Longitudinal Parameter Estimation of Aerospace Vehicle with Different Noise Levels

Longitudinal Parameter Estimation of Aerospace Vehicle with Different Noise Levels

Bijily Rose Varghese

Department of Electrical and Electronics Engineering, MBCET, Kerala University,

Trivandrum, India

Ms. Manju G

Assistant Professor,

Department of Electrical and Electronics Engineering, MBCET, KeralaUniversity,

Trivandrum, India.

Abstract This paper aims to estimate the longitudinal aerodynamic parameters of the aerospace vehicle from the available measurements with different noise levels. In this current work Filter Error Method (FEM) which accounts for both process and measurement noise, is used to estimate the aerodynamic parameters from vehicle data. FEM algorithm is developed in MATLAB environment. With the developed algorithm studies are carried out at different instance of the vehicle and the estimated parameters are compared with wind tunnel predictions.

Keywords Aerodynamic parameter; Filter Error Method; Gauss Newton Method; Kalman Filter.

1. INTRODUCTION

   Parameter estimation, is the subfield of system identification, which determines the best estimates of the parameters occurring in the model. Aerospace vehicle parameter estimation is the best example of system identification. An aircraft motion is described by equations of motion derived from the Newtonian mechanics, considering the vehicle as a rigid body. The aerodynamic forces and moments cannot be

   Fig. 1. Aerodynamic forces and moments

   Fig.1 shows the different forces and moments acting on the vehicle along the three axis. Aerodynamic forces acting on the vehicle with respect to longitudinal plane are given from (1)-(2). [1]

   measured directly. However, aerodynamic modeling followed by parameter estimation helps to determine the aerodynamic parameters. Conventional methods of parameter estimation are (i)Equation Error Method[2] (ii) Output Error Methods (OEM)[3,4] and (iii) Filter Error Methods (FEM). Out of these methods Filter Error Method (FEM), is the most general stochastic approach for aircraft parameter estimation, which

   Fx CAqS

   FZ CN qS

   Aerodynamic moment is given by (3).

   M CmqSc

   (1)

   (2)

   (3)

   accounts for both process and measurement noise. In this current work Filter Error Method (FEM), is used to estimate the aerodynamic parameters. FEM algorithm is developed in MATLAB environment. State estimation is carried out with Kalman Filter and the parameters are updated using Gauss Newton Method. With the developed algorithm studies are carried out at different instance of the vehicle and the

   Where q is the dynamic pressure, S is the reference area, c

   is

   the longitudinal reference length, CA ,CN ,Cm are the total axial force coefficient, total normal force coefficients and total pitching moment coefficients. The state equations are given from (4)-(7)

   estimated parameters are compared with wind tunnel predictions.

2. LONGITUDINAL DYNAMICS Aerospace vehicle experiences aerodynamic forces and

   V uu vv ww

   u2 v2 w2

   uw wu

   u2 w2

   (4)

   (5)

   moments during their motion in atmosphere.

   1 cos

   (q cos r sin )

   (6)

   C qSc I (r2 p2 ) rp(I I ) I ( p qr) I q m zx zz xx xy yz

   Iyy

   (r pq)

   (7)

3. EFFECT OF NOISE

   The real aerospace vehicle measurements are affected by both

   Where u, v, w are the translational velocity, p, q, r are the

   measurement noise and process noise. To study the effect of

   the noise on the estimated co-efficients, noise is added in q,

   body rates, V is the vehicle velocity, is the angle of attack,

   ax , az by specifying the signal to noise ratio. The nosie

   Ixx , I yy , Izz

   are the moment of inertia and Ixy , I yz , Izx

   are

   added is shown in table 1.

   the product of inertia, ,, are the euler angles. The aerodynamic coefficients are modelled in linear form as:

   Table 1: Noise added in the variable

   CA CA0

   CA

   C

   A e1e1

   CA e2e2

   CA r1r1

   CA r 2r 2

   (8)

   C C C C

   C

   C C

   (9)

   N N 0 N

   N e1 e1

   N e2 e2 N r1 r1

   N r 2 r 2

   C C C C

   C C

   C

   m m0 m

   (10)

   m e1 e1 me2 e2

   m r1 r1 m r 2 r 2

   Variable	Noise added (signal to noise ratio)
   	Case1	Case 2	Case3	Case 4
   q	–	40	50	80
   ax	–	40	50	80
   az	–	40	50	80

   Due to the presence of process noise, Equation Error Method

   where CA0,CN 0,Cm0,CA ,CN ,Cm are the basic coefficients and CA e1,CA e2 ,CA r1,CA r 2 ,

   CN e1,CN e2 ,CN r1,CN r 2 , Cm e1,Cm e2 ,Cm r1,Cm r 2 are

   the incremental coefficients due to control surface deflections. Thus the unknown parameters to be estimated are given as:

   T [C C C C C C C C

   ,Output Error Method estimation techniques yield poor estimation results. Therefore, Filter Error Method [5] is used in this work which account for process and measurement noise. Since the system is stochastic in nature a steady state Kalman filter is used for obtaining the true state variables from the noisy measurements.

4. RESULTS AND DISCUSSION Estimation is carried out for a period of 10s with 500

A0 A A e1 A e2 A r1 A r 2 N 0 N

CN e1CN e2CN r1CN r 2Cm0Cm C Cm e2Cm r1Cm r 2 ]

Observation equations are given by (12)-(18)

Vm V

m

m e1

(11)

(12)

(13)

samples. Region considered for the estimation process is for the vehicle time 310-320s. The initial values of the estimates are taken from the wind tunnel data. The variation of angle of attack, dynamic pressure, Mach number, relative velocity and control surface deflections during this region are shown in Fig.3 and 4. The estimated longitudinal aerodynamic coefficients are shown in Fig 5,6 and 7.

C qSc I

m

qm q

(r2 p2 ) rp(I

• I ) I

( p qr) I

(r pq)

(14)

(15)

3.2

Mach Number

3.1

3

2.9

10000

Dynamic Pressure(Pa)

9000

8000

7000

qm

m zx zz xx xy yz

Iyy

a CAqS xm m

(16)

(17)

2.8

Relative Velocity(m/s)

1000

0 5 10

Time(s)

6000

22

Alpha(deg)

21

0 5 10

Time(s)

azm

CN qS

m

(18)

950

20

900

Where, m is the mass of the vehicle, V , , , q are the 19

m m m m

measured velocity, angle of attack, euler angle, and body

850

0 5 10

18

0 5 10

rate, qm is the measured angular accelerations and

axm , azm

Time(s)

Time(s)

are the measured accelerations.

Fig. 3. Mach number, relative velocity, dynamic pressure and alpha during the estimation region.

Left Elevon Deflection(deg)

2

0