Realtime implementation of neural network augmented fault tolerant flight controllers for an advanced fighter aircraft on a target digital signal processor.

In recent years Neural Networks (NNs) have been proposed for identification and control of linear and non-linear dynamic systems [5,6 and 7]. For NN applicability to adaptive control systems the following properties are important:

* Applicability to non-linear systems [8]

* Parallel distributed processing and hardware implementation

* Learning (either on-line or off-line)

* Applicability to multi-variable systems

The appeal of neural networks in control architecture is their potential to learn the dynamics of the process under control. However, when neural networks are used in real time control of dynamic processes such as the auto-landing problem, the training time is excessive in comparison to the time of evolution of the process under consideration. Another vital point in real time control applications is that, whatever adaptation algorithm is ultimately employed to adjust the weights in a neural network, it must ensure stability of the controlled process. It is by this process of weight alteration that the network "learns" how to control the dynamic process. Both, BTFC as well as EMRAN architectures have been successfully validated with software simulations. However, despite the promising capabilities, there are only limited ongoing efforts in the scientific community to successfully validate and demonstrate NN-based control and estimation schemes within an actual FCS by implementing the same on a suitable hardware platform. This is due to different reasons. One reason is quite simple; most of the gain scheduling-based control laws in a flight control system, designed with classic control and estimation linear theory, are well proved and have provided over the years satisfactory performance. This is the case for the majority of autopilot and stability augmentation systems for commercial aviation, which, however, are not designed to provide fault tolerance capabilities. Another reason is the lack of validation and verification tools for NN-based control and estimation schemes. Finally, an additional reason is related to implementation issues. The computational effort associated with the learning of a single or multiple parallel NNs with and high number of neurons and/or complicated activation functions could be quite substantial.

This paper presents the results of a research focused on the last issue. This research presents hardware implementation of classical and neural-aided classical controller that enhance the fault tolerant capabilities of a high performance fighter aircraft during the landing phase when subjected to severe winds and failures such as stuck control surfaces. The control scheme uses Radial Basis Function Networks (RBFN) in the feedback error learning mechanism. The dynamic RBFN employed is the EMRAN which uses only on-line learning and does not need prior training. The information about actuator failures is not available to the controller for use in reconfiguration. Particularly, this effort shows the feasibility of implementing complicated online learning NN flight controller schemes for two conceptually different control architectures on a Digital Signal Processor.

Aircraft Mathematical Model, Auto-landing Problem and Failure Scenarios

The aircraft model used in this research is that of a high performance fighter aircraft [1]. For the purposes of this study, the elevator and aileron control surface aerodynamic data has been split into two parts corresponding to left and right surfaces using CFD computations. The aerodynamic model also contains a ground effect model. The aircraft has two elevators (-25 to 25 deg deflection), which can be moved together or in differential mode. It also has a pair of ailerons (-20 to 20deg deflection) and a rudder (-30 to 30 deg deflection). The engine model (without dynamics) completes the six-degree of freedom simulation. The aircraft has hydraulic actuators, which drive the primary control surfaces that are modeled as first order lags with a time constant of 50msec. The rate limits for the actuators is set at 60deg/sec.

The auto-landing problem[2] studied in this research consists of a high performance fighter aircraft following a flight path consisting of flight segments such as a wing-level flight, a coordinated turn, glide slope descent and finally the flare maneuver and touchdown on the runway. The trajectory segments as shown in Figure 2 corresponding to these phases have to be flown in the presence of severe winds. These tend to cause deviation of the aircraft from the specified trajectory. However, we must ensure that all trajectory deviations are within specified limits. The touch down conditions is given with tight specifications, named for convenience as the touch-down pill box as depicted in Table 1. The controller is first designed to meet pill box specifications for all these phases under no failure conditions of the actuators. We then augment the controller to be able to handle the same flight segments but with the occurrence of certain failure conditions of the actuators.

An aircraft has three degrees of freedom, which are the Pitch, Roll and Yaw. The pitch of the aircraft is controlled by control surfaces called Elevators. They are present on the rear of the aircraft and are placed symmetrically on either side of the aircraft axis. Under normal flight conditions both the elevators are given identical control signals. If one of the elevators fail or gets stuck at a certain position, the other one can be used to restore the aircraft to equilibrium. Elevators are therefore responsible for longitudinal dynamics of the aircraft. The roll motion of the aircraft is controlled by surfaces known as Ailerons. The two ailerons are present on either wing and are generally operated in differential mode. In case one of the ailerons fails, the other can be used to make the aircraft stable. The yaw motion of the aircraft is controlled by the rudder which is located on the tail of the aircraft. The mechanism of rudder operation is similar to the way the rudder of a ship operates. Ailerons and Rudder therefore control the lateral dynamics of the aircraft.

In this research we have considered five types of failures as shown in Table 2 including single control surface failures as well as the failure of a combination of control surfaces. We have ignored the case of the failure scenario where both the elevators fail because this case is in general, not recoverable.

As previously stated, under normal flight conditions the two elevators are always commanded together. But when they are used differentially they can be used to produce roll moment as well. Examination of the input matrix shows that in the differential mode, the elevators are about 60% as effective as the ailerons in producing roll moment. As a result the elevators can be used to produce pitching and roll moment. This is as opposed to the ailerons that are not effective in producing any pitching moment. Hence we can consider the case where both the ailerons fail and by using elevators in differential mode we can get the aircraft back to equilibrium.

Controller Architecture

The overall scheme for the neural controller is shown in Figure 1. The landing task is autonomous, hence there is a navigation function incorporated in the block called 'Tracking Command generator".

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The output of this block consists of reference commands (labeled as 'r' in the Figure), which are input to the Baseline Trajectory Following Controller (BTFC) called "Classical Feedback Controller" in the figure. Under normal conditions, the BTFC is designed to cause the aircraft outputs 'y' to follow the reference vector 'r'. The neural controller (EMRAN) uses the reference signals and the aircraft outputs to generate its command signal. It also uses the output of the BTFC to learn the inverse dynamics of the plant (in this case the aircraft) as in the feedback error learning scheme [9].

Review of BTFC

The BTFC designed using the classical loop shaping SISO design technique is first considered for hardware implementation. As reported in [3] it is assumed that the angle of attack and sideslip is not used for feedback. The reference command generator or tracking controller determines the offset of the aircraft from the desired ground track for each segment of the flight and computes the reference commands consisting of altitude, velocity and cross distance from the desired track and the angular error of the aircraft velocity from the desired track vector. The segments of trajectory are either straight lines or arcs of circles. Thus, the cross distance is simply the length of the perpendicular in case of the line segments. In case of the circular arc, this quantity is the difference between the distance to the center of the circular arc and the radius of the turn. Similarly, the angular error can be calculated using the components of the aircraft velocity in the X-Y plane and the direction of the desired trajectory nearest to the aircraft. Once these quantities are known, the velocity and altitude references are obtained by linear interpolation between the end point values at the ends of each segment.

Review of EMRAN

There are regimes during which the aircraft has to fly at high angle of attack. The control laws for such maneuvers are very non-linear. This non-linearity arises due to non-linear aerodynamics and the non-inertial couplings in this flight regime. These control laws are based on inverting the dynamic and the kinematics equations of motion. During this inversion process, the state variables are measured and then these are used to model the forces and moments corresponding to the undesired aerodynamic, gravitational or the inertial contributions. Here we deal with Nonlinear Dynamic Inversion (NDI) controllers for fault tolerance to control surface faults [2]. The non-linear inverse functions appearing in the NDI controller are approximated online using Radial Basis Functions Neural Networks. The function approximation algorithm is called Extended Minimum Resource Allocation Network, which is based on RBFNN. This algorithm is based on the feedback error learning strategy proposed by Gomi and Kawato [9].

The first neural architecture considered for hardware implementation is EMRAN. It is the fast implementation of the MRAN as reported in [2]. Unlike MRAN wherein parameters of all the hidden neurons is estimated, EMRAN controller presented here uses the estimation before control strategy to improve the fault tolerance of the BTFC design. Only the parameters of the nearest neuron are updated. In all other respects the EMRAN update algorithm is similar to the MRAN.

Hardware Implementation of Neural Network Aided Flight Controllers

Matlab/Simulink models of the flight controllers discussed in Sections 3.1 and 3.2 are implemented in real time by porting these models onto a target processor using Real Time Workshop. Also Code Composer Studio (CCS) is used to assemble the code and load it onto the Target processor TMS 6713.

Simulink is a software package for modeling, simulating, and analyzing dynamic systems. It supports linear and nonlinear systems, modeled in continuous time, sampled time, or a hybrid of the two. Systems can also be multirate, i.e., have different parts that are sampled or updated at different rates.

Real-Time Workshop

Real-Time Workshop builds applications from Simulink diagrams for prototyping, testing, and deploying real-time systems on a variety of target computing platforms. Users of Real-Time Workshop can direct it to generate source code that accommodates the compilers, input and output devices, memory models, communication modes, and other characteristics that their applications may require.

Real-Time Workshop is an extension of capabilities of Simulink and MATLAB. It automatically generates packages and compiles source code from Simulink models to create real-time software applications on a variety of systems. By providing a code generation environment for rapid prototyping and deployment, Real-Time Workshop is the foundation for production code generation capabilities. Along with other tools and components Real-Time Workshop provides:

* Automatic code generation tailored for a variety of target platforms.

* A rapid and direct path from system design to implementation.

* Seamless integration with MATLAB and Simulink.

* A simple graphical user interface.

* An open architecture and extensible make process.

Embedded Target for the TI TMS320C6000 DSP Platform

Embedded Target for the TI TMS320C6000 DSP Platform integrates Simulink and MATLAB tools. The software collection lets us develop and validate digital signal processing designs from concept through code. The Embedded Target for TI C6000 DSP consists of the TI C6000 target that automates rapid prototyping on our C6000 hardware targets. The target uses C code generated by Real-Time Workshop and development tools to build an executable file for our targeted processor. The Real-Time Workshop build process loads the targeted machine code to our board and runs the executable file on the digital signal processor.

Additionally, one of the Real-Time Workshop build options builds a Code Composer Studio project from the C code generated by Real-Time Workshop. All the features provided by Code Composer Studio (CCS), such as tools for editing, building, debugging, code profiling, and project management, work to help us develop applications using MATLAB, Simulink, Real-Time Workshop, and our supported hardware. When we use this target, the build process creates a new project in Code Composer Studio and populates the project with the files the project requires.

Pre-requisite for hardware implementation

The model files are inspected thoroughly to find out if any of the blocks are of Continuous nature. If found they are to be replaced by equivalent Discrete blocks. Also the sampling time is set to a constant value 0.02s in this design. Using the Simulink Library Browser the continuous blocks are replaced by their corresponding discrete blocks retaining the initial conditions specified. The subsequent steps involved in the hardware implementation process are:

* Creating wrapper files for S-function blocks

*Creating MEX (MATLAB EXecutable file) for S-Function Wrapper

* Automatic S-Function Wrapper Generation

The build process then compiles and links model_sf.c with model.c and the other Real-Time Workshop Embedded Coder generated code modules, building a MEX-file. The MEX-file is named model_sf.mexext. (mexext is the file extension for MEX-files on our platform, as given by the MATLAB mexext command.) The MEX-file is stored in our working directory. Finally, Real-Time Workshop creates and opens an untitled model containing the generated S-Function block.

The following limitations apply to ERT S-function wrapper generation:

(i) Continuous time is not supported when generating an ERT S-function wrapper. The Support continuous time option does not apply to generation of ERT S-function wrappers.

(ii) It is not possible to create multiple instances of a Real-Time Workshop Embedded Coder generated S-Function block within a model, because the code uses static memory allocation.

[FIGURE 4a OMITTED]

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Results and Discussion

Figure 4a depicts the trajectory of the aircraft in the XY plane obtained from simulation for type I fault (Left elevator stuck at 2 degrees). The fact that the trajectory halts at (0, 0) in the XY plane indicates successful landing.

Figure 4b is the same plotted using values for X and Y co-ordinates obtained from the hardware for the same fault (Left elevator stuck at 2 degrees). It is seen that both the XY graphs are identical. Hence for this iteration of elevator failure, the results from the simulation and hardware are in agreement.

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Comparison of left elevator failure tolerance envelope-Type I Fault for BTFC/EMRAN

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Comparison of left elevator failure tolerance envelope-Type II Fault for BTFC/EMRAN

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Comparison of Left elevator failure aileron Failure tolerance envelope-Type III Fault for BTFC/EMRAN

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Comparison of Left elevator-right aileron Failure tolerance envelope-Type IV Fault for BTFC/EMRAN

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Comparison of Left aileron-right aileron Failure tolerance envelope-Type V Fault for BTFC/EMRAN

Hardware implementation results for both classical as well as neural network augmented classical controller are in total agreement with the simulation results as reported in Figures 5-9. But there are a few missing points in the map, attributed to the accuracy and precision of the DSP TMS 6713, used for the real time implementation.

Identical results were obtained for the entire gamut of fault scenarios for both the flight controllers. The same has been presented as a comparison of the fault tolerance envelopes for BTFC and EMRAN in Figures 5-9.

Acknowledgement

The authors would like to acknowledge and thank Prof. N. Sundararajan, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore for permission to use the aircraft model for this work.

References

[1] L. T. Nguyen, M. E. Ogburn, W. P. Gilbert, K. S. Kibler, P. W. Brown, P. L. Deal, Simulator Study of Stall/Post-Stall Characteristics of a Fighter Airplane with Relaxed Longitudinal Static Stability. NASA Technical Paper 1538, Dec. 1979.

[2] Y. Li, N. Sundararajan and P. Saratchandran, 'Robust Neuro-H8 Controller Design for Aircraft Auto-Landing', IEEE Transactions in Aerospace And Electronic Systems Vol. 40, No. 1, January 2004.

[3] A. A. Pashilkar, N. Sundararajan and P. Saratchandran, "A Fault-tolerant Neural Aided Controller for Aircraft Auto-landing", Journal of Aerospace Science & Technology (Elsevier), Vol. 10, Issue 1, January 2006, pp. 49-61.

[4] A. A. Pashilkar, N. Sundararajan and P. Saratchandran, "A Fault-tolerant Neural Aided Controller for Aircraft Auto-landing", Journal of Aerospace Science & Technology (Elsevier), Vol. 10, Issue 1, January 2006, pp. 49-61.

[5] A.A. Pashilkar, Nagaraj .R, et. al, Improved Fault Tolerance for Auto-landing using Adaptive Back-stepping Neural Controller, 2007 IEEE International Multi Conference on Systems and Control, Singapore.

[6] Hunt, K.J., Sbardato, D., and Gawthrop, P.J., "Neural Networks for Control Systems-A Survey", Automatica, vol 28, no 6, pp 1083, 1992

[7] Narendra, K.S., Partasarathy, K., "Identification and Control of Dynamical Systems Using Neural Networks", IEEE Transactions on Neural Networks, Vol. 1, No. 1, March 1990

[8] Cybenko, G., "Approximation by Superposition of Sigmoidal Functions", Mathematics of Control Signals and Systems, vol 2, no 4, pp. 303-309, 1989

[9] H. Gomi and M. Kawato, "Neural network control for a closed-loop system using feedback-error- learning", Neural Networks, Vol. 6, No. 7, 1993, pp. 933-946.

Dr. Nagaraj Ramrao (1), Dr. Abhay A Pashilkar (2), Dr. T.V. Rama Murthy (3)

(1) Director, Centre for Cognitive Technologies, Department of Electronics & Communication Engineering, R. V. College of Engineering, Bangalore, INDIA (2) Scientist E2, Head, Flight Simulation Division, National Aerospace Laboratory, Bangalore, India (3) Professor & HOD, Department of Tele- Communication Engineering, Dayananda Sagar College of Engineering, Bangalore, INDIA E-mail: [e-mail]