Robust Level Flight Control Design For Scaled Yak-54 Unmanned
Aerial Vehicle using Single Sliding Surface.
Ussama Ali, M. Zamurad Shah, Raza Samar and Aamer Iqbal Bhatti
Abstract— This paper deals with devising robust nonlinearcontrol strategy for benchmark system of scaled Yak-54 Un-manned Aerial Vehicle. Authors considered the applicationsof sliding mode controllers to the longitudinal flight dynamicsof the Yak-54 UAV for executing maneuvers over full flightenvelope. Unlike the classical technique of the two slidingsurfaces for the two loops a single surface is selected for thelevel flight. Control of unmanned aerial vehicle involves theproblem of incomplete measurements, modeling uncertaintiesand external disturbances which makes flight dynamic analysisand control system design difficult. We present an innovativerobust control strategy based on powerful tools provided bythe theory of sliding mode control algorithms. First ordersliding mode controller are designed but they provide chatteringat the control input thus a non linear second order supertwisting controller is used to provide chattering free controlwith improved robust stabilization.
Index Terms— Sliding Mode Control SMC, Higher OrderSliding Mode Control HOSM, Strong Reachability ConditionSRC
U ,V ,W Components of aircraft velocity, ft/s
P ,Q,R Angular velocity components rad/sec
ψ,φ,θ Euler angles rad
α Angle of attack (AoA), rad
xE ,yE ,zE Aircraft cordinates with fixed axsis
Ixx,Iyy ,Izz Moments of inertia slug ft2
Ixy ,Iyz ,Ixz Products of inertia slug ft2
Fx,Fy ,Fz Aerodynamic force components
S Wing area, ft2
c Mean aerodynamics chord, ft
b Span length, ft
δe,δa,δr Elevator, Aileron and Rudder deflection
δT Thrust Ratio
CL,CD,CY Lift, drag and side force coefficients
Cm,Cl,Cn Pitch, roll and yaw moment coefficients
Table. 1. Nomenclature
I. INTRODUCTION
Analysis and control of uncertain aerial systems is one
of the most challenging problems in system and controls
theory. Linear time varying plants can be controlled by
many traditional techniques, the classical idea is to design
a controller for mid point and then to change the gain of
the controller based on some observed parameter which
This work was supported by Control and Signal Processing ResearchGroup, CASPR
{Ussama Ali, Zamurad Shah, Aamer Iqbal Bhatti and Raza Samar}are with Faculty of Electronic Engineering, Mohammed Ali JinnahUniversity, Islamabad, Pakistan [email protected],[email protected], [email protected] [email protected]
corresponds to certain flight conditions e.g dynamic pressure
[12]. The aim of the gain scheduling is to keep the natural
frequency of the dominant closed loop poles more or less
constant during the complete flight envelope. H∞ technique
is utilized for control designing in which full order [3] or
approximated reduced order control laws [13] are derived.
Based on these controllers a single gain scheduled controller
is obtained using transformation according to least square
fit using measured parameter such as Mach no or dynamic
pressure. An organized approach is developed when the
underlying differential inclusion are assumed to exist in a
convex polytopic. A few severe operating points are selected
in the flight envelope as the vertex points and all other possi-
ble operating points corresponds to convex combinations of
these nodes. Then LMI (linear matrix inequalities) methods
are utilized to obtain gain scheduled controller [2]. A variety
of robust multi variable approaches such as H∞ control,
linear quadratic optimal control (LQR/LQG), and structured
singular value μ-synthesis have been used in control design
process, of which an excellent and comprehensive literature
can be found in [11]. Dynamic inversion as a nonlinear
design technique have been adopted in [1], while a strategy
that combines the qualities of control design methods i.e
the model inversion control with an on line adaptive neural
network to enhance the capability of the design is elaborated
in [16].
[17] considered a sliding mode control SMC design based
on linearization of the aircraft, with the altitude h and
velocity V (Mach number) as the trim variables. The primary
design objective is model-following of the pitch rate q, which
is the preferred variable for aircraft approach and landing.
Regulation of the aircraft velocity V (or the Mach-hold
autopilot) is also considered as a secondary objective. It
was shown that the inherent robustness of the SMC design
provides a convenient way to design controllers without gain
scheduling, with a steady-state response that is comparable
to that of a conventional gain-scheduled approach with
integral control, but with improved transient performance.
[19] proposed a design of HOSM controller for unmanned
combat aerial vehicle UCAV in which the author divided
the complete flight envelop in different manoeuvring modes
where each mode is defined by a specific state constraint.
Recently, [15] proposed a multi-gain sliding mode based
controller for the pitch angle control of a civil aircraft. The
proposed controller is based on the concept of the sliding
mode controllers in which multiple gains are being used to
control the pitch angle of an aircraft and make it insensitive
to parameter variations while reducing the chattering and
1209978-1-4577-2074-1/12/$26.00 c©2012 IEEE
guaranteeing the stability of the closed loop system.
Performance of controlled manoeuvres under heavy un-
certain conditions still remains among the main topics of
control theory. The sliding-mode control is one of the main
techniques in the field of nonlinear control design and is
extensively discussed in [20], [4]. The inherent robustness
on this methodology is based on the order reduction which
makes it insensitive to certain degree of parameter variations.
Although very robust, this approach has a major drawback,
the high frequency control switching against the constrained
manifold results in the so-called chattering phenomenon
which in turn may cause damage to the actuators as they
have slower response time [10]. To get rid of chattering,
SMC gave birth to many variants. Some of these include high
gain control with saturation, continuous approximation of the
discontinuities, multi gain sliding mode, the sliding sector
method [5], dynamic sliding mode control and asymptotic
state observers. However, when plants include uncertainties
with the lack of information about the bounds of unknown
parameters, higher order sliding mode specially the super
twisting algorithm [9] approach is more convenient.
All of the aforementioned methods had some shortcoming
in the sense of heavy chattering, constrained motions with
the design of mode and low performance. In this work,
these problems are handled with the use of a super twisting
controller. Moreover, the robustness of the controller is
confirmed by inducing parametric variation in the stability
derivatives. These claims are verified via the simulation
results. The structure of the paper is as follows: The aircraft
model and its nonlinear dynamics is presented in Section
II. In Section III, the details of SMC and HOSM (Super
Twisting Algorithm) used in the control system design are
provided. Section IV contains the simulation results dis-
played to validate the control methodology for achieving
tight control of longitudinal dynamics. Section V contains
some conclusions followed by references and appendix.
II. AIRCRAFT MODEL
The traditional development techniques used to develop
a dynamic aircraft model (parametric models, wind tunnel,
CFD, system identification) are not available for use with
the Yak-54 UAV. Instead it makes use of one of two
modeling techniques Advanced Aircraft Analysis (AAA)
and AVL to characterize the vehicle dynamics in such a way
that is helpful to the flight control system designer [7]. A
complete 6DOF nonlinear aircraft dynamic model [18] (with
body fixed frame) is presented in the forthcoming discussion.
u = rv − qw − (g′
0)sinθ + Fx/mv = −ru+ pw − (g
′
o)sinφcosθ + Fy/mw = qu− pv + (g
′
o)sinφcosθ + Fz/mφ = p+ tanθ(qsinφ+ rcosφ)θ = qcosφ− rsinφψ = (qsinφ+ rcosφ)/cosθp = (1/(IxIz − I2xz)) [(Ixz[Ix − Iy + Iz]pq − [Iz(Iz − Iy)
+I2xz]qr + IxzL+ IxN)
q = (1/Iy)(Iz − Ix)pr − Ixz(p2 − r2) +M
r = (1/(IxIz − I2xz))[([Ix(Ix − Iy) + I2xz]pq − Ixz
[Ix − Iy + Iz]qr + IxzL+ IxN)
xN = u(cosθcosψ) + v(−cosφsinψ + sinφsinθcosψ
+w(sinφsinψ + cosφsinθsinψ)
xE = u(cosθsinψ) + v(cosφsinψ + sinφsinθcosψ)
+w(−sinφsinψ + cosφsinθsinψ)
h = u(sinθ)− v(sinφcosψ)− w(cosφcosθ)
Consequently the state vector becomes
XT =[u, v, w, φ, θ, ψ, p, q, xN , xE , h
](1)
The force and moment components (Fx, Fy, Fz, L,M,N) in
the 6 DOF equations must be broken into aerodynamic and
thrust contributions. The general origins of the aerodynamic
forces that produce the usually important stability derivatives
are discussed and illustrated
L = qS[CL0
+ CLαα+ CLu
uV∞
+ CLδeδe+ (CLq
q) c2V∞
]D = qS
[CD0
+ CDαα+ CDu
uV∞
+ CDδeδe +
C2
L
πeAR
]FAY
= qS[CYβ
β + CDu
uV∞
+ CYδaδa + CYδr
δr
]+(CYp
p+ CYrr) bqS
2V∞
M = qSc[Cm0
+ Cmαα+ Cmu
uV∞
+ Cmδeδe + Cmq
q c2V∞
]L = qSb
[Clββ + Clδaδa + Clδrδr + (Clpp+ Clrr)
b2V∞
]N = qb
[Cnβ
β + Cnδaδa+ Cnδr
δr + (Cnpp+ Cnr
r) b2V∞
]
These aerodynamic force and moment components are
reliant on deflection of the control surfaces, these deflections
render the form of control inputs to the model [18]. Throttle
setting is another control input therefore the implied input
vector of the nonlinear model takes the form.
UT = [δt, δe, δa, δr] (2)
The control objective includes the stability of the system over
complete flight envelope, its robustness against parametric
variations which occurs in the stability derivatives and to
meet the performance specification like rise time, settling
time with minimum overshoots.
III. CONTROL SYSTEM DESIGN
Sliding mode control uses very high frequency [15] control
input to cope up with the nonlinearity associated with the
plant while stabilizing it. The main benefits of sliding mode
control are the inherent properties and the capacity to divide
higher order and complex problems into smaller tasks of
relatively simpler scope [14]. The mathematical foundation
necessary for controller design is presented in the subsequent
subsection. Consider a general nonlinear system with the
following mathematical form.
x = f (x, t) + b (u, t) + η (x, t) (3)
Where x(t) ∈ Rn is the state vector, u(t) ∈ R is the control
input and y(t) is the output of interest. f : RnR → Rn
1210 2012 24th Chinese Control and Decision Conference (CCDC)
and b : RnR → Rn are measurable nonlinear functions
of time and states. The term η(x, t) is norm bounded
uncertainty. control objective is that the desired output must
track a specific time varying state xd in the presence of
model imprecision, uncertainties and parameter variations on
f(x, t) and b(x, t). For the design purpose a time varying
linear surface s(x, t) is defined as follows
s = C1e+ e (4)
where e = x − xd is the error vector and C is a positive
constant coefficient vector which may be treated as the
performance parameter of the system.
x = f(x, t) + bu(t) + ζ (5)
The time derivative of (4) along the nonlinear system (3),
takes the following form
s = C1(x− xd) + (f(x, t) + bu(t) + ζ + xd) (6)
It is assumed that the term b(x, t) is invertible and the
system is independent of uncertainty. Then the corresponding
equivalent control law becomes
ueq = 1/b {−C1(x− xd)− (f(x, t) + ζ + xd)} (7)
In real applications, systems operate under uncertainties
which may be parametric variations, unmodeled dynamics or
external disturbances. Thus, in order to make the control law
robust against uncertainties a discontinuous term is added
[20] and the final expression of the control law becomes
u = ueq −Ksign(s) (8)
With this control input the s render the form
s = −Ksign(s) + ζ (9)
where K is the switching gain which can be selected accord-
ing to the following expression
K > ‖Cζ(x, t)‖+ α (10)
where α is some positive constant. The control law in (8)
stabilizes the system but the control input bears chattering
phenomenon due to switching imperfections. The local at-
tractivity of the sliding surface can be expressed by the
condition [14].
ss < 0 (11)
If the reachability condition is changed to
ss ≤ −η|s| (12)
Indeed, the control input u with s = Ks + K1sign(s)ensures asymptotic convergence and the above condition is
often replaced by, so called strong or η reachability condition
[14]. The basic theory of the HOSM is the same as that of
SMC but for the HOSM design the constraints that have
to be fulfilled are s = s = s = 0. In order to avoid
chattering, it was proposed to suitably modify the dynamics
within a small vicinity of the discontinuity surface in order to
avoid real discontinuities and at the same time preserve the
important properties of the system as a whole [10]. The main
problem in implementation of HOSM is the unavailability
of derivatives s, s, , s(r−1). Thus the only known exclusion
is so-called ”super-twisting” 2-sliding controller [14], which
needs only measurements of s. The continuous control law
u is constituted by two terms. The first is defined by means
of its discontinuous time derivative, while the other is a
continuous function of the available sliding variable [8]. A
super twisting controller appears in the following form
x = a(t) + b(t)u (13)
and suppose that for some positive constants
C,KM ,Km, UM , ρ and |a| + UM |b| ≤ C, 0 ≤ Km ≤b(t, x) ≤ KM , |a/b| ≤ ρUM , 0 < ρ < 1. The following
controller does not need measurement of x. Let
u = −λ|s|ρsign(s) + u1 (14)
u1 =
{−u |u| > UM
−KSign(s) |u| ≤ UM
}(15)
With Kmα > C and λ sufficiently large the controller
provides for the appearance of a 2-sliding mode x = x = 0attracting the trajectories in finite time. The control u enters
in finite time the segment [−UM , UM ] and stays there.
IV. LEVEL FLIGHT CONTROLLER
Fig. 1. Control System Design
The strategy discussed in the [21] encouraged the authors
to design a new control algorithm in which transient per-
formance is the same but it requires less information in its
implementation. For the previous design technique the extra
data required is the angle of attack α and the vehicles true
air speed in the implementation of the altitude controller
in the external loop. So measurement of these parameters
from sensor or an observer is required to implement the
controller. In both the ways computational complexity is
increased. The new design control strategy is referred as
single surface control strategy (SSS) and provides same
measures of performance and robustness against uncertainties
and delays. Fig. 1 shows the control design of single surface
strategy in which the only sensor data required is the actual
height h, pitch angle θ and pitch rate q.
V. SINGLE SURFACE CONTROL STRATEGY (SSS)
A nonlinear sliding mode controller is developed that
compensates for uncertainties and requires less information.
Instead of developing a two loop control design to solve
the attitude and altitude tracking problem, the controller
in this section is developed using single loop. A robust
2012 24th Chinese Control and Decision Conference (CCDC) 1211
HOSM control method is used to mitigate the chattering and
disturbances. In addition, potential single sliding manifold
achieves the desired height profile and takes pitch rate to
zero. This section describes the first time appliance of the
single surface strategy (SSS) for the Yak-54 UAV. For this
purpose the frequency domain control structure is modified
by adding complexity in the single loop and at the same time
preserving our control objectives.
A. Controller Designing
In SSS, for the altitude control, three different set of
controllers are designed using 1st Order sliding mode control
(SMC), 1st Order sliding mode control with strong reacha-
bility (SMC with SRC) condition and higher order sliding
mode (HOSM) based super twisting algorithm.
a) 1st Order SMC: The control system design proce-
dure includes an SSS (Single Surface Strategy). The single
loop consists of flight path variables which were used to
express maneuvers such as climb, decent and level flight.
Desired height profile is used as input and the controller
tracks the desired angular position and regulates the body
angular rate profile to zero. The design of SMC is pursued
to track the desired height via defining the switching surface
in (16), the switching manifold is designed as such in which
the height is being tracked and the angular position and rates
are adjusted accordingly.
s = (h− hd) + C1θ + C2q (16)
s = h− hd + C1θ + C2q (17)
The expresion for q is
q = (1/Iy)(Iz − Ix)pr − Ixz(p2 − r2) +M (18)
Since cross inertial product Ixz = 0 therefore
q = (1/Iy) {(Iz − Ix)pr +M} (19)
For the equivalent control
M = qCmSc (20)
Simplifying Cm =
X︷ ︸︸ ︷Cm0
+ Cmαα+ Cmu
u
V∞
+Cmδeδe
Y︷ ︸︸ ︷+(Cmq
q + Cmαα)
c
2V∞
(21)
M = q(X + Cmδeδe + Y )Sc (22)
M =
η︷ ︸︸ ︷q(X + Y )Sc+
γ︷ ︸︸ ︷qCmδe
Sc δe (23)
The expression of q has the form
q = (1/Iy) {(Iz − Ix)pr + η + γδe} (24)
The time derivatives of (16) along the aircraft dynamics and
in order to make the control law robust a discontinuous term
is added and the final expression of the control law becomes
as shown
s = ksign(s) (25)
ksign(s) = V Sin(θ − α)− hd + C1q
+C2
Iyy((Iz − Ix)pr + η + γδe)
(26)
The expression for the elevator control input i.e δe takes the
following form
δe = −IyV Sin(θ − α)
C2γ+
Iyhd
C2γ−
C1qIyC2γ
−(Iz − Ix)pr + η
γ−
ksign(s)IyC2γ
(27)
b) 1st Order SMC with SRC: To avoid chattering
and to obtain better results equivalent control with strong
reachability condition (SRC) was designed which reduces
chattering but at the cost of tracking error in the beginning
of the process. The expression of δe with the use of
s = ksign(s) + k1s (28)
ksign(s) + k1s =V Sin(θ − α)− hd + C1q
+C2 {(Iz − Ix)pr + η}
Iy+
C2γδeIy
(29)
The expression for the elevator control input i.e δe takes the
following form
δe =−IyV Sin(θ − α)
C2γ+
Iyhd
C2γ−
C1qIyC2γ
+(Iz − Ix)pr + η
γ−
ksign(s)IyC2γ
−k1sIyC2γ
(30)
c) Super Twisting Algorithm: First order sliding mode
with strong reaching conditions is used to eliminate chatter-
ing but some undesirable oscillations appear in very begin-
ning of the input and the surface converges to vicinity of
zero as shown in Fig. 4. Since in the case of higher order
sliding mode control the discontinuous term is present in
the higher derivatives, the effect of chattering is minimized.
In designing the controller the HOSM is often considered as
better choice due to the very reason that even a discontinuous
term is present it provides a continuous control law and
most important the accuracy of the design is improved. The
sliding manifold defined in (16) is utilized in super twisting
control law (14) and (14). And the expression on δe retains
the following form.
δe = −λ|(h− hd) + C1θ+C2q|ρsign((h− hd)
+ C1θ + C2q) + u1
(31)
u1 =
{−δe |δe| > UM
−ksign((h− hd) + C1θ + C2q) |δe| ≤ UM
}(32)
The sliding manifold depicts the two tasks, controller in the
reaching phase applies force to track the desired reference
height while generating the desired pitch angle and pitch
rate. In the sliding phase the desired reference height is
achieved while pitch angle and pitch rate profiles are adjusted
accordingly. This controller performs far better than the
other two controllers (27), (30), mentioned in the above
discussions.
1212 2012 24th Chinese Control and Decision Conference (CCDC)
B. Simulation
1) Nominal Case with Altitude Change: The objective of
the simulation was to show that the designed controllers were
successful in stabilizing the angular rates and angular posi-
tion. We now proceed to simulations and compare the results
of sliding mode controller (SMC), sliding mode controller
with strong reachability condition (SMC with SRC) and
super twisting algorithm. The input of the system is desired
Fig. 2. Height Tracking and Control Input δe using SMC Laws underNominal Case
reference height profile. Simulation results for following the
reference input in absence of any disturbances or parametric
uncertainties is shown in Fig. 2, Fig. 3 and Fig. 4. From
Fig. 2, it is evident that the reference profile is followed by all
the three controllers very closely. Considerable chattering can
be observed in Fig. 2, and the control input frequently hits the
upper limit in SMC control law design. As we earlier said,
chattering excites the high-frequency unmodelled dynamics,
degrades performance of the system, cause actuator wear, and
even result in instability. In order that chattering be avoided,
we must consider the qualities of HOSM. The HOSM offers
a way to retain transient performance of ideal SMC and
achieve zero steady-state error, without having chattering at
the control input, and this is readily inferred from Fig. 2.
Fig. 3 shows the desired pitch angle required to maintain
the specific height and the accordingly changing pitch rate.
Higher order sliding mode, i.e the super twisting controller
provides much superior performance as compared to popular
methods 1st order sliding mode and 1st order sliding mode
with strong reachability control law’s. The effectiveness of
the super twisting technique in avoiding chattering was also
highlighted. Lastly, before we summarize our results in this
section, we briefly mention that all our simulations have
concentrated on the design of control inputs δe in controlling
Fig. 3. Pitch Angle θ and Pitch Rate q Using SMC Laws under NominalCase
Fig. 4. Surface Convergence Using SMC Laws under Nominal Case
the pitch angle θ and pitch rate q for attaining the desired
level flight.
2) HOSM with Parametric Uncertainty: Further, the ro-
bustness of the HOSM controller in the presence of paramet-
ric uncertainties is validated. Longitudinal stability deriva-
tives are the essential parameters in level flight control
system. These derivatives may contain error due to mod-
eling uncertainties and unmodelled dynamics. Therefore, the
robustness of the controller is verified by inducing parametric
variation in the stability derivatives.
For the robustness analysis of control algorithm authors
decided to induce parametric uncertainty in the stability
derivatives. Fig. 5 and Fig. 6 shows the desired height, the
height attained and automated required pitch angle generated
by the single surface strategy SSS under heavy uncertain
2012 24th Chinese Control and Decision Conference (CCDC) 1213
Fig. 5. Desired Height and Control Input δe with Parametric Uncertainty
Fig. 6. Desired Pitch Angle with Parametric Uncertainty
conditions. By inducing the parametric uncertainty the con-
trol algorithm keeps the output of the system perfect but
at the cost of deteriorating the control input by introducing
oscillations as shown in Fig. 5.
VI. CONCLUSIONS
In this work, a set of different controllers is designed
which can track desired pitch angle and attain reference
height in 6 DOF full flight envelope. We presented a new
approach to the design of pitch-rate control for the lon-
gitudinal dynamics of YAK-54 UAV. This approach is an
application of the Sliding Mode Control technique for robust
regulation of nonlinear system, uniformly in a compact
set of uncertain parameters. The control system has been
developed using Single Surface Strategy (SSS) on the 6 DOF
nonlinear aircraft model. Overall system has been tested via
simulations and it is clear that the system has the capability
of attaining good performance and good robustness. Research
into reconfigurable control and other means of obtaining
increasing robustness and performance continues to march
forward throughout many industries, it is hoped that this
research has taken one step along the path toward a feasible
and elegant solution.
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1214 2012 24th Chinese Control and Decision Conference (CCDC)