hardware -in -the -loop simulation for an uav...

American Institute of Aeronautics and Astronautics1

Hardware-In-The-Loop Simulation for an UAV Example

H. Tam* and H.H.T. Liu†

University of Toronto, Toronto, Ontario, M3H 5T6, Canada

and

C.A. Rabbath‡

McGill University, Montreal, Quebec, H3A 2K6, Canada

This paper presents a hardware-in-the-loop simulation for a UAV digital flight controller. In asimplified flight mission, the hardware-in-the-loop simulations validate the controller design. TheKalman filter is employed to demonstrate the possibility in performance improvement for the digitalcontrol implementations.

Nomenclatureu = X-axis speed component of the body-axis frame (m/s)v = Y-axis speed component of the body-axis frame (m/s)w = Z-axis speed component of the body-axis frame (m/s)p = Roll Rate (rad/s)q = Pitch Rate (rad/s)r = Yaw Rate (rad/s)φ = Bank Angle (rad)θ = Pitch Angle (rad)ψ = Heading (rad)VA = Airspeed (m/s)α = Angle of Attack (rad)β = Sideslip Angle (rad)h = Altitude (m)δe = Elevator Deflection (rad)δp = Throttle Deflection (rad)δa = Aileron Deflection (rad)δr = Rudder Deflection (rad)tr = Rise Time (seconds)ts = Settling Time (seconds)Mp = Percent Overshootτe = Time Constant for Elevator Servo (seconds)τp = Time Constant for Throttle Servo (seconds)τa = Time Constant for Aileron Servo (seconds)τr = Time Constant for Rudder Servo (seconds)

I. IntroductionNINHABITED aerial vehicles (UAVs) have drawn considerable attention in both civilian and military

applications and their flight control system development is of our interest. The University of Toronto Institutefor Aerospace Studies (UTIAS) is in the process of developing an UAV for teaching and research purposes. Usingthis model, we conducted preliminary work on the autopilot design for multiple design specifications. Our previouswork reported in Ref. 4 addressed the implementation challenges associated with quantization and discretization,especially at low-resolution and sampling rates. In this paper, we present the hardware-in-the-loop simulationresults to demonstrate the controller implementation and validation process.

* Research Assistant, Institute for Aerospace Studies, 4925 Dufferin Street, AIAA Member† Associate Professor, Institute for Aerospace Studies, 4925 Dufferin Street, AIAA Member‡ Adjunct Professor, Department of Mechanical Engineering, 817 Sherbrooke Street West

U


Quantization and discretization pose significant challenges to digital controller design. Low sampling rates, non-linear quantization behavior, large transients, and instability are some challenges among them. In order to improvethe performance, an optimal observer is used in the digital controller development. The Kalman filter isimplemented and presented in this paper. Simulation results are compared with previous simulation results.

The rest of this paper is organized as follows. In Section II, the previous research work on multi-objectivecontroller design and its digital implementation are summarized. The hardware-in-the-loop simulation test-bed andits setup along with evaluation methods are presented in Section III. Simulation results are also included. Finally, theconcluding remarks and future work are addressed in Section IV.

II. Multi-Objective Description Control and Its Digital ImplementationThe controller design involved a longitudinal and a lateral autopilot. The longitudinal controller is responsible

for airspeed and altitude while the lateral controller is responsible for the sideslip angle and heading. The proposedcontroller must meet a set of multiple objective requirements and be able to follow the desired trajectory insimulations. The eigenstructure assignment (EA) technique was adopted for this purpose. Details were presented inRef. 4. The equations of the longitudinal and lateral flight vehicle system are given as follows:

x Ax Bu

y Cx

= +=

&(1)

iu Ky K r= − − (2)

( )x A BKC x BK ri= − −& (3)

where K K Kp i= M ,

c

c

VArh

∆∫=

∆∫

,

p

u

w

q

hx

e

VAh

θ

δδ

∆

=∆∆

∆∫

∆∫

&

&

, and

VA

q

y

h

VAh

α

θ

∆

=

∆∫

∆∫

for longitudinal mode,

and c

cr

β

ψ∫

∫=

,

v

p

r

x

a

r

φψδδβψ

=∆∆

∫∫

&

&

, and

p

r

y

β

φψβψ

=

∫∫

for lateral mode.


III. HIL Simulation

A. Hardware-In-The-Loop (HIL) Test-bedA computer cluster delivered by Opal-RT Technologies is

used as a real-time system simulator at UTIAS. This systemconsists of four real-time nodes running on QNX6 and threehost computers running on MS Windows 2000. It is able toconduct hardware-in-the-loop simulation with real-time userinteraction. The IO channels include digital IO, analog todigital (A/D), digital to analog (D/A), timer, and quadraturedecoder.

Four low-cost electric servos and four optical angularquadrature encoders are connected to the HIL test-bed. Servoscontrol the position of the control surfaces and encodersmeasure the position of servo arms for updating the states offlight equations.

B. HIL SetupIn order to perform hardware-in-the-loop experiments,

servo command signals must be generated and deflection of aservo has to be measured. To generate the pulse-widthmodulated signals to command servos, timers on the HIL test-bed are utilized. Several sample signals are illustrated inFigure 1.

To measure angular deflections, angular quadratureencoders are employed. The encoders generate two set ofpulses with a 90° phase shift. The relative position isdetermined by the number of pulses and the direction ofrotation is determined by the lead-lag relationship between thetwo signals. A sample signal is demonstrated in Figure 2. Apicture of a servo and encoder is illustrated in Figure 3 and alist of actuators and sensors is presented in Table 1.

To combine all the components required in this experiment, an interface board is made. This interface boardsimply ensures proper voltages are supplied to individual components as well as ensuring consistent pinassignments. A sample connection is illustrated in Figure 4.

Using this configuration, control surface commands can be generated and servo deflections can be recorded.With the measured deflections, the states of the flight dynamics equations can be updated with respect to themeasured values.

C. Evaluation MethodTwo criteria are defined to evaluate the performance of the flight control system: control effort and mean square

tracking. They are defined in the equations (4) and (5) where k is the time step and n and m are the first and lastsample of a test segment. The reasons for using n to m instead of zero to m are to eliminate the transient responsecaused by the initial condition and to focus on specific maneuvers. Equation (4) and (5) are:

[ ] [ ] [ ] [ ]2 2 2 2m

c e p a rk n

e k k k kδ δ δ δ=

= + + +∑ (4)

[ ] [ ]( ) [ ] [ ]( ) [ ]( ) [ ] [ ]( )2 2 2 2

C

mA A C C

trackingk n

V V h hMSE

m n

k k k k k k kβ ψ ψ

=

− + − + + −=

−∑ (5)

Figure 2. Quadrature Encoder Signals

Figure 1. PWM Sample Signals


Two trajectories are utilized to evaluate the performance ofthe control system. Commands of the trajectories aredemonstrated in Figure 6 and Figure 7. In Test Case #1, thecommands are further divided into two segments. The firstsegment, also referred as the active segment A, is composed ofvarious turns and climbs. Hence, the n is the sample number at 30second and m is the sample number at 210 second. The secondsegment, or the steady-state segment B, simply tests thecontroller’s steady-state response. In this case, n equals to thesample number at 210 second and m equals to the sample numberat 250 second. Test Case #2 attempts to demonstrate thebehavior of the controller under band-limited white noisecommands. This test can illustrate the stability of the controlsystem and its tolerance to noisy inputs. In both test cases, thefirst 30 seconds of the data is discarded due to transient responseof filters.

D. Simulation ResultsQuantization and sampling constraints are added since the

controller was intended for a digital system. The sampling rate ofthe controller is assumed to be 50 Hz and its quantizationconstraints are listed in Ref. 4. However, no specific controllerboard has been chosen at this point.

Using Matlab with the HIL test-bed, offline and hardware-in-the-loop simulations for the controllers are performed. Figure 8to Figure 11 illustrates the states and outputs of the hardware-in-the-loop simulation with respect to Test Case #1 and #2. Table 2then offers a set of normalized result of offline and hardware-in-the-loop simulation for comparison.

From Table 2, the results from the active segment of TestCase #1 are similar in both offline and HIL simulations. Notsurprisingly, the digital controller experiences more performancedegradation than its discrete counterpart, mainly due to thequantization effect. It is especially obvious from the controleffort point of view. Such phenomenon is further verified underreal-time (RT) environment. When the HIL simulation isperformed, a slight improvement of performance is observed.This is most likely contributed by those low-cost actuators.Electric servos have low bandwidth and finite resolution,therefore there are limits to certain high-frequency deflections.

E. Kalman Filter ImplementationThe Kalman filter offers a possible solution to the large control effort problem. Detailed derivation of the

discrete Kalman can be found in Ref. 3 and Ref. 7. A block diagram of the discrete Kalman filter is presented inFigure 5. In this filter, a discrete-equivalent flight dynamics is used for estimation. Quantization error is modeled asuniformly distributed noise over a quantization range. The noise power can be determined by:

( )2 2 2

2 2 2

2 2

1

12p e p e de e deσ

∆ ∆

−∆ −∆

∆= = = =

∆∫ ∫ (6)

where Δ is the quantization level, e is the error associated with quantization, and p(e) is the distribution of the error.If a linear system has the following discrete state-space equation with state noise w and output noise v:

ActuatorsModel DescriptionHitec HS-322 Elevator and Aileron ServoHitec HS-81 Rudder ServoHitec HS-55 Throttle ServoSensorsModel DescriptionUS Digital E2 Optical quadrature encoder

Table 1. HIL Equipment List

Figure 4. HIL Setup Block Diagram

Figure 3. Servo and Quad. Encoder


[ ] [ ] [ ] [ ][ ] [ ] [ ]

1

v

x n Ax n Bu n w n

y n Cx n v n

+ = + +

= + (7)

and the estimate for [ ]x n is [ ]x̂ n , the error of the estimation is:

[ ] [ ] [ ]ˆe n x n x n= − (8)

and hence its steady state covariance is given by:

[ ] [ ] [ ]TP n E e n e n= (9)

where [ ][ ] 0E w n = , [ ][ ] 0E v n = , [ ] [ ]TE w n w n Q= , and [ ] [ ]TE v n v n R=

The optimal estimate of the above system is given by:

[ ] [ ] [ ] [ ] [ ]( )[ ] [ ] [ ]( )

[ ] [ ] [ ] [ ]( ) [ ]

1

ˆ[ ]

ˆ ˆ

v

v

v

x n Ax n Bu n L y n Cx n

x n x n M y n Cx n

y n Cx n CM y n Cx n Cx n

+ = + + −

= + −

= + − =

(10)

where L and M are the Kalman gain and the Innovationgain respectively.

To compute the Kalman filter gain L and theInnovation gain M, two weighting parameters, Q and R, arerequired to solve the discrete algebraic Riccati equation. Inour experimental case, the R is simply the quantizationnoise power of sensors. The Q matrix is related to the statenoise power. Since state noise does not exist, Q is aparameter that must be tuned to obtain desirable result.After a trial-and-error process, the Q matrix in this paper ischosen as:

0.01 0

0 0.01Q =

With the Kalman filter, a set of offline simulations are performed with respect to Test Case #1 and #2. Figure 12and Figure 13 demonstrate the outputs of the simulation with discrete Kalman filter and Table 3 lists a set ofnormalized results for comparison in the offline environment. From Table 3, we can clearly observe the reduction incontrol effort while maintaining similar level of tracking performance.

IV. ConclusionThe hardware-in-the-loop simulations demonstrate the digital control implementation and validation. Using the

proposed Kalman filter, the control effort has been significantly reduced. The simplified flight path and its multipleobjectives are satisfied. Other considerations, such as the microprocessor capability, input sensors modeling, and amore sophisticated set of multiple design specifications, are topics of on-going research. A more in depth study onthe Kalman filter and the numerical solver are also required.

Figure 5. Kalman Filter Block Diagram


0 50 100 150 200 25015

20

25

30

VA

Com

man

d

(m/s

)

Test Commands (Test Case #2)

0 50 100 150 200 250

280

300

320

h Com

man

d(m

)

0 50 100 150 200 250

−200

0

200

yC

omm

and

(deg

)

0 50 100 150 200 250−1

0

1

b Com

man

d(d

eg)

time (second)

Figure 7. Test Case #2This test case consists of noise commands. Usingthese inputs, the noise rejection capability of thecontrol system can be tested.

Figure 6. Test Case #1This test case consists of various climbs, turns,and straight and level segments. This test case isprimarily used for testing the trackingperformance of the control system.

Offline HILDiscrete Digital Discrete Digital

Test Case 1Active

Control Effort 1.00 0.96 0.96 0.97MSE 1.00 1.01 1.01 1.01

Steady-StateControl Effort 1.00 9.39 0.81 7.20

MSE 1.00 1.79 0.87 1.28

Test Case 2Control Effort 1.00 1.62 0.79 2.77

MSE 1.00 1.01 1.00 1.01Table 2. Normalized Results (Against Discrete Time Results)

Offline SimulationDiscrete Digital With Kalman Filter

Test Case 1Segment A

Control Effort 1.00 0.96 0.72MSE 1.00 1.01 0.99

Segment BControl Effort 1.00 9.39 1.82

MSE 1.00 1.79 1.06

Test Case 2Control Effort 1.00 1.62 1.13

MSE 1.00 1.01 1.01Table 3. Normalized Results (with Kalman Filter)


0 50 100 150 200 2501820222426

Longitudinal Outputs (Offline Digital (Kalman))

VA

(m/s

)

0 50 100 150 200 250−5

0

5

a(d

eg)

0 50 100 150 200 250−10

0

10

q(d

eg/s

)

0 50 100 150 200 250−10

0

10

q(d

eg)

0 50 100 150 200 250

300

400

500

h(m

)

0 50 100 150 200 250−5

0

5

b(d

eg)

Lateral Outputs (Offline Digital (Kalman))

0 50 100 150 200 250−10

0

10

p(d

eg/s

)

0 50 100 150 200 250−10

0

10

r(d

eg/s

)

0 50 100 150 200 250

−100

10

f(d

eg)

0 50 100 150 200 2500

50100150

y(d

eg)

0 50 100 150 200 250−20

0

20

elev

(deg

)

0 50 100 150 200 250−20

0

20

thro

ttle

(deg

)

time (second)

0 50 100 150 200 250−5

0

5

aile

ron

(deg

)

0 50 100 150 200 250−5

0

5

rudd

er(d

eg)

time (second)

Figure 12. Digital with Kalman Filter Tracking

0 50 100 150 200 2501820222426

Longitudinal Outputs (RT−HIL Digital)

VA

(m/s

)

0 50 100 150 200 250−5

0

5

a(d

eg)

0 50 100 150 200 250−10

0

10

q(d

eg/s

)

0 50 100 150 200 250−10

0

10

q(d

eg)

0 50 100 150 200 250

300

400

500

h(m

)

0 50 100 150 200 250−5

0

5

b(d

eg)

Lateral Outputs (RT−HIL Digital)

0 50 100 150 200 250−10

0

10

p(d

eg/s

)

0 50 100 150 200 250−10

0

10

r(d

eg/s

)

0 50 100 150 200 250

−100

10

f(d

eg)

0 50 100 150 200 2500

50100150

y(d

eg)

0 50 100 150 200 250−20

0

20

elev

(deg

)

0 50 100 150 200 250−20

0

20

thro

ttle

(deg

)

time (second)

0 50 100 150 200 250−5

0

5

aile

ron

(deg

)

0 50 100 150 200 250−5

0

5

rudd

er(d

eg)

time (second)

Figure 9. HIL Digital TrackingIn the digital domain, more “spikes” are observed due tolarge transient caused by quantization. (Black lines arecommands and red lines are outputs.)

0 50 100 150 200 25015202530

Longitudinal Outputs (HIL Discrete − White Noise Input)

VA

(m/s

)

0 50 100 150 200 250−0.4−0.2

00.2

a(d

eg)

0 50 100 150 200 250

−1012

q(d

eg/s

)

0 50 100 150 200 250−0.5

00.5

1

q(d

eg)

0 50 100 150 200 250250

300

350

h(m

)

0 50 100 150 200 250−4−2

024

b(d

eg)

Lateral Outputs (HIL Discrete − White Noise Input)

0 50 100 150 200 250

−200

20

p(d

eg/s

)

0 50 100 150 200 250−20

0

20

r(d

eg/s

)

0 50 100 150 200 250

−100

10

f(d

eg)

0 50 100 150 200 250

−2000

200

y(d

eg)

0 50 100 150 200 250

−100

10

elev

(deg

)

0 50 100 150 200 250

−100

10

thro

ttle

(deg

)

time (second)

0 50 100 150 200 250−5

0

5

aile

ron

(deg

)

0 50 100 150 200 250

−5

0

5

rudd

er(d

eg)

time (second)

Figure 10. HIL Discrete Noise RejectionThis graph demonstrates the noisy input rejectioncapability. The controller rejects a significant amountof noise commands. (Green lines are commands andmagenta lines are outputs.)

0 50 100 150 200 2501820222426

Longitudinal Outputs (RT−HIL Discrete Time)

VA

(m/s

)

0 50 100 150 200 250−5

0

5

a(d

eg)

0 50 100 150 200 250−10

0

10

q(d

eg/s

)

0 50 100 150 200 250−10

0

10

q(d

eg)

0 50 100 150 200 250

300

400

500

h(m

)

0 50 100 150 200 250−5

0

5

b(d

eg)

Lateral Outputs (RT−HIL Discrete Time)

0 50 100 150 200 250−10

0

10

p(d

eg/s

)

0 50 100 150 200 250−10

0

10

r(d

eg/s

)

0 50 100 150 200 250

−100

10

f(d

eg)

0 50 100 150 200 2500

50100150

y(d

eg)

0 50 100 150 200 250−20

0

20

elev

(deg

)

0 50 100 150 200 250−20

0

20

thro

ttle

(deg

)

time (second)

0 50 100 150 200 250−5

0

5

aile

ron

(deg

)

0 50 100 150 200 250−5

0

5

rudd

er(d

eg)

time (second)

Figure 8. HIL Discrete TrackingThe command tracking performance of the EA control indiscrete time domain with hardware-in-the-loop isdemonstrated. (Green lines are commands and bluelines are outputs.)

0 50 100 150 200 25015202530

Longitudinal Outputs (HIL Digital − White Noise Input)

VA

(m/s

)

0 50 100 150 200 250−1

0

1a

(deg

)

0 50 100 150 200 250

−505

q(d

eg/s

)

0 50 100 150 200 250

−5

0

5

q(d

eg)

0 50 100 150 200 250250

300

350

h(m

)0 50 100 150 200 250

−202

b(d

eg)

Lateral Outputs (HIL Digital − White Noise Input)

0 50 100 150 200 250−40−20

02040

p(d

eg/s

)

0 50 100 150 200 250−10

0

10

r(d

eg/s

)

0 50 100 150 200 250−20

0

20

f(d

eg)

0 50 100 150 200 250

−2000

200

y(d

eg)

0 50 100 150 200 250

−100

10

elev

(deg

)

0 50 100 150 200 250

−100

10

thro

ttle

(deg

)

time (second)

0 50 100 150 200 250−10

0

10

aile

ron

(deg

)

0 50 100 150 200 250−4−2

024

rudd

er(d

eg)

time (second)

Figure 11. HIL Digital Noise RejectionThis diagram demonstrates the noisy input rejectioncapability of the digital controller. (Magentas lines arecommands and cyan lines are outputs)

0 50 100 150 200 25015202530

Longitudinal Outputs (Offline Digital − White Noise Input)

VA

(m/s

)

0 50 100 150 200 250−1

0

1

a(d

eg)

0 50 100 150 200 250−2

024

q(d

eg/s

)

0 50 100 150 200 250

−202

q(d

eg)

0 50 100 150 200 250250

300

350

h(m

)

0 50 100 150 200 250

−2

0

2

b(d

eg)

Lateral Outputs (Offline Digital − White Noise Input)

0 50 100 150 200 250

−200

20

p(d

eg/s

)

0 50 100 150 200 250−10

0

10

r(d

eg/s

)

0 50 100 150 200 250−20

0

20

f(d

eg)

0 50 100 150 200 250

−2000

200

y(d

eg)

0 50 100 150 200 250

−100

10

elev

(deg

)

0 50 100 150 200 250

−100

10

thro

ttle

(deg

)

time (second)

85 90 95 100 105 110−10

−505

aile

ron

(deg

)

0 50 100 150 200 250

−202

rudd

er(d

eg)

time (second)

Figure 13. Digital with Kalman Filter Noise Rejection


ReferencesBooks

1Brian L. Stevens, Frank L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, Inc, 1999.2Bernard Etkin, Lloyd Duff Reid, Dynamics of Flight Stability and Control Third Edition, John Wiley & Sons, Inc, 1996.3 C.L. Phillips, H. T. Nagle, “Digital Control System Analysis and Design Third Edition”, Prentice Hall, 1995.

Proceedings4 H. Tam, H.T. Liu, C.A. Rabbath, J.D. DeLaurier, “Modeling and Real-Time Simulation of Multi-Objective Control for an

UAV Example”, AIAA Modeling and Simulation Technologies Conference Proceedings, AIAA 2004-4914, 16-19 Aug. 2004

Reports, Theses, and Individual Papers5 J.M. de la Cruz, P. Ruipérez, J. Aranda, “RCAM Design Challenge Presentation Document: an Eigenstructure Assignment

Approach”, GARTEUR, TP-088-22, 1997.6 Peter Lee, Matthew Naylor, A.J. Kossman, Julio Palma, Luke Ng, Samuei Lai, “Design, Construction and Evaluation of an

Unmanned Air Vehicle”, Internal Report, University of Toronto Institute For Aerospace Studies, 2002.

Computer Software7Control System Toolbox, Matlab R12, The Mathworks Inc., Natick, MA.

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