30120130406002

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME

AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 6, November - December (2013), pp. 08-18
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI)
www.jifactor.com

IJMET
©IAEME

EXPERIMENTAL VALIDATION OF A NOVEL CONTROLLER TO
INCREASE THE FREQUENCY RESPONSE OF AN AEROSPACE ELECTRO
MECHANICAL ACTUATOR
Praveen S. Jambholkar, Prof C.S.P. Rao
Cybermotion Technologies, Hyderabad, Dept. of Mechanical Engineering,
National Institute of Technology, Warangal

ABSTRACT
For aerospace applications, such as an air-to-air missile, the system specifications are very
high, since the target is a supersonic aircraft capable of sharp manoeuvring. Fin actuation system of
such missiles is known as Electro Mechanical Actuators. Unlike general motion control systems,
noise level and speed of response are critical. In Electro Mechanical Actuator there is no trajectory
generator. The target position has to be reached at the earliest. There is no luxury of a controlled
acceleration and declaration. The common challenge in EMA design of various Aerospace projects is
that they generally have poor frequency response, primarily due to phase lag. Phase lag results due to
reciprocator nature of these actuators across a NULL position .Control systems such as Proportional
Integral Differential (PID), Pole Placement , Linear Quadratic Regulator (LQR), Linear Quadratic
Gaussian are not ideal for this class of actuators since on their own, they cannot solve the primary
problem of phase lag .The main theme of this paper is to reduce the phase lag of an Electro
Mechanical Actuator (EMA) by a novel concept, “Piecewise Predictive Estimator (PPE)”. The PPE
technique in conjunction with an existing controller can increase the frequency response by up to
15% without any adverse effects on noise characteristics of the EMA. An experimental result based
on EMA of an air-to-air missile has been used and instrumentation based on Lab View is used. There
is an increase in performance and it matches with the simulation results we achieved using Simulink.
Keywords: PID (Proportional Integral Derivative), LQR (Linear Quadratic Regulator),
PPE Piecewise Predictive Estimator), BLDC (Brush Less DC), EMA (Electro Mechanical Actuator),
SDRE (State Dependent Ricatti Equation)

8


1. INTRODUCTION
In this class of motion control application, noise is a major concern.
We have to satisfy two criteria. Step response will show speed of response as well as noise
levels. Bodes plot will show the system bandwidth in hertz, primarily limited by the -90 degrees
phase lag , as well as giving us phase margin , which should be more than 60 degrees. PID
controllers can be either be tuned for high gain, high bandwidth, but will result in high noises. LQR
controllers by very definition minimize the cost function consisting of state error and effort required.
We require speed of response at any cost.
Various sources of process noise are gear or ball screw backlash, BLDC motor [1] cogging,
commutation current disturbances, MOSFET switching noise, DC-DC converter noise, Load
variations.
Sources of measurement noises are position sensor noise (Potentiometer or LVDT), ADC
quantization noise, control circuit’s EMI coupling to sensor feedback path. As mentioned earlier, the
two primary objectives for EMA design are low noise and high speed of response (bandwidth).
This paper proposes a unique combination of signal processing and control technologies to achieve
these two objectives of low noise and high bandwidth response.
2. HARDWARE DESCRIPTION
2.1 Rotary EMA
Rotary EMA consists of a Brush Less DC (BLDC) motor. The output is a rotary motion from
+250 to -250 across a null position. A planetary gear box and a sector gear with a high gear ratio of
207:1. The position feedback is through a potentiometer (pot).

Fig. 1 Cross sectional view of Rotary EMA
2.2 Linear EMA
Linear EMA consists of BLDC motor connected to a ball screw.
Here the linear motion is across a null position.
2.3 BLDC Motor
DC motor has an ideal torque vs. speed characteristics.
BLDC motors consist of permanent magnet rotor and stator has a set of coils. Many disadvantages of
DC motors are overcome, such as torque density, etc.
Another advantage of using a BLDC motor is that its behavior in terms of current, torque, voltage
and rpm is linear.
9


3.

MODELLING OF ELECTRO MECHANICAL ACTUATOR

The modelling of the Electro Mechanical Actuator [2] [9] is done in stages. By using the
mechanical properties and electrical properties and equating with Newton’s and Kirchhoff’s laws, we
get the transfer function.
u = Output of the plant model (voltage).
Motor Parameters:
J = Inertia Constant.
Kt = Torque Constant
B= Friction Coefficient. .
R = Resistance
L = Inductance
Kp = Gain
Parameters
(J=0.01, K=0.01N.m/A, L=330 µH , R=0.39 , b=0.1).
This can be converted to a continuous state space model using Matlab command ss (tf), or directly by
replacing mechanical parameters in the A, B, C and D matrices
Ra
+

La
θ = wt
BM

Gear

+

Kgear

Ea = Kawr

Load

–

TL

–

Fig. 2 DC Motor
di
=
dt

–

k
R
I
ia – a ωr +
ua
La
La
La

(1)

Newton 2nd law
ΣT

= Vα = J

dω
dt

(2)

Te = k a ia

(3)

Tviscous = Bωr

(4)

dωr
I
=
dt
J

(5)

=

(Te − Tviscous − TL )
I
(kaia − Bωr − TL )
J

di
R
K
I
=–
ia –
ωr +
ua
dt
La
La
La

Va

(6)
10


dω r
I
= (k a ia − Bmωr − TL )
J
dt

(7)

d
dt
S .θ r ( s ) = ωr (s )

S=

K
I
R

ω ( s ) + Va ( s )
 S + ia (s ) = −
L
La
La


(8)

B
I
I

 S + ω r (s ) = k a ia ( s ) − TL ( s )
J
J
J


(9)

The dynamic equation in state space form

d
dt

 ra
−
 i   La
= 
 
θ   k a
 J


ka 
La 

Bm 
−
J 

−

i   I 
θ  +  L V
  0
 

(10)

Fig.3 Simulink Block Diagram of Servo Actuated by DC Motor
4. CONTROLLER DESIGN
4.1. PID Controller Design
A Proportional integral derivative controller is a generic control loop feedback mechanism
(controller) and commonly used as feedback controller.
In PID controller, the ‘e’ denotes to be tracking error which is been sent to the controller. The
control signal u from the controller to the plant to the derivative of the error.

∫

u = k p e + k1 edt + k D

de
dt

(11)
11


Parameter of PID controller were choose to accomplish design objectives in terms of fast,
non-overshooting transient response and accurate steady state operating small differential gain is
required because it stabilizes the system, while integral gain influences fast transient responses. The
designer should know the process characteristics, and accordingly must decide on the combination
and values of P, I, D parameters to keep [4].
PID controller may not be optimal in many cases since increasing gain will also increase
process noise leading to instability. Designers have attempted to modify PID equations to improve its
performance [5] [6].
4.2 LQR Design
LQR family of controllers are very effective for linear systems. LQR controllers are designed
to minimize the cost function comprising of state error and input effort [7].
∞

J=

∫ (x

T

)

Qx + Ru 2 dt

(12)

0

∞

∫

J = [(trackingerror ) 2 Q + (input ) 2 R]dt

(13)

0

J is cost function to be minimized; R and Q are two matrices of the order of state and input.
Q and R matrices are selected by designers by trial and error. If Q is large, to keep J small, input u
has to be big.
If R is large, to keep J small, input u must be small.
And control input u is
u = − R −1 B T Px (t )

(14)

Where P is calculated by solving the Ricatti equation [9]
u = Px + AT P − Q + PBR −1 B T P

(15)

Below figure shows the designed LQR state feedback configuration.

Figure 4: Linear Quadratic Regulator Structure

12


LQR control can be used for non-linear, time-varying plant by using SDRC (State Dependent
Ricatti Equation) [8], where the plant model is based on Euler-Lagrange equations [10].
.

X = A( x )x + B ( x )u

(16)

4.3 Piecewise Predictive Estimator (PPE)
Predicting / estimating the target for an air-to-air missile is critical. One approach is to model
the target acceleration as first order Gauss- Markov process [11].
Here an attempt has been made to develop a predictor to enhance the hit capability of an airto-air missile EMA. We name this Piecewise Predictive Estimator (PPE) since we can have finite
piecewise estimation of the target position.
The origins of PPE are in numerical calculus. Z transform is the foundation of most signal
processing.
Zx n = xn+1

(17)

Delta operator is defined as
∆xn = xn +1 − xn

(18)

Del operator is defined as
∇xn = xn − x n−1

∇=

(19)

∆
1+ ∆

xn +1 =

(20)
1

(21)

(1 − ∇ )xn

Using equation (17), we can predict the next sampled value. And also,
xn+ 2 = ∇ 2 xn = ∇(∇xn )

(22)

If a missile has to track a moving target, it is desirable to be able to make a judicious
prediction of future location of the target.
Since the target does not follow any continuous function, we can only approximate the target
trajectory piecewise, where each piece is continuous within this region.
Since Taylor’s series representation is valid for a continuous function, we have,
f (x ) = f (0 ) + f ' (0) +

x 2 ''
x 3 '' '
f (0) +
f (0) + .. (23)
2!
3!

Expanding equation (2) as Taylor’s series, we have

(

)

xn+1 = 1 + ∇ + ∇ 2 + ∇ 3 + ...... xn

(24)
13


Using equation we can have a finite prediction horizon. Although finite, this prediction can
improve the target tracking capability considerably by reducing the phase lag without undue increase
in gain. This will serve the dual purpose to reduce the phase lag and to reduce the system noise, since
we are not resorting to gain increase.
The algorithm of PPE is as follows. This algorithm remains the same in Simulink’s
embedded Matlab function block C code , as well as in C code of Code Composer Studio which is
used to compile firmware for Texas Instruments 32 bit DSP[3] TMS320F2812. Block diagram of
this controller shown below figure 7;

Fig. 5 Block Diagram of DSP TMS320F2812 based Controller

Fig. 6 Simulink Block Diagram of Plant Model with PPE

14

(IJMET),

Fig. 7 Flow Chart for PPE Embedded Function

15


4.

EXPERIMENTAL VALIDATION

4.1 Experimental setup
The experimental setup consists of an Electro Mechanical Actuator from an Aerospace
project, 28V, 30A power supply. Frequency Response Analyzer, DSP processor, Digital drive and
Function generator. A sweeping sine wave from 40Hz to 0Hz at ±1V peak to peak is applied as
command input. Input and output full scale are ±10V corresponding to a rotary motion of ±25°. Input
and output signals are given to the Frequency Response Analyzer to generator Bede’s plot of phase
lag, gain vs. frequency.
The bandwidth of a system is both measure of tracking speed of the system. We also get
stability information through gain margin and phase margin.
Electro Mechanical Actuator
PC

Analyzer

Fin control

Command

Command
DAQ

Feedback

Feedback

Power
Supply

Fig. 8 Block Diagram of Experimental Setup of EMA System

Fig. 9 Experimental Setup of EMA System
4.2 Experimental Result
We have prepared an experimental setup consisting of Electro Mechanical Actuator,
Frequency Response analyser, Power supply and sinusoidal signal generator to find out the effect of
stochastic filter along with a PD controller. For the same noise levels of 100mV for a +-10V
feedback signal, the bandwidth jumped from 22 Hz to 25 Hz. This is a significant increase in
applications where low noise and high speed response are critical.
16


Fig. 10 Bandwidth Response (22 Hz) with PID Controller

Fig 11: Bandwidth Response (25 Hz) with PID and PPE
CONCLUSION
We have experimentally verified that there is a significant improvement in frequency
response due to reduction in phase lag at higher frequencies, from 22Hz without PPE, to 25Hz with
PPE, thus meeting our goal.
17


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