1. Bilal A. Siddiqui (DSU) Sami El-Ferik (KFUPM) M. Abdelkader (KAUST)
ThM21.5
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)

2. 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
SSSC’16

3. Flight Control Robust to Faults/Uncertainties
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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
SSSC’16

4. Fault Tolerant FCS Literature
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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]
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

5. Problem Statement Nonlinear Dynamics of Aircraft
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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.
Modelling uncertainty, fault, disturbance etc
Measurement Noise
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

6. Proposed Fault Tolerant Algorithm
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
Proposed Fault Tolerant Algorithm
Model Identification
Nominal Model
Model Predictive Control (Outer Loop)
Sliding Mode Control (Inner Loop)
Aircraft Dynamics
Actuators
Denoising Filters
Sensors
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

7. Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

8. System Modeling Introduction Literature Review Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
System Modeling
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

9. Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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
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
12.7
6.3
-0.2 fy
-1.4
-7.0
2.6
-5.9
4.1
-0.1 gy
-3.5
3.9
-1.5
17.8 hy
-2.9
-19.9
-8.2
8.7
9.9
-7.2
-5.8 iy
-2.2
-0.7
0.4 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 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
0.1 oy
2.2
-9.0
-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
-7.3
r9,10
7.8
-3.8 sy
-4.9
-1.1
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

10. Deadzone for chattering
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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
Deadzone for chattering
Command Filter
Kp=Kr=0.4 and Kq=4
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

11. Equivalent Control Introduction Literature Review Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
Equivalent Control
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

12. Close-Loop System Identification
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

13. Close-Loop System Identification-2
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
Close-Loop System Identification-2
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

14. Outer Loop MPC Controller
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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 sec for both long/lat controllers.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

15. Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

16. Simulation 1 – Air Combat Maneuver with Parametric Uncertainty
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

17. Simulation 2 – Severe Turbulence
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
Simulation 2 – Severe Turbulence
Bank to bank reversals in severe wind turbulence of 3σ = 35 knots as specified in (MIL-F-8785C ) standards
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

18. Simulation 3 – Severe Cross-Wind and Gusts
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

19. Simulation 4 – Sensor Fault
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

20. Simulation 5 – Control Surface Loss
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
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.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16

21. Thankyou Thankyou. You are welcome to question. airbilal@dsu.edu.pk
Introduction
Literature Review
Problem Statement
SMC-MPC Algorithm
System Modeling
Simulations
Conclusion
Thankyou
Thankyou.
You are welcome to question.
Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-based Predictive Control
SSSC’16