International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 1438 ISSN 2229-5518 IJSER © 2014 http://www.ijser.org Quadrotor Comprehensive Identification from Frequency Responses Abubakar Surajo Imam, Robert Bicker Abstract— Design and development of a quadrotor model-based flight control system entails the use of the vehicle's dynamic model. It is quite challenging to use the physical laws and first principle-based approaches to model the quadrotor dynamics as they are highly nonlinear, characterized by coupled rotor-airframe interaction. However, system identification modeling method provides a less challenging approach to modeling the dynamics of highly non-linear systems such as a quadrotor. This paper presents the frequency-domain system identification procedure for the extraction of linear models that correspond to the hover flight operating conditions of a quadrotor. Frequency response identification is a versatile procedure for rapidly and efficiently extracting accurate dynamic models of aerial vehicles from the measured response to control inputs. During the extraction of the quadrotor's model, flight test manoeuvres were used to excite the variables of concern for flight dynamics and control by adopting a systematic selection procedure of the model structure for the parameterized transfer-function model and the state-space model. The technique provides models that best characterized the vehicle's measured responses to the controls commands, and can be used in the design of a flight control system. Index Terms— Dynamic model, flight control system, frequency-domain system identification, flight dynamic and control, excitation and measured responses, quadrotor. ——————————  —————————— 1 INTRODUCTION Recently, the use of small-scale rotorcraft unmanned aerial vehicles (UAVs) for surveillance and monitoring tasks is be- coming attractive. Amongst the various configurations of the small-scale rotorcraft, the use of a quadrotor gained more prominence, particularly in the research community [1], [2], [3], [4], [5]. A quadrotor is a small responsive four-rotor vehi- cle controlled by the rotational speed of its rotors. It is com- pact in design with the ability to carry a high payload. The dynamics of rotorcraft is substantially more complex than that of a fixed-wing aircraft [6], the complexity increases as the vehicle become smaller. The high non-linear nature of a quadrotor makes difficult the use of physical law and first principle-based approach to model its dynamics. The quad- rotor dynamics is characterized by the coupled rotor-airframe dynamics. Hence, system identification method is needed to model the dynamics of non-linear systems such as a quad- rotor, and the procedure is conducted in either time or fre- quency domain. A number of studies have reported the use of system identification procedure to identify the dynamics of rotorcraft [7], [8], [9], [10]. For instance, a method for system identification using Neural Networks was proposed in [7], where input-output data was provided from nonlinear simula- tion of X-Cell 60 small-scale helicopter, and the data was used to train the multi-layer perceptron combined with NNARXM time regression input vector to learn nonlinear behavior of the vehicle. A rotorcraft system response data was acquired in carefully devised experiment procedure in [8], and a time do- main system identification method was applied in extracting a linear time-invariant system model. The acquired model was used to design a feedback controller consisting of inner-loop attitude feedback controller, mid-loop velocity feedback con- troller and outer-loop position controller, when implemented on the Berkeley RUAV, the controllers showed remarkable hovering performance. Similarly, parametric and non- parametric models for a rotorcraft were identified using data collected through identification method in [10], after which two control laws were designed for the vehicle attitude stabili- zation. In [11], system identification method was applied to examine a high-bandwidth rotorcraft flight control system design. In the study, flight test and modeling requirements were illustrated using flight test data from a BO-105 hingeless rotor helicopter. A systematic way is adopted in this study to derive a quadrotor dynamics models using the frequency- domain system identification method. Once the models are determined, a single-input-single-output (SISO) and multiple- input-multiple-output (MIMO) control loops can be designed and implemented on a quadrotor 2 SYSTEM IDENTIFICATION CONCEPT System identification is the procedure for deriving a mathematical model of a system based on experimental data of the system’s control inputs and measured outputs. The procedure involves derivation of a mathematical mod- el based on experimental data of the vehicle's control in- puts and measured outputs; it also provides an excellent tool for improving mathematical models used for rotorcraft flight control system design. System identification method can be used for derivation of both parametric and nonpar- ametric models: examples of nonparametric models in- clude impulse and frequency response models, and exam- ples of parametric models are transfer function and state space models. The nonparametric models are directly de- rived using experimental data and provide an input– output (I/O) description of the system. These model types are based on collections of data and do not require any knowledge of the system structure. However, the challenge IJSER