Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-Based Predictive Control

Fault Tolerant Flight Control Using
Sliding Modes and Subspace
Identification-based Predictive
Control
Bilal A. Siddiqui (DSU)
Sami El-Ferik (KFUPM)
M. Abdelkader (KAUST)
June 23, 2016 6th Symposium on System Structure and Control (SSSC2016)
ThM21.5

Outline
• Introduction
• Problem Statement
• Fault Tolerant Control Algorithm
• System Modeling
• Simulation Results
Fault Tolerant Flight Control Using Sliding Modes and Subspace
Identification-based Predictive Control
2
SSSC’16

Flight Control Robust to
Faults/Uncertainties
• Aircraft can suffer fatal loss due to
▫ Structural damage
▫ Sensor malfunctioning
▫ Severe Weather Conditions
▫ Untuned Controller due to change in aircraft
dynamics
• Two approaches for Fault Tolerant FCS
▫ Robust control (SMC)
▫ Reconfigurable control (Identification
based MPC)
3Introduction Literature Review Problem Statement SMC-MPC Algorithm System Modeling Simulations Conclusion
SSSC’16

Fault Tolerant FCS Literature
• Multiple model-based adaptive estimation and
control [Maybeck 1991]. Model reference adaptive
control based on RLS parameter identification
[Shore 2005].
• Model predictive control (MPC) [Kale 2004].
• Multi-model fault detection and optimal control
allocation [Urnes 1990].
• Sliding Mode Control (SMC) based control
allocation [Edwards 2010]
SSSC’16

Problem Statement
• Nonlinear Dynamics of Aircraft
• Physical Constraints on Under-actuated System
• For applying multi-variable SMC, consider a square subset of the
output space ,such that the remaining outputs are stable
•
• The above requirement is not conservative if y2(t) can be stabilized as it is
common in aerospace cascaded autopilot design. A slower outer loop for
controlling y2(t) which produces virtual commands in terms of y1(t) can serve
as the desired trajectory for a faster inner loop controlling y1(t). In such a case,
the loops have to obey some time scale separation.
5Introduction Literature Review
Problem
Statement
SMC-MPC Algorithm System Modeling Simulations Conclusion
SSSC’16
Modelling uncertainty,
fault, disturbance etc Measurement Noise

Proposed Fault Tolerant Algorithm
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Aircraft Dynamics
Sensors
Denoising
Filters
Actuators
Sliding
Mode
Control
(Inner
Loop)
Nominal
Model
Model
Identification
Model
Predictive
Control
(Outer
Loop)

System Modeling
• Aircraft model used is the nonlinear model of an F-16, based on
extensive wind-tunnel tests, represented in polynomial form
using global nonlinear parametric modelling based on
orthogonal functions.
• Control limits
• Inertial Measurement Unit for linear accelerations, 3σ = 0.06 g,
Gyro measurements for Euler’s angles, 3σ = 0.35°, Air Data
Probe providing measurements of angles of attack and sideslip,
3σ = 0.15° and forward speed, 3σ=0.1m/s.
• For angular rates, we assumed military grade sensors providing
3σ = 1°/hr [25]. The sensor noise was simulated as band-limited
white noise with correlation time Tc=10.5ms (much smaller than
the system bandwidth).
• The aircraft is flying level initially at a pitch angle of 10°, at a
speed of 160 kts and an altitude of 6km.
SSSC’16

System Modeling
SSSC’16

Nominal Model
• We will assume that the
aerodynamic coefficients are
known with an accuracy of
20% only.
• This uncertainty may be
because of structural
damage, as it is ‘big’ enough
to cater for quite off nominal
conditions
9Introduction Literature Review Problem Statement SMC-MPC Algorithm
System
Modeling
Simulations Conclusion
SSSC’16
Table 2 Best Estimates of Parametric Values
Param. % Error in Estimate Value (% of nominal values)
xy x1 x2 x3 x4 x5 x6 x7 x8
ay -20.1 0.5 11.7 -5.3 -8.9 10.7 -4.4 ----
by 9.4 2.5 1.5 -8.6 6.7 ---- ---- ----
cy -8.1 4.2 0.7 ---- ---- ---- ---- ----
dy -2.7 3.5 1.3 -6.2 ---- ---- ---- ----
ey 0.7 12.7 6.3 -0.2 ---- ---- ---- ----
fy -1.4 -7.0 2.6 -5.9 4.1 -0.1 ---- ----
gy -3.5 -8.6 3.9 -1.5 17.8 ---- ---- ----
hy -2.9 -19.9 -8.2 8.7 9.9 0.5 -7.2 -5.8
iy -2.2 -0.7 0.4 -2.9 ---- ---- ---- ----
jy 2.3 16.2 -6.7 5.8 -4.3 ---- ---- ----
ky -4.0 -4.2 4.4 0.2 11.4 -2.4 -7.8 ----
ly 8.0 -10.7
-
11.6
-14.6 3.7 -7.7 -2.7 ----
my -11.2 8.1
-
10.5
-11.9 6.1 6.8 6.2 9.1
ny -3.3 -0.4 -2.1 4.9 -7.7 0.1 ---- ----
oy 10.7 2.2 -9.0 -7.8 -2.5 0.9 3.4 ----
py 18.5 -17.5 0.6 5.6 8.5 ---- ---- ----
qy 9.2 -4.6 -3.7 ---- ---- ---- ---- ----
ry -7.5 3.5 0.4 1.3 -7.3 3.7 6.2 -4.2
r9,10 7.8 -3.8 ---- ---- ---- ---- ---- ----
sy -4.9 -1.1 9.4 0.4 -6.7 0.1 ---- ----

Inner Loop SMC
• The inner loop represents the controller for
tracking virtual commands in angular rates
y1=[p,q,r] produced by the outer loop.
• We define the sliding surfaces as
SSSC’16
1
0 0 0
32
s (p,t)= +0.1 dτ, s (q,t)= +0.3 dτ, s (r,t)= +0.25 dτ
t t t
p p q q r r  
 eq
1-
ˆ+K hgu u dsat(s)=
1
0 s
s 1
1 s
ds
1
at(s)=
1
s
s
  
 
  




 
    


Kp=Kr=0.4 and Kq=4
d d d
2 2 2
p 4q 0.81r
p(s)= , q = , r =
s +2s+1 s +
(s) (s) (
3s+4 s +1.
s)
(s)
8s+
(s)
0.81
Command
Filter
Deadzone for
chattering

Equivalent Control
SSSC’16
a,eq
4 3 22
4 3 2 1 0
a xz x 2 3 2
x 3 2 1 0
2
xz x z y z xz x
2 2xz
2 1 02
z xz x 2 4 3 2
4 3 2 1 0
ˆ ˆ ˆ ˆ ˆr(j j j j j )QSb
p I pq / I
ˆ ˆ ˆ ˆ2VI p(i i i i )
I pq / I I qr (I I )(pq I qr / I )
2VI
ˆ ˆ ˆQSb (q q q )
(I I / I )
ˆ ˆ ˆ ˆ ˆQSb (p p
r
p p )p p
 
        
  
        
   
    

        


%
y z
x
3 2 3 2
x 7 6 1 0 xz 6 3 1 0
xz 2
2 3 2xz x
x xz x 6 3 1 0
xz
2
I I
qr
I
ˆ ˆ ˆ ˆˆ ˆ ˆ Î (r r r r ) I (k k k k )
QSbI
(Iz I / I ) ˆ ˆ ˆ Î (Iz I / I ) (k k k k )
I
 
 
 
 
 
 
 
 
  
             
 
      
 
 
 
 
 
 
 


     -1
1eq 1 1,
û h f -ˆ +λ, =- hg λdy yy & %%

Close-Loop System Identification
• For MPC in outer loop, we must have a prediction model
for the inner loop closed loop plant.
• While the relationship between Euler angles <φ,θ,ψ>ε y1
and body angular rates <p,q,r> ∈ y1 is a well known
nonlinear kinematic relation , the relation with flow angles
<α,β>∈y2 depends on the vehicle’s aerodynamics.
• Aircraft is persistently excited with PRBS inputs (pd,qd,rd).
• Using the N4SID (Numerical Algorithms for Subspace
State-Space System Identification) method, two discrete
state-space models were identified (θ0=α0=10°), one for
longitudinal mode, and another for lateral
SSSC’16

Close-Loop System Identification-2
SSSC’16

Outer Loop MPC Controller
• Even though the models identified are valid in the vicinity
of the initial conditions, due to the inherent robustness of
MPC, the models were seen to be adequate for the flight
envelope, even for aggressive maneuvers.
• The constraints placed on manipulated variables are
|y1,d|≤60°/s. Output variables were constrained at -10°
≤(α-α0)≤35° and |β| ≤ 5°.
• Weights on the inputs were Rc=1 for each input, while the
weights on outputs were 10 on each of φ and β, 50 for θ, 20
for α
• Prediction horizon was 1 sec, and the control horizon was
0.25 sec for both long/lat controllers.
SSSC’16

Simulation Results
• Several simulations were performed to show robustness
and fault tolerance in the event of
▫ parametric uncertainty
▫ measurement noise
▫ severe wind turbulence
▫ strong gusts
▫ actuator/sensor faults
• Very aggressive combat-like maneuvers were
considered.
SSSC’16

Simulation 1 – Air Combat Maneuver
with Parametric Uncertainty
• Minute long air-
combat-maneuvre
(ACM) involving 40°
banking reversals
followed by a pitch-
up to 45°, typical of
dog-fights, showing
robustness to
parametric
uncertainty and
measurement noise.
SSSC’16

Simulation 2 – Severe Turbulence
Bank to bank reversals in severe wind turbulence of 3σ = 35
knots as specified in (MIL-F-8785C ) standards
SSSC’16

Simulation 3 – Severe Cross-Wind and
Gusts
• FAR.25 specifications
for cross-wind and
gust tolerance are 25
knots
• We consider severe
gusts of 30 knots in
horizontal and vertical
direction and a severe
cross wind of 50 knots
during the 45° pitch-
up maneuver.
SSSC’16

Simulation 4 – Sensor Fault
• Pitot-system for measuring
airspeed often malfunctions,
and is responsible for some
major air disasters.
• Effect of pitot blockage is
simulated by fixing sensor
readings α=10° and β=0°,
altitude reading to be fixed
at 6km and airspeed
indicator to read a constant
airspeed of 70 knots which
is much below the stall
speed (110 knots), and 40%
of the actual speed (160
knots), which are typical
results of pitot blockage
SSSC’16

Simulation 5 – Control Surface Loss
• The level of fault tolerance is
inversely proportional to the
usage of the control surface for
that maneuver in the healthy
aircraft’s case.
• A 50% loss of control surface
area of all three surfaces, i.e.
elevator, rudder and aileron is
considered.
• ACM task was achieved with the
same performance as the
undamaged case.
• Actuators were saturated for
longer periods, which suggest
that instability may occur if
more aggressive maneuvers,
particularly in severe gusts and
turbulence are attempted.
SSSC’16

Thankyou
• Thankyou.
• You are welcome to question.
• airbilal@dsu.edu.pk
SSSC’16

Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-Based Predictive Control

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Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-Based Predictive Control