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

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

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Outline•Introduction

•Problem Statement

•Fault Tolerant Control Algorithm

•System Modeling

•Simulation Results


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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)Fault Tolerant Flight Control Using Sliding Modes and Subspace

Identification-based Predictive Control

Introduction

Literature Review

Problem Statement

SMC-MPC Algorithm

System Modeling

Simulations Conclusion

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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]


Introduction Literature Review

Problem Statement

SMC-MPC Algorithm

System Modeling


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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.



Problem Statement

SMC-MPC Algorithm

System Modeling


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Modelling uncertainty, fault, disturbance etc

Measurement Noise

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Proposed Fault Tolerant Algorithm



Problem Statement SMC-MPC Algorithm System

ModelingSimulations Conclusion

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Aircraft Dynamics

SensorsDenoising Filters

Actuators

Sliding Mode

Control (Inner Loop)

Nominal Model

Model Identificatio

n

Model Predictive Control

(Outer Loop)

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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=0.06g,

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.



Problem Statement

SMC-MPC Algorithm

System Modeling


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System Modeling



Problem Statement

SMC-MPC Algorithm

System Modeling


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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


Introduction Literature Review Problem Statement

SMC-MPC Algorithm

System Modeling


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Table 2 Best Estimates of Parametric ValuesParam.

% 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 -4.2r9,10 7.8 -3.8 ---- ---- ---- ---- ---- ----sy -4.9 -1.1 9.4 0.4 -6.7 0.1 ---- ----

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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





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10 0 0

32s (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

eq1-ˆ+K hgu u dsat(s)=

10 s

s 1

1 s

ds1

at(s)=1

ss

Kp=Kr=0.4 and Kq=4 d d d

2 2 2

p 4q 0.81rp(s)= , q = , r =

s +2s+1 s +(s) (s) (

3s+4 s +1.s)

(s)8s+

(s)0.81

Command Filter

Deadzone for chattering

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Equivalent Control





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a,eq

4 3 224 3 2 1 0

a xz x 2 3 2x 3 2 1 0

2xz x z y z xz x

2 2xz2 1 02

z xz x 2 4 3 24 3 2 1 0

ˆ ˆ ˆ ˆ ˆr( j j j j j )QSbp I pq / Iˆ 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 2x 7 6 1 0 xz 6 3 1 0

xz 22 3 2xz x

x xz x 6 3 1 0xz

2

I Iqr

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 & %%

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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>εy1

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





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Close-Loop System Identification-2





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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.





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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.



Problem Statement

SMC-MPC Algorithm

System Modeling


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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.



Problem Statement

SMC-MPC Algorithm

System Modeling


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



Problem Statement

SMC-MPC Algorithm

System Modeling


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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.



Problem Statement

SMC-MPC Algorithm

System Modeling


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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



Problem Statement

SMC-MPC Algorithm

System Modeling


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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.



Problem Statement

SMC-MPC Algorithm

System Modeling


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Thankyou• Thankyou.• You are welcome to question.• [email protected]



Problem Statement

SMC-MPC Algorithm

System Modeling


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mailto:[email protected]

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

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