at BSc level as defined by the Bologna declaration, while the four following semesters correspond to the MSc training level. 4.1 Curriculum at BSc level in Control Theory First semester: Transfer function modeling and feedback control of SISO linear systems is introduced. Since many students have a previous knowledge in this area, taught in general in a very theoretical way, a large importance is given to the systems engineering approach of real physical systems through mathematical modeling. Different applications are considered in the field of sensors and actuators modeling: for instance, study of the performances of a vario-meter with a complementary filter structure, modeling and PID control of an electro hydraulic servo actuator for an aileron of a wide body aircraft. Second semester: Modeling and feedback control of SISO non linear systems with for instance application to the study of pilot induced oscillations (PIO) when the rate limitation of an elevator is active. Numerical flight simulations are also used to display the non linear nature of flight dynamics, mainly when considering energy aspects. 4.2 Curriculum at MSc level in Control Theory Third semester: -State representation of linear MIMO systems, where modal analysis (eigen values and eigen vectors of the state matrix) provides a systematic way to identify the aircraft natural dynamic modes (phugoƒd, short oscillation, Dutch roll, roll and spiral mode) as well as the main couplings between modes and flight variables. A valuable side product of the classical controllability study of aircraft lateral motion is a justification of the choice of the yaw axis to install a mechanical back up for lateral control. In annex 1 the text of a possible directed study is presented. - Linear control theory (state feedback control with model following control and mainly modal control, Luenberger state estimator) with application to the design of flight augmentation and basic flight control functions. It is shown that in general, the direct application of state feedback control to the design of control laws for guidance are not acceptable (aircraft structure, flight safety, passenger comfort) and that basic modes sequencing must be used to perform acceptable guidance maneuvers. This is where pilot’s flight deck organization can be discussed. - Optimal control with application to flight plan optimization issues: analysis of optimality conditions and comparison with actual airline practice (in flight
cost index tuning) for vertical profile optimization, minimum time solutions for lateral flight plan optimization. Practical work with an FMS emulator is also performed where realistic flight control conditions are reproduced for a full flight. Fourth semester: - Stochastic processes with for instance application to the modeling of processes such as atmospheric turbulence and error propagation in inertial reference systems. - Kalman filtering with flight control, fault detection and hybridization of navigation sensors applications. (see annex 2). Here the accent is given to the understanding of the way Kalman filtering works so that the students are able to develop news applications with possibly extended Kalman filters. - A specific teaching about Airborne Flight Control Systems is performed where the emphasis is given to the different functions which are performed , their integration and the distribution of flight control authority between the auto flight systems and the pilot. A simulation software, ICARE, developed at ENAC with full flight mechanics and with a reconfigurable set of built-in auto flight functions, is used to illustrate this teaching. Fifth semester: - Advanced control topics are considered to conclude the Control Theory Education. They are divided into model based (Non Linear Inverse control, Flatness) and non model based (fuzzy control and neural control) topics. - A sequence of conferences about airborne flight control systems are performed by engineers from the aeronautical industry (Airbus, Thales, Dassault, Smith, etc). Auto flight systems and interfaces are mainly described and development and evaluation methods and tools are displayed and discussed. Sixth semester: This semester is devoted to the realization of a final personal project. This project is performed within industry and depending of the subject, the acquired Control Theory knowledge can be applied in a real industrial environment. 4.3 Towards PhD in Control Theory and Aeronautics ENAC has been associated in Toulouse to the “Systems” doctoral school and more recently to the new multidisciplinary doctoral school in “Aeronautics and Aerospace”. So during the fifth semester, selected students can complete the Control Theory education with lectures provided by the Systems doctoral school. Then, during the sixth semester, these students perform a study which has been agreed both by ENAC as a final personal project and by the Systems doctoral school as an initial research project. These studies can be performed either in a research laboratory such as LAAS/CNRS, CERT/ONERA or LARA/ENAC in Toulouse, in other French or European research laboratories or even in industry. Then, if successful, the students are able to apply to a three years PhD research project. Subjects such as flight plan optimization, 3D and 4D trajectory tracking, trajectory generation, aircraft ground guidance, auto land control law design and
relative guidance, have been tackled at the PhD level with advanced control concepts. 5. CONTROL THEORY EDUCATION AND RESEARCH ACTIVITIES Research activities in the field of Control Theory and applications to Flight Control have started at ENAC in the early nineties (Mora-Camino, et a.l, 1993; MoraCamino, et al., 1995) and been pursued (Hagelauer , et al., 1997; Miquel, et al., 2003; Lu, et al., 2005) with a strong collaboration of a large research laboratory, LAAS/CNRS, located in the immediate vicinity. More recently, research activities have been structured at ENAC and the LARA has been created to perform studies and research activities in the field of Control Theory and applications in air transportation. Research activities have been chosen taking into account at the same time the new research fields considered by the control community (robust control, fault detection and identification, fault tolerant control, fuzzy and neural control, non linear inverse control and differentially flat systems, etc) and new needs in the field of air transportation automation (flight control law scheduling, normal load factor control, flight plan optimization, ground guidance, automatic separation, formation flight, relative guidance, etc). The active participation to specialized conferences such as IFAC Aerospace Conference, Guidance Navigation and Control-GNC from AIAA and to Digital Avionics Systems Conference-DASC from IEEE, have been a large source of inspiration and of bibliography for students and researchers. Students at ENAC can be, as early as during their fourth semester, with small personal projects, be associated to research activities performed by the LARA laboratory. They can pursue this research activity during the fifth semester and during the personal final project. Examples of topics considered have been: non linear control techniques applied to the steering of the front wheel of a grounded aircraft, neural inversion of flight guidance dynamics for trajectory tracking, design of virtual airborne sensors for fault tolerant data acquisition, aircraft attitude estimation from GPS data, etc. In different cases, this activity has been completed by a PhD research within the aeronautical industry. This has been the opportunity to strengthen the ties between ENAC and industry and to better understand the real needs in Control Theory education directed to this field of industrial activity. 6. CONCLUSION AND PERSPECTIVES Aircraft flight dynamics appears as a wide field of application for the most various approaches developed by Control Theory to design efficient and safe control systems. Then, the teaching of Control Theory in a civil aviation engineering school is a very challenging activity with constantly renewed problems as new auto flight control functions are needed to face the continuously changing reality of air transportation. Often, advanced concepts from Control Theory are necessary to solve these problems and it is naturally
that these topics should find their place in the curriculum of a civil aviation engineering school. A good start for that appears to be through early association of students to research activities while tight connections with industry remain essential to catch better its present and future needs.
REFERENCES
Nelson, R.C. (1989).Smith, S.E. (1991). Flight Stability and Automatic Control, McGraw-Hill, New York. McLean, D. (1990), Automatic Flight Control Systems, Prentice Hall International, Cambridge. Blakelock, J.H. (1991), Automatic Control of Aircraft and Missiles, John Wiley & Sons, New York. Pratt, R.W., editor (2000), Flight Control Systems, Progress in Astronautics and Aeronautics, Volume 184, Paul Zarchan Editor-in-Chief , copublished by AIAA and IEEE, Cambridge. SIMULINK, Simulink User’s Guide (1994), The MathWorks,Inc. Mora-Camino, F. and Achaibou, K. (1993), Design of guaranteed performance controllers for systems with varying parameters, AIAA Journal of Guidance ,Control and Dynamics, Vol.16, n…6, nov.1993. Mora-Camino, F. and Achaibou, K. (1995), From flight qualities to flight control law design, 2nd International Conference on Simulation in Engineering Education, SCS, Las Vegas, USA, January. Hagelauer, P. and Mora-Camino, F. (1997), Evaluation of practical solutions for on-board aircraft 4D guidance, Journal of Guidance, Control and Dynamics, Vol.20, n…5, September. Miquel,T., Mora-Camino, F., Loscos J.M., and Achaibou,K. (2003), Design of a supervised flight control system for aircraft relative Guidance, 22nd Digital Avionics Systems Conference (DASC), Indianapolis. Lu, W.C., Mora-Camino, F. and Achaibou, K., (2005), New approaches for flight guidance based on neural networks, SICPRO, Moscow, 25-28 January 2005, 987-997,11p. 7. ANNEX 1: CONTROL LAW DESIGN FOR AIRCRAFT LATERAL DYNAMICS The lateral motion of a wide body aircraft (mass of 130 t, centering :18%) in cruise condition at FL310 with a Mach number of 0.8 (TAS=241.23 m/s), is given by the linearized state space model: dx/dt = A x + B u
(1)
with x = (,p,r,)' and u = (p ,r)' 0.13
A = 6.77 2.35 0
0.01 0.99 0.041 1.38 0.412 0 , 0.026 0.32 0 1 0.01 0
B=
0 0.82 0.06 0
(2) 0.030 0.940 1.51 0
(3)
7.1 Design of an augmentation system for lateral dynamic modes : Identify and analyze the natural modes of this aircraft for these flight conditions. Can the system be stabilized using feedback state control laws applied to the rudder ? If affirmative, find a control law such that the closed loop lateral mode eigen values become -1 j and -2 j. Explain the choice of these values. Do the same with the ailerons deflection as input and compare solutions. What can be the practical applications of this result? Find the state feedback control gain G for a law applied simultaneously to the ailerons and the rudder which produces the same result. Compare the solution obtained with the previous ones. Simulate the response of the system with and without this control law when initial conditions are x0 = (/180, 0, 0 , 0)’. 7.2 Design of a bank angle control law. Here, the objective is to control the bank angle while maintaining near zero the side slip angle . The feedback control law designed before is supposed to be active. Find the direct gain H such that there is no position error for the bank angle. What is the resulting response time? When the reference value of the bank angle is such that c = 0.1 rad, identify the flight situation obtained in permanent regime. Starting from a straight level equilibrium state, study the evolutions of the bank and side slip angles when c = 0.1 radians. 7.3 Design of heading control law Here, the objective is to control the heading angle while maintaining near zero the side slip angle . Complete the lateral dynamics state representation. Complete the lateral stabilizer law such that a new stable mode, associated to an eigen value of -0.5, is added to the others. Find the direct gain F which provides perfect position accuracy. Starting from a straight level equilibrium state at =0, study the evolutions of heading, bank and side slip angles when c = /4. Is this acceptable? Then, justify the operational practice adopted for air transport systems to perform heading acquisition and maintain maneuvers. 7.4 Design of decoupling law for manual lateral control To ease the manual control of lateral dynamics , a decoupling control law between roll rate (input : control wheel) and sideslip angle (input : pedals) is considered . Try to find a solution from multidimensional modal control techniques, then try to find a solution from linear inverse control techniques. Compare the two approaches. 8. ANNEX 2: HYBRIDIZATION FOR NAVIGATION BY KALMAN FILTERING
The inertial navigation system (INS) is for an aircraft an autonomous mean to obtain position, speed and attitude information. In this study we consider a simplified position computation channel composed of an accelerometer and two integrators, with: (4) x i ai a w where a is the true acceleration, ai is the inertial acceleration, vi is the inertial speed and xi is the inertial position. The accelerometer noise w is supposed to be a centered Gaussian white noise of covariance W =2 10-4 (m/s2 )2 . 8.1 Absolute position estimation The initial position and speed are supposed exactly known, study the evolution of the errors in the inertial speed and position channel. Write: x = xi -x and v= vi –v (5) Matlab simulations will be performed for periods of time of one and three hours. The GPS provides another estimation of the position of the aircraft. A simplified mono dimensional functional view of this system can be such as: (6) x gps x v where the measurement error is supposed to be a centered Gaussian white noise of covariance V = 104 m2 . Find the expression of the position observation equation. Find the expression of the Kalman filter which allows the estimation of the position error. The Kalman filter will be supposed to be placed in cascade with the measurement devices (INS and GPS). Starting from a perfectly known position, simulate the evolution of the estimation error x* resulting from the use of the Kalman filter.. Find the following transfer functions: x*(p)/x(p), x*(p)/(p) et x*(p)/w(p), where x*(t) = xi(t) - x*(t) and p is the Laplace variable. Draw and analyze the corresponding Bode locus . Now, the computation channel is supposed to include the Kalman filter estimates of the aircraft speed and position errors. Propose a graphical view of the system and find the new expression of the estimates of speed and position. Find the expression of the transfer function linking x to x*. What are the advantages of this solution over the former? 8.2 Speed estimation A Doppler radar is used to measure the inertial speed of the aircraft. A simplified expression of the error model is: (7) V dr V z where V is the true ground speed, Vdr is the Doppler radar speed, z is supposed to be a stationary noise with a zero mean and a covariance given by: Ez22 exp(-) with = 0.01 m h-1 et = 0.1 h-1 .
(8)
Show that z can be obtained from a centered gaussian white noise of covariance 2 2 which is applied to a generator filter of transfer function: F(p) = 1/(p+) (9) Propose an architecture for the speed estimator based on the use of a Kalman filter. Find the expression of the corresponding Kalman filter and evaluate its performances through a simulation study. 8.3 Relative position estimation The TCAS is a device which generates alert and advisory messages to the pilot when "intruders" fly into the neighborhood of the reference aircraft. The detection channel of the TCAS provides then information about the position of other aircraft within range. Data links to perform the direct exchange this kind of information between aircraft are today under development. Now we consider the situation in which two aircraft fly within the same area (the separation rules are supposed to be respected at least initially). Aircraft number 1 and aircraft number 2 are equipped with INS and GPS and exchange data through a numerical communication system. We want to design a device to estimate at best the relative position of aircraft number 2 with respect to aircraft number 1 by making use of all available information (measurement data and statistical data about noises).Two cases are considered: In the first case aircraft number 2 sends to aircraft number 1 its already hybridized inertial-GPS position and speed (see part 8.1). In the second case, aircraft number 2 sends separately to aircraft number 1 its inertial situation (position and speed) and its GPS position. In this case it is considered that the error in the difference between the two raw GPS positions is a centered white noise of covariance DV= 400 m2. Answer, for these two cases, to the following questions: -Find the expression of the Kalman filter which allows a best estimation of the error of the relative position. -Starting from a known situation, simulate the evolution of x* , the Kalman filter estimation error for the relative position. Starting from a situation characterized by inertial position and speed errors for each aircraft, simulate the evolution of x* , the Kalman filter estimation error for the relative position. Finally, compare the performances of the solutions obtained through these two designs.