Automated Flight Test and System Identification for Rotary Wing Small Aerial Platform using Frequency Responses Analysis  Widyawardana Adiprawita* ,   Adang Suwandi Ahmad   = = = =   and Jaka Semibiring +  *School of Electric Engineering and Informatics  Institut Teknologi Bandung, Bandung, Id. e-mail: wadiprawita@stei.itb.ac.id  = = = =   School of Electric Engineering and Informatics Institut Teknologi Bandung, Bandung, Id. e-mail: asa@isrg.itb.ac.id  +   School of Electric Engineering and Informatics Institut Teknologi Bandung, Bandung, Id. e-mail: jaka@ itb.ac.id  Abstract  This paper proposes an autopilot system that can be used to control the small scale rotorcraft during the flight test for linear-frequency-domain system identification. The input frequency swept is generated automatically as part of the autopilot   control   command.   Therefore   the   bandwidth coverage   and   consistency   of   the   frequency   swept   is guaranteed   to   produce   high   quality   data   for   system identification. Beside that we can set the safety parameter during the flight test (maximum roll / pitch value, minimum altitude,   etc)   so   the   safety   of   the   whole   flight   test   is guaranteed. This autopilot for automated flight test will be tested using hardware in the loop simulator for hover flight condition.  1   Introduction  With the ability to take off and land vertically and hover, along with natural agility and controllability, rotorcraft will extend the potential roles for UAVs. Helicopters already have an irreplaceable role among aircraft, indispensable for a   variety of   tasks ranging   from medical   evacuation to transportation   to   construction   in   confined   areas.   Such rotorcraft UAVs (RUAV) are already greatly valued by the military for applications for a range of battlefield tasks, such as exploration and even combat operation. There are also numerous examples for civilian applications including filmmaking   (allowing   both   steady   and   dynamic   aerial views), close up inspection (bridges, buildings, dams) and digital terrain modeling (where a small vehicle, because of its   potential   for   closer   proximity   to   the   terrain   and structures, could gather more detailed features). Small-size   rotorcraft   tend   to   be   naturally   mode maneuverable and mode responsive than traditional full- scale rotorcraft. The maneuverability of such vehicles can offer   a   tremendous   operational   advantages   if   harnessed during autonomous flight. Taking full advantage of the small-scale helicopter's natural abilities, however, has been a major challenge to its use as a UAV platform. Simply speaking, helicopters are difficult to fly. They are unstable, requiring continuous attention from the pilot. Four primary inputs are necessary to control their motions: the longitudinal and lateral cyclic for horizontal motions in their respective directions; collective for vertical motion; and pedal for yaw (heading) motion.  1.1   Vehicle Dynamics Model  A number of available control design methods could, in theory, be applied to address the rotorcraft control issues (described later in this chapter). To be successfully applied, these methods require accurate vehicle dynamics models. The physical approach to modeling involves deriving the equations   of   motion   from   the   ground   up,   using   the fundamental laws of mechanics and aerodynamics. This approach is referred to as first-principle modeling. For a system involving numerous physical effects, the resulting equations   of   motion   are   typically   high-order   nonlinear coupled   vector   differential   equations.   A   first   principles approach   requires   considerable   knowledge   of   and experience with all the phenomena involved in rotorcraft flight. This makes the first-principles approach difficult to do. For   control   design   applications,   as   well   as   for   flying qualities studies, simpler linear models are often sufficient. Linear model have been sued extensively and successfully for rotorcraft. At a precise operating point, and even within a certain region around that point, linear models accurately capture the essential effects of the vehicle dynamics. This is advantageous,   since   numerous   analysis   and   design ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 50 © 2007 ICIUS
techniques are available for linear system. However, to cover the entire flight envelope, multiple linear models and therefore multiple controllers are necessary. An effective approach to deriving accurate linear models of a plant is linear system identification.  1.2   System Identification and CIFER  System identification uses experimental input-output data collected   from   a   plant   to   produce   a   mathematical representation of the system's dynamics. This method is attractive because it is direct, it is based on real data, and integrates   validation   and   model   refinement   into   the modeling process. In the 1980s, rotorcraft experts undertook important efforts in developing effective identification methods and tools. CIFER   (Comprehensive   Identification   from   FrEquency Responses from the US Army/NASA Rotorcraft Division, is one of today's standard tools for rotorcraft identification). Advanced high-bandwidth flight control design requires models that are accurate at higher frequencies. A very effective   and   accurate   way   to   obtain   linear   rotorcraft models   is   trough   linear-frequency-domain   system identification. In this   methods, frequency responses are estimated from the collected input-output data. Then, the parameters of a linear model capturing the key vehicle dynamics are identified by tuning them to fit the estimated frequency responses.  Figure 1:   Frequency-domain system identification procedure  However,   the   flight   test   which   is   suitable   for   linear- frequency-domain system identification is difficult to be conducted by human pilot. This especially the case with the small scale rotorcraft. The pilot controls the small scale rotorcraft using visual feedback from safe distance. The delay of response based from visual feedback make the pilot difficult to produce the needed quality of frequency input-output   data.   Beside   that   human   pilot   can   not accurately covers the whole frequency needed for the test. This paper proposes an autopilot system that can be used to control the small scale rotorcraft during the flight test for linear-frequency-domain system identification.  Figure 2:   Typical input output pair needed for frequency domain system identification 2   Methodology  The whole experimentation in this research is conducted in X-Plane   simulation.   This   approach   is   taken   based   on previous successful development of fixed wing autopilot based on X-Plane hardware in the loop simulation. So the big picture of the methodology are : 1.   Development of PID based rotary wing autopilot 2.   Development of frequency-sweep input algorithm 3.   Development of simulation system in X-Plane 4.   Processing the simulation data in CIFER 5.   Hardware design of automated flight test system 6.   Hardware in the loop (HIL) simulation 7.   Processing the HIL simulation data in CIFER 8.   Real world experimentation to get flight data 9.   Processing the real world experimentation data in CIFER 10.   Optimal Multiple Input Multiple Output (MIMO) control system development based on vehicle's model identified in CIFER 11.   Real   world   experimentation   to   test   Optimal MIMO control system The research has been completed until the 4th step, so step 1 to 4 will be presented in this paper. The remaining steps hopefully will be completed in near future. ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 51 © 2007 ICIUS
3   PID Based Rotary Wing Autopilot  A safe controller for rotary wing platform is needed to control the platform during frequency swept flight test. It has been mentioned before that frequency-domain system identification is difficult to be conducted by human pilot. For now, only hover condition will be implemented in the autopilot. Forward flight condition will be implemented in future development. It has been shown in several previous research conducted by other institution that PID based controller can be used to control   small   rotary   wing   platform.   This   controller   is developed   based   on   empirical   approach   without   any mathematical model. Of course the controller is not optimal (because   no   mathematical   can   be   used   to   justify   this optimality),   but   this   kind   of   controller   proved   to   be relatively safe. The objective of this research is to developed a rotary wing mathematical   model   based   on   flight   test,   and   not   first principle approach. So PID based controller is the logical choice for the automated flight test. Based on empirical experience, a PID cascaded controller is implemented.  Figure 3:   PID cascaded controller for rotary wing  This   PID   controller   is   tested   in   X-Plane   simulation environment. There are two main reason why X-Plane is used : 1.   X-Plane is very interesting for non aerodynamicist developer, because we can make an airframe based only   on   its   geometric   dimension.   The   physics model is based on a process called Blade Element Theory. This set of principles breaks an airframe down   by   geometric   shape   and   determines   the number of stress points along its hull and airfoils. Factors   such   as   drag   coefficients   are   then calculated at each one of these areas to ensure the entire plane is being affected in some way by external forces. This system produces figures that are   far   more   accurate   than   those   achieved   by taking averages of an entire airfoil, for example. It also   results   in   extremely   precise   physical properties   that   can   be   computed   very   quickly during flight, ultimately resulting in a much more realistic flight model. The X-Plane accuracy of the flight model is already approved by FAA, for full motion simulator to train commercial airline pilot. 2.   X-Plane's functionality can be customized using a plug in. A plug in is executable code that runs inside X-Plane, extending what X-Plane does. Plug ins are modular, allowing developers to extend the simulator without having to have the source code to the simulator. Plug ins allow the extension of the flight simulator's capabilities or gain access to the simulator's data.  Figure 4:   X-Plane based simulation  Figure 5:   PID controller flow chart  After spending several hours of tuning the gain parameters, the cascaded PID controller can hover the small rotorcraft (RC-02) in X-Plane reliably. ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 52 © 2007 ICIUS
Figure 6:   PID controller hovering RC-02 in X-Plane 4   Automated frequency-sweep input  Reference [] mentioned that computer-generated frequency- sweep input can be both effective and time efficient in many   flight   application,   but   they   must   be   properly synthesized   in   order   to   obtain   the   desired   frequency spectrum. Tischler have developed an automated frequency- sweep testing approach, using an exponential sweep and white   noise.   Here   is the   formulation of the   automated frequency-sweep input :  ) (   min max min  ω  ω  ω  ω   − + =   K   (1) where  ] 1 ) [exp(   1 2   − =  rec T t C C K   (2) The   previously   developed   PID   controller   need   to   be modified to accommodate the this frequency-sweep input. Here is the modification needed : 1.   Frequency-sweep input need to conducted in four input channel (roll/lateral cyclic, pitch/longitudinal cyclic, yaw or pedal and collective axis) 2.   PID controller need to be active on all control axis except the one where the frequency-sweep input is conducted 3.   There will be several safety criteria (maximum absolute roll angle, maximum absolute pitch angle, minimum and maximum altitude, and maximum absolute yaw rate) during frequency-sweep input. If   one   of   the   safety   criteria   is   violated,   the frequency-sweep   input   is   aborted   and   the   PID controller will be activated on all control axis to bring   the   platform   back   into   steady   hover condition. 4.   All flight parameter need to be logged into CIFER text input format.  5   Data Processing using CIFER  Frequency responses fully describe the linear dynamics of a system. When the system has nonlinear dynamics (to some   extent   all   real   physical   systems   do),   system identification determines the describing functions which are the best linear fit of the system response based on a first harmonic approximation of the complete Fourier series. For the identification, we used a frequency domain method, developed by the U.S. Army and NASA, known as CIFER (Comprehensive Identification from Frequency Responses). While   CIFER   was   developed   specifically   for   rotorcraft applications, it has been successfully used in a wide range of fixed wing and rotary wing, and unconventional aircraft applications. CIFER provides a set of utilities to support the various steps of the identification process. All the tools are integrated around a database system which conveniently organizes the large quantity of data generated throughout the identification process. In this research we are using CIFER Student Edition. The steps involved in the identification process are: 1.   Collection   of   flight   data.   The   flight-data   is collected during special flight experiments using frequency sweeps. This step is completed using data logged from X-Plane simulation. 2.   Frequency   response   calculation.   The   frequency response for each input-output pair is computed using a Chirp-Z transform. At the same time, the coherence function for each frequency response is calculated. This step is completed using FRESPID utility from CIFER. 3.   Multivariable   frequency   domain   analysis.   The single-input single-output frequency responses are conditioned   by   removing   the   effects   from   the secondary inputs. The partial coherence measures are   computed.   This   step   is   completed   using MISOSA utility from CIFER. 4.   Window Combination. The accuracy of the low and   high   frequency   ends   of   the   frequency responses   is   improved   through   optimal combination   of   frequency   responses   generated using   different   window   lengths.   This   step   is completed   using   COMPOSITE   utility   from CIFER. 5.   State-space   identification.   The   parameters (derivatives)   of   an   a   priori-defined   state-space model are identified by solving an optimization problem driven by frequency response matching. This   step   is   completed   using   DERIVID   utility from   CIFER.   Due   to   limitation   in   the   CIFER Student Edition (5 state, 2 input),   we have to separate lateral and longitudinal dynamics. ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 53 © 2007 ICIUS
6.   Time Domain Verification. The final verification of the model accuracy is performed by comparing the time responses predicted by the model with the actual helicopter responses collected from flight experiments using doublet control inputs. This step is completed using VERIFY utility from CIFER.  5.1   Frequency response calculation  The flight test simulation in X-Plane produced four kind of frequency-sweep   data   for   each   of   control   axis   (lateral, longitudinal, rudder/pedal and collective). Data is recorded in 50Hz frequency. After flight test the data is processed using FRESPID. Here we only present one example from those 4 control axis (the other are typically same).  Figure 7:   Frequency-sweep input (lateral axis)  Figure 8:   Frequency-sweep output P / roll rate (lateral axis)  To   measure   the   frequency   coverage   of   the   frequency sweep-input we can see the input auto spectrum plots. This is the same as probability density function. The following figure can give us the illustration of how good the coverage of the automated frequency-sweep input algorithm.  Figure 9:   Frequency-sweep input auto spectrum (lateral axis)  The frequency response (magnitude and phase response) for each   input-output   pair   is   computed   using   a   Chirp-Z transform in this step. This can be viewed as single-input single-output characteristic of the rotary wing platform.  Figure 10:   Magnitude frequency response (lateral axis)  Figure 11:   Phase frequency response (lateral axis) ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 54 © 2007 ICIUS
A key metric to verify that the flight data is satisfactory for the   purpose   of   system   identification   is   its   coherence. Typically coherence value of larger than 0.6 is expected.  Figure 12:   Coherence value (lateral axis) 6   State-space identification  After   conducting   single-input   single-output   frequency responses conditioning by removing the effects from the secondary inputs using MISOSA and optimally combining frequency   responses   generated   with   different   window lengths using COMPOSITE, we can start constructing the state space model. The state space form used by CIFER are :  ) (  τ − + =  •  t Gu Fx x M   (3) And the measurement output  ) (  τ − + =   t Ju Hx y   (4) In this research only lateral response will be studied and only basic forces will be used as state variable. M is identity matrix. J is zero matrix. H is identity matrix. and             =  Ay R P x   (5) Where  τ   is zero, so         =   rudder aileron u   (6) So we only need to find F and G matrix. We use DERIVID utility to find F and G matrix. Here is the result :             =  00 + .5749E - 00 + 0.0000E 00 + 0.6056E 00 + 0.0000E 02 + .6803E - 00 + 0.0000E 02 + 0.3766E 00 + 0.0000E 02 + .6411E -  F  (7)             =  01 + 0.1000E 00 + .4814E - 03 + 0.1713E 01 + 0.1000E 01 + 0.1000E 02 + 0.8700E  G   (8) Then we can verify the resulting state space model using flight data and VERIFY utility. Here are the result :  Figure 13:   Aileron input to verify state space model  Figure 14:   Aileron to P from flight data compared with state space model result ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 55 © 2007 ICIUS
Figure 15:   Aileron to Ay from flight data compared with state space model result 7   Concluding Remarks  There are still many steps to complete this research. But there are several concluding remarks that can be drawn until now, here they are : 1.   Simple PID flight controller dan assist the flight data   collection   for   system   identification   using frequency response analysis. The data (input auto spectrum plots) proved that this system can give very good frequency input coverage which is quite difficult to get using manually controlled flight especially for unmanned system. 2.   The data collected give very good coherence for single-input and single-output frequency response. 3.   The verification of state space model gave correct qualitative   result,   but   still   did   not   gave satisfactorily   result.   There   are   still   many experimentation steps to increase the state space model accuracy. Among those alternatives are :  o   Try different window length in FRESPID and COMPOSITE.  o   Increase the frequency of data recording  o   Develop parameterized state space model template using first principle approach  References  [1]   Mark B. Tischler, and Robert K. Remple,   Aircraft and Rotorcraft   System   Identification   :   Engineering Methods   with   Flight   Test   Examples ,   American Institute of Aeronautics and Astronatics, 2006 [2]   Bernard   Mettler,   Identification   Modeling   and Characteristics   of   Miniature   Rotorcraft ,   Kluwer Academic Publishers, 2003 [3]   Bernard   Mettler,   Takeo   Kanade,   and   Mark   B. Tischler,   System Identification Modeling of a Model- Scale Helicopter , Carnegie Melon University, 2003 [4]   Widyawardana   Adiprawita,   Development   of   Simple Autonomous Fixed Wing Unmanned Aerial Vehicle Controller   Hardware   (Internal   Report),   School   of Electric   Engineering   and   Informatics,   Bandung Institute of Technology, 2006 ICIUS 2007 Oct 24-25, 2007 Bali, Indonesia ICIUS2007-A009 ISBN 978-979-16955-0-3 56 © 2007 ICIUS