Fault tolerant controller design for component faults of

The 8th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2011) Nov. 23-26, 2011 in Songdo ConventiA, Incheon, Korea

Fault tolerant controller design for component faults of a small scale unmanned aerial vehicle Vishnu Kumar Kaliappan1, Hanmaro Young2, Agus Budiyono3, and Dugki Min4*

1,2,4

School of computer Science and Engineering, Konkuk University, Seoul, 143-701, Korea (Tel : +82-2-450-3490; E-mail: [email protected], {maro1076,dkmin}@konkuk.ac.kr) 3 Department of Aerospace Information Engineering, Konkuk University, Seoul, 143-701, Korea (Tel : +82-2-450-3817; E-mail: [email protected]) Abstract - In this paper additive fault detection and isolation method coupled with fault tolerant control architecture are developed in order to deal with component faults for a rotorcraft based unmanned aerial vehicle (RUAV). The failure considered is malfunction with internal components of the helicopter which occurs during the maneuvers: rotor angular rate variations, etc. These faults lead from trivial to catastrophic damage of the system. The proposed fault detection and reconfiguration control is based on a parameter estimation approach which drives a reconfigurable control system (RCS) build with the Pseudo-inverse method. The complete setup is implemented under Hardware-in-the-loop-simulation (HILS). The PC104 board with QNX RTOS platform is used for simulation. Simulation results illustrate the efficiency and effectiveness of the proposed approach. Keywords –Fault tolerant controller, unmanned aerial vehicle, pseudo-inverse method, and reconfigurable controller.

1. Introduction The Unmanned aerial vehicles are essentially useful not only for military application, but also for civil purpose [1] like exploring unknown environment, mapping the terrain [2], cooperative fire detection[3], autonomous deployment of sensor network for civil monitoring system [4] and more. In many applications the usefulness of the aerial vehicles is the best way to get information or to deploy equipment without any interaction of human. To accomplish this application successful there must be highly efficient autonomous intelligent infrastructure for autonomous control systems. Even if the system is highly efficient the fault is normal cause in dynamically changing environments. It is vital to develop an autonomous fault identification and adaptation operation when carrying out such operations. Moreover, rotor-craft do not tolerate like fixed wing aircraft in the case of fault. Thus, a small failure in any part of the system leads to catastrophic damage. It is necessary to monitor their status so that faults may be addressed before the result in massive failures. Fault detection and identification technique has been widely used in aerospace field to detect component, sensor and actuator faults. If the fault has been detected the controller can be changed to get the best possible response. Several methods have been used for FDI in UAVs. Neural network is used to detect * Dugki Min is a corresponding author to provide phone: 82-2-450-3490 email:[email protected]

the sensor faults [5,6] and more complete fault detection methods is reported in [7]. In this paper, fault tolerant controller design for component faults is investigated. The fault detection model is obtained with parameter based identification method. Fault detection model is implemented with intelligent multi-layered architecture used for JR Voyager G-260 RC helicopter.

2. Rotorcraft based unmanned aerial vehicle (RUAV) Model The equation of motion for the small scale helicopter is adopted from our previous research [8]. The dynamics can be derived from the law of linear and angular momentum in the form of Euler-Newton equations as follows: K JK dV m =F dt I (1) K JJK K dω =M I dt I K K With F = [ X , Y , Z ]T and M = [ L , M , N ]T are the vector of total forces and moments acting on the helicopter center of gravity. These total force and moments are generated by the main rotor, tail rotor, fuselage, horizontal fin and vertical fin, and also gravitational force. The motion of the vehicle in three-dimensional space is represented by the position of the center of mass and the Euler angles describing the vehicle attitude. Equation.1 can be presented with respect to body coordinate system as the following equations. K K K K mV + m (ω × V ) = F (2) K K K K I ω + m (ω × I ω ) = M K

With vector V = [ u , v , w ]T and ωK = [ p , q , r ]T are the vehicle velocities and angular rates in body coordinate system. For the helicopter moving in six degrees of freedom, the above equations produce six differential equations describing the vehicle’s translational motion and angular motion in three references axes. X MR + X TR + X fus = m ( u − rv + qw) + mg sin θ

YMR + YTR + Y fus = m ( v − pw + ru ) − mg sin ϕ cos θ

Z MR + ZTR + Z fus = m ( − w − qu + pv ) − mg cos ϕ cos θ

(

)

LMR + LTR + L fus = I xx p − I yy − I zz qr M MR + M TR + M fus = I yy q − ( I zz − I xx ) pr

(

(3)

)

N MR + NTR + N fus = I zz r − I xx − I yy pq

ϕ = p + ( q sin ϕ + r cos ϕ ) tan θ θ = q cos ϕ − r sin ϕ ψ = ( q sin ϕ + r cos ϕ ) sec θ For small scale helicopter the equations are represented by the rigid body dynamics appended by the dynamics of the main rotor. It can be shown that the dynamics is dominated by the contribution from the rotor systems. Thus the aerodynamics modeling of the rotor plays a major role in determining the accuracy of the modeling. Using the simplest approximation from the tip-path plane theory with uniform inflow model, the main rotor thrust equation can be obtained by the following expression. 2 2 (4) TMR = ρ ( ΩR ) MR π R C MR TMR Where the thrust coefficient is given by:

( )

⎡1 ⎤ μ zMR − λ0 MR ) + ⎥ ( ⎢ 1 2 CT = aMRσ MR ⎢ ⎥ MR 2 ⎢⎛ 1 + 1 μ 2 ⎞ θ ⎥ ⎢⎣⎜⎝ 3 2 MR ⎟⎠ 0 MR ⎥⎦ λ0 MR =

μ MR =

CT wiMR MR = 2 2 (ΩR ) MR 2η w μ MR + (λ0 MR − μ zMR ) 2 2 u a + va (ΩR ) MR

μ zMR =

wa (ΩR ) MR

The torque of main rotor can be expressed as below 2 2 QMR = ρ ( ΩR ) MR π R R C (5) MR MR QMR 1 ⎛ 7 2 ⎞ = σ MR ⎜ 1 + μ MR ⎟ C D MR + CQ 3 0 MR 8

( ) ⎝

( λ0MR − μ zMR ) CTMR

⎠

Tail rotor thrust and normal velocity component to the tail rotor can be expressed by the following equation: TTR = mYδ δ r + mYv vTR r (6) vTR = va − lTR r + hTR p The tail torque will be as below 2 2 QTR = ρ (ΩR )TR (π R )TR RTR CQTR (7) The expressions for main rotor flapping motions are:

τ e a1s = − a1s +

∂a1s ∂a1s ua + ∂μ MR (ΩR ) MR ∂μ zMR

wa + … − τ e q + Aδ δ (ΩR ) MR Long Long

τ eb1s = −b1s − Bδ Where aBδ

∂b1s va −τe p + ∂μ MR (ΩR ) MR

δ Long Long

Long

, Aδ

Long

are the steady-state lateral and

longitudinal gains of the main rotor flap angles.

3. Fault modelling Faults are event that take place in different parts of the helicopter. In general the faults are classified according to the location of occurrence in the system, they are actuator faults, sensor faults and components fault [9]. Actuator faults represent the partial or total loss of the control action. Sensor faults denote the incorrect readings from the sensor or failure of the sensor itself. Finally component faults occur if there is any change in internal component. Further, the faults can be modeled in two ways; they are additive faults and multiplicative faults. The additive faults can be modeled for component faults in the system, while the multiplicative faults are suitable for sensor and actuators. In this paper we focus more on additive faults. For instance the linear parameter-varying system can be formulated by the following state space representation x (t ) = Ax (t ) + Bu (t ) (8) y (t ) = Cx(t ) Where A, B, C are matrices of appropriate dimension and u is the inputs variable, y is the output measurable variables. If the changes f a of the states x (t ) and f m of the output y (t ) then, Eq. (8) can be written with state-space model S a with additive faults as ⎧ x (t ) = Ax(t ) + Bu (t ) + Ff a (t ) (9) Sa ⎨ ⎩ y (t ) = Cx(t ) + Ef m (t ) m Where f a , f m is the fault vectors. f a ∈ \ is a parameter vector representing the component faults.

3. Intelligent RUAV fault tolerant architecture 3.1 Intelligent architecture

In the following, the fault tolerant system is developed as a part of intelligent RUAV architecture described in [10]. The architecture for unmanned helicopter consists of two levels as exemplified in Fig.1. (a) High Level: Guidance and navigation (GnC) in which planning routine, the waypoint, mission tasks from command center are executed. (b) Low Level: Reconfigurable flight control stabilizes the flight and follows the command trajectory from upper layer. Each of the layers are described below.

Fig. 1. Intelligent reconfigurable multilayered architecture [10].

A. High Level: Guidance and navigation (GnC) Guidance and navigation component translates a high level mission task to low-level task. The mission can be accomplished as a sequence of action like fly to a desired destination and hover, while flying maintain same velocity, avoid obstacle in between the waypoints. In this layer the steering behavior control for obstacle avoidance is adopted from our previous research [11].

B. Low Level: Reconfigurable flight control The purpose of the low level controller is to stabilize the vehicle and force it to follow the commanded trajectory generated by the high level controllers. This is achieved by limiting the control vector with state feedback gain. The forward speed hold system is realized by the following commands respectively.

( ) δ lat = k ∅ ( ∅ cmd − ∅ ) + k q .q δ lon = kθ θ cmd − θ + k q .q

(10) (11)

While, the altitude and heading hold system is achieved by command control in the collective and rudder channels as follow δ col = kh.hcmd (12)

δ rud = kψ .ψ cmd

(13)

3.1 Fault detection, isolation and reconfiguration

Fault detection, isolation and reconfiguration is to identify, isolate the probable fault and reconfigure the

control to stabilize the system. The detail of fault detection identification and reconfiguration control is follows. The component failure detection can be achieved by detecting variation in the angular rates. The flow diagram of fault detection reconfiguration is exemplified in Fig.2. The fault detection method uses the sliding window data from the flight dynamics. It detects the faults by measuring the rate of change of data with respect to time. Assume the LPV (linear parameter varying) systems faults are detected with the following

⎛ dy p (t ) − uci (t ) ⎜ dt ⎝

Sr (t ) = max ⎜

⎞ ⎟⎟ ⎠

(14)

⎧⎪0 if sr (t ) < T D(r ) = ⎨ ⎪⎩1 if sr (t ) > T Where dy p (t ) is the output produced by the dynamics as a function of time t . Diagnostic signal D (r ) takes the value of one if the threshold value T has been exceeded. Fault isolation is to make decision about the appearance of a specific fault with simple threshold logic. FI i > Ti → rpi (t ) ≠ 0 where i ∈ {1, 2, ...., L}

Where L is the total number of faults ( fi ) to be isolated and Ti (i = 1, 2,..., L ) are the threshold corresponding to residuals rpi (i = 1, 2,....., L ) .Reconfiguration is achieved with PIM (pseudo-inverse method) [12]. To provide graceful degradation in the case of failure, the state feedback gain K can be reassigned. Normal closed loop system can be defined as x (t ) = ( Ax(t ) + Bu (t ) K ) (15) y (t ) = Cx(t )

Assume the closed-loop dynamic model, in which failure occurs is given as

computer, GcS (Ground control Computer) and 6-DOF simulator (plant model).The bridging application uses a simulation library to communicate with FlightGear and connects to the embedded PC104 board, emulating the inputs and outputs from the helicopter model. FCC outputs raw data in packed binary identical to the packet produce by the Flightgear and helicopter model. It also accepts command outputs from GCS. This provides a realistic test of remaining components of the system. The FlightGear forwards a raw data to FCC. The given data are in engineering unit. Therefore, the HIL Bridge application must perform reverse conversion on the data before sending it to the PC104 embedded board. Similarly the control surface position received from the embedded board is in raw format the HIL Bridge converts normalized positions to helicopter plant model.

Fig. 2. Flow diagram of fault injection, detection and reconfiguration process

x (t ) = ( Ax(t ) + Bu (t ) K ) + Ff a (t )

(16) y (t ) = Cx(t ) + Ef m (t ) Where K is the state feedback gain, the new close-loop system can be in the form of x (t ) = ( A x(t ) + B u (t ) K ) f f f f (17) y (t ) = C x(t ) f f Where K f is the new feedback gain. The approximate solution of the system for K f is given by K = B u (t )+ ( Ax(t ) − A x(t ) + Bu (t ) K ) (18) f f f Where B f u(t )+ is pseudo-inverse of B f u (t ) . K f is calculated for many probable failures and stored in the flight control computer (FCC).

4. Experimental test bed The system infrastructure is setup to emulate a fully integrated RUAV. In cases like real time testing, most effective method to build an embedded system is to bond embedded system to real plant. Most of the system cannot be validated in real time due to the cost effectiveness. There are numerous approach used to validate control system, among that HILS (Hardware-in-the-Loop Simulation) is a well-known method. One of the HILS systems we developed used pc104 based xPC target as a controller unit [13]. This section describes the details of development of simulation environment based on real-time operating system QNX neutrino. Hardware-in-the-Loop for autonomous system, as shown in Fig.3 composed of four independent systems. They are flight visualization computer and sensor data emulator (FlightGear), QNX based autopilot embedded

Fig. 3. Software architecture for HILS (Hardware- inthe-Loop Simulation) Flightgear is an open-source flight simulator developed and maintained by Curt Olson. FlightGear objective is to create a professional flight simulator framework to use in both academic and research environments. In this work the FlightGear was investigated to develop cost effective environment for testing our control algorithms which equal to real time testing. More complete platform setup is briefed in [14].

5. Experimental test results In this section the experimental test results of RUAV fault tolerant controller is discussed. To test our designed controller the fault in main rotor angular rate is considered. When there is any change in the rotor angular rate, the RUAV’s heading and altitude hold system affects instantaneously. These faults occur due to the wear and tear of bearing in rotational equipment, friction due to lubricant deterioration, tooth breakage and crack in gear of a gearbox system, etc. Aforementioned faults may have trivial to catastrophic damage to the system.

The 8th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2011) Nov. 23-26, 2011 in Songdo ConventiA, Incheon, Korea

Table 1 Feedback gain with respect to component faults Number

1 2 3 4 5 6

Fault injection Main rotor angular rate

Reconfiguration Stability feedback gain Forward speed hold

Altitude hold

Heading hold

Ωcom

Kh

K dh

KΨ

Ki

K cp

K ci

Kθ

Kq

K cp

K ci

Kφ

Kp

129.8021 119.8021 115.8021 110.8021 104.8021 100.8021

0.01 0.01 0.01 0.025 0.034 0.050

-0.01 -0.01 -0.01 -0.025 -0.034 -0.050

0.45 0.45 0.50 0.75 0.95 1.80

0.02 0.02 0.03 0.0351 0.040 0.040

0.05 0.05 0.05 0.05 0.05 0.05

0.001 0.001 0.001 0.001 0.001 0.001

0.3 0.3 0.3 0.3 0.3 0.3

-0.02 -0.02 -0.02 -0.02 -0.02 -0.02

0.1 0.1 0.1 0.1 0.1 0.1

0.002 0.002 0.002 0.002 0.002 0.002

0.3 0.3 0.3 0.3 0.3 0.3

-0.01 -0.01 -0.01 -0.01 -0.01 -0.01

Thus, it is extremely crucial to diagnose these faults at early stages in order to avoid catastrophic damages to the system. The main aim is to detect smaller variation in the system and make the RUAV to stabilize. After stabilizing the system, RUAV check for the landing zone and executes the landing sequence. We utilized our previously developed auto-landing algorithm [14]. Fault f p was injection to the dynamic model which makes RUAV to oscillate its assigned trajectory Fig.4. The time based software fault injection method is used to add faults to the dynamic engine. Based on the fault, controller should respond and reassign its state feed-back gain to stabilize the controller. These gains are calculated with pseudo inverse methods and few with trial and error method. Table.1 illustrates the feedback gain for component faults.

Side speed hold

feedback gain to the new predefined gain. From Fig.5 and Fig.6 at time 2100 seconds the RUAV executes normal trajectory even the RPM of the helicopter is at 110.8021 rad/sec. For understanding the fault clearly, the delay of 700 S is added after fault detection process.

Fig. 5. Response of control signals in the occurrence of fault and reconfiguration

Fig.4. Trajectory generated by RUAV during the execution of waypoints During the course of flight the additive faults are injected to the internal component of the RUAV. Due to the fault, RUAV’s angular rate reduces from 129.8021 rad/sec to 110.8021 rad/sec. Figure. 5 (a) shows the change in engine speed at time 1400 seconds. Due to the change in engine speed the Heading and altitude of the RUAV distracted. From Fig.4 it is clear that when the fault is injected, the RUAV misalign to its trajectory. Base on the angular fault the other controller angular rate is changed Fig.6. The Fault detection module detects the engine speed fault and flags the ID. Based on the flag ID the reconfiguration manager module Fig.1. reassign the

Fig. 6. (a) Engine speed, (b) side velocity, (c) pitch angle, (d) Roll angle

5. Conclusion Autonomous helicopter need highly efficient autonomous intelligent infrastructure for autonomous control systems. This intelligent control system should focus more about safety condition to avoid potential accidents. Fault detection, isolation and reconfiguaration control plays an important role in this context. This paper has presented a design of fault tolerant control using parameter based estimation method and reconfiguataion with pseudo-inverse method. Experiment with HILS based on QNX RTOS with PC104 has conducted. Several faults are generated using software algorithm. The FDI system has detected the injected fault at rotor angular rate and stabilized the system by reconfiguring the feedback gain. Our simulation result proves that robustness and efficiency of the proposed approach.

Acknowledgement This work was supported by the Konkuk University in 2010.

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