SYSTEM IDENTIFICATION OF UNMANNED HELICOPTER

Abstract

In this paper, we have developed a dynamic model to replicate the motions a helicopter. Unmanned helicopters have more advantage over manned as they are perfect for performing missions autonomously,which is vital to understand a dynamic model to enable the development of control and state estimation algorithms. This article presents a comprehensive method for identification of a nonlinear model of the unmanned helicopter.The accuracy of the developed model is verified by the comparison between predicted and actual responses from the model and the flight experiments, and between key parameters and the theoretical values. This report describes the process and results of the dynamic modeling of modelscale unmanned helicopter using system identification.

…………………………………………………………………………………………………….... Introduction:-
Helicoptersare highly regarded because they are easilymaneuverable and are able to hover, making them perfect for flying in closed environments while streaming data to the ground. Autonomous flight is necessary for these missions because of the fast and unstable dynamics of the aircraft, which are exacerbated by any transmission delays of sensor data and control inputs. The research and development of UAVs have gained much attention in academic and industrial fields. Researchers have explored the considerable potential of UAVs for various military and civilian applications. For successful application to these missions, control system for an autonomous flight should be designed and implemented.Compared to conventional fixed-wing aircraft, obtaining a state-space model for helicopter is more difficult. The complexity of helicopter flight dynamics makes modeling difficult, and without a good model of the flight-dynamics, the flight-control problem becomes inaccessible. A system model can be obtained in two ways, through first principles modeling and system identification. A pure first principle modeling is unsuitable for a small-scale helicopter because this approach requires extensive knowledge of helicopter flight mechanics. Moreover, unlike in a quad copter, the helicopter has coupling between its various parameters which has to be taken into account and thus makes the modeling much more difficult.Helicopter rotors add dynamics that couple with therigid body fuselage motions and the surrounding flowfield, introducingcomplex aerodynamics which manifest in partas rotor/wake and rotor/fuselage interactions. We therefore go for system identification method to get the dynamic model. Thedynamics of the helicopter are represented as a rigidbodywhich can be coupled to additional dynamics such asthe rotor or engine/drive-train dynamics. Includingthese subsystems improves the accuracy of the model making it more consistent for a range of frequencies.

Angular Dynamics:-
The frequency response of therolling and pitching rates p and q to the lateral andlongitudinal cyclic inputsδ ,δ shows a pronounced underdamped secondorderbehaviour.In this modelling approach, the lateral and longitudinal blade flapping dynamics are represented by two coupled first-orderdifferential equations.
Heave Dynamics:-With respect to heave dynamics, a first order system can successfully capture this part of the helicopter dynamics.

Yaw Dynamics:-
Here the yaw response has a nature of second order system. The differential equations used for state space model are as follows.

State Space Model:-
The aim of system identification is to construct a suitable model, such that the input output behavior of the model approximatesthe input-output behavior of the helicopter system, i.e. for a small positive constant.
Wherein1 is the order (or equivalent delay) of the system, d is the relative degree of the function. A 6-degrees-of-freedom linear rigid body helicopter model with first-order approximation is given by a differential equation. X =AX+BU The system identification analysis used a control vector consisting of the four pilot joystick inputs, consisting of the roll angle, pitch angle, translational velocities, rotational velocities, and rotor speed. These are written symbolically as-=
The key dynamics of the helicopter are seen from reference to the system's Eigen values and eigen vectors. The first 4 roots are on the real axis, of which 2 are stable and 2 are unstable. The unstable modes involve the horizontal velocities with both altitudes and longitudes. The stable modes involve horizontal and vertical velocities. The eigen value 5 is associated with heavy response. The Eigen pair 6 and 7 is associated with the closed-loop yawing mode resulting from the active yaw damping system. The pitching mode (eigenvalues #8-9), which has a considerable roll coupling component, has a frequency that is nearly exactly the square root of the pitch flap spring. The coupled rolling mode with slight pitching component (Eigen values #10-11), has a frequency that corresponds to the square root of the roll flap spring.
518  This approach introduces a set of N basis functions, one for each data point. The output of the mapping is then taken to be a summation of the basis functions, i.e.
The idea is to find the "weights" such that the function goes through the data points. It is easy to determine equations for the weights: The radial basis network is a two-layer network. First, in layer 1 of the RBF network, instead of performing an inner product operation between the weights and the input (matrix multiplication), we calculate the distance between the input vector and the rows of the weight matrix. The second layer is the linearization layer.

520
We then run the code in MATLab to find the fit between the estimated model and the helicopter model. There may not always be a perfect fit as there will always be some kind of discrepancy in the data, error in measurement readings and the inability of the network to keep up with the changes in the data etc. The effective one is to follow the bird which is nearest to the food.In the proposed algorithm, an agent of the swarm, called a particle, learns from the best position that it has occupied and also the best position that any particle of the swarm might have encountered. These positions are saved in memory of each particle and constantly updated to direct the swarm to the global best position. The best position of a particle is called cognitive index -pBest, and the best of the swarm the social index -gBest. The equations that govern the change in positions of a particle are: +1 = w* + ( * 1 *( -)) + ( * 2 *(( -)) +1 = + +1 The flow of the PSO algorithm can be described by Algorithm 1,mis the number of particles. Where x is the position of the particles, i.e., the potential solutions, v is the velocity of the particles, and is the best fitness value and position for individual particles. and is the best fitness value and position for the group. The algorithm is as follows-1. Initialize the number of particles-m value.
f 11. x Here we take the number of particles to be 100 and the number of iterations to be 1000.

Multi Layer Perceptron (MLP):-
Artificial Neural Networks provides a method for learning arbitrary mapping between two data sets. A typical ANN contains a number of adjustable parameters called weights. Supervised learninginvolves finding a set of weights that minimizes the mapping error. Here mapping error is defined as the difference between observed output and NN's output. Fig.8 shows a typical MLP ANN [4, 6]. In this case also, we find out the state space model of the system which is as follows.

Conclusion:-
The overall consistency of these models provides good evidence that the identified models are accurate and that the methods used are appropriate for identifying miniature helicopters. We can see from the graphs that we have not obtained the best fit possible as there are some discrepancies in the data.PSO is a powerful optimization tool in the realm of controltheory, particularly for the time-domain state space systems,where performance tuning has not been well-studied in thepast.When analysing identification results, caremust be taken by the user to consider what frequency range is of interest.Concerning the different methods and approaches investigated in the thesis, itcan be stated that a general agreement across all methods has been seen in the estimated models. We can therefore conclude here the radial basis gives a better model to work with as the graphs show a better fit to the model than particle swarm optimization method. To improve upon PSO method, we must go into quantum optimization.