Model Predictive Attitude Control of VarioUnmanned Helicopter

Mahendra Kumar Samal, Matthew Garratt, Hemanshu Pota and Hamid Teimoori SanganiSchool of Engineering and Information Technology, UNSW@ADFA, Canberra,

ACT-2600, Australia, e-mail: {m.samal, m.garratt, h.pota, h.teimoori}@adfa.edu.au

Abstract—This paper presents a Model Predictive Control(MPC) based attitude stabilisation system for a rotary-wing un-manned aerial vehicle. We have enhanced the MPC performanceby augmenting the helicopter model with servo dynamics duringthe prediction phase. The inclusion of servo dynamics and timedelay yields a smoother control response. A linear state spacereduced order model for longitudinal and lateral dynamics of thehelicopter is used for controller design. The applicability of theproposed MPC scheme is evaluated on a nonlinear simulationmodel of an unmanned helicopter for autonomous hover andlow speed forward flight. Numerical simulation on the nonlinearmodel illustrates improved performance of the closed-loop systemin presence of servo dynamics and time delays.

I. INTRODUCTION

Rotary-wing Unmanned Aerial Vehicles (RUAVs) or minia-ture helicopters are a class of unmanned or pilot-less aerialvehicles which have unique aerodynamic and propulsion char-acteristics. The unique propulsion characteristics enable it tohover, take-off and land vertically. This special feature of theRUAVs to hover, take-off and land on rough terrain to carry-out mission critical operations without endangering the lifeof human pilots has an added advantage over the unmannedfixed-wing aircrafts which require a runway for take-off andlanding.

RUAVs have been an active area of research in the lastdecade due to their increasing role in both civilian and militaryapplications. This can be attributed to the use of UAVs toconduct monotonous as well as dangerous operations withoutthe intervention of a human pilot. RUAVs can be successfullyused for real-time reconnaissance, surveillance, search andrescue missions, weather data collection, bush fire monitoring,agricultural crop dusting and different airborne operations [1]–[4]. Success of these missions depend primarily on the flightcontrol system.

In general, actuator dynamics are not taken into accountduring the control design phase [5]. Actuators with significanthard constraints and time delay are integral part of any system.Actuator constraints and input delay can limit the bandwidthof the control system and deteriorate the performance of theclosed-loop system. In order to provide desired control input tohelicopter control surface, it is required to generate necessarycontrol signal to the actuators which takes actuator constraintsand time delay into account. Hence, actuator dynamics andtime delay must be considered during the controller design.In this work, we propose a Model predictive control (MPC)

scheme which considers actuator dynamics and time delayduring the controller design process.

Model predictive control due to its high computational de-mand was earlier restricted to systems with slower dynamics.But the improvement in computer technology (both processingpower and miniaturisation of computers) have enabled it to beapplied for systems with fast dynamics such as helicopters.MPC solves optimal discrete control problem for linear andnonlinear systems in the presence of input output constraints.The important feature of MPC are that it can be used formulti-variable process, systems with time delays and uncertainparameters, systems with non minimum phase behavior andmost importantly, it can handle constraints on both input andoutput variables. This work describes a MPC applied towardsattitude control of Vario helicopter.

Fig. 1. Vario XLC carrier helicopter

The Vario XLC carrier autonomous helicopter platformshown in Fig. 1 is under development at UNSW@ADFA withan objective to develop flight control system for fully au-tonomous flight. The platform is equipped with avionics builtin-house and instrumented with sensors for data collection. Asimulation model of RUAV is developed at UNSW@ADFAto test and verify different identification and control algorithmand for conducting closed-loop experiments before real-flightimplementation.

The rest of the paper is organised as follows. Section IIbriefly describes the helicopter platform used as a test-bed forimplementing MPC controller algorithm. The proposed MPC

978-1-61284-971-3/11/$26.00 ©2011 IEEE 570

scheme is presented in Section III. The helicopter dynamicmodel used for the model prediction is presented in Section IV.Results and discussions are presented in Section V. The paperis concluded in Section VI.

II. VARIO HELICOPTER PLATFORM

The helicopter design incorporates a main rotor, and a tailrotor for anti torque compensation. The Vario helicopter doesnot have a flybar (flybar is a common feature of miniaturehelicopters to increase the stability and help pilot fly thehelicopter smoothly). The helicopter is driven by a 8 kW (11LE) gas turbine engine. Servo actuators for collective (δcoll),aileron (δlat), elevator (δlon) and tail rotor pitch (δped) are usedto control the helicopter. Technical specifications for the VarioXLC carrier Helicopter platform are given in Table I.

TABLE IVARIO HELICOPTER PLATFORM TECHNICAL SPECIFICATION

Parameter ValueMain rotor diameter 2500 mmTail rotor diameter 840 mmMaximum weight 22.774 kgNumber of blades on main rotor 3Number of blades on tail rotor 4Height 1000 mmLength 2450 mmWidth 700 mmFuel capacity 9.5ltMotor type (gas turbine) 8 kW (11 LE)

A high fidelity Simulink R© model for an unmanned Variohelicopter is designed and programmed at UNSW@ADFA.This simulation model incorporates the servo dynamics, windgust and turbulence effects to provide a desired match withexperimental data. It is used as a virtual platform for develop-ment of sensor data fusion algorithms, design and validationof controllers. The model can simulate hover, rearwards, side-ways and forward flight conditions. The following factors have

Fig. 2. Vario helicopter Simulation Model

been taken into consideration while developing the simulationmodel shown in Fig. 2:

• Nonlinear rigid body equations of motion• Main rotor flaping dynamics

• Servo dynamics• Fuselage and tailplane aerodynamics• Wind gust and turbulence effects.

The ground effects, interaction of rotor downwash with thefuselage and rotor lead-lag mechanisms are not taken intoconsideration for the design of the model. In the next section,the model predictive controller strategy used for the attitudecontrol of the helicopter is presented.

III. MPC WITH SERVO AND DELAY CONSTRAINTS

Model Predictive Controller is a class of modern controltechnique which makes use of process model to computecontrol commands to achieve optimum control. The processmodel is used to predict the helicopter behaviour over aspecified period of time. The design of model predictivecontroller consists of the following basic steps:

1) Use the process model to predict the plant behaviourover the prediction horizon

2) Construct a cost function (2) which depends upon theerror between the reference and predicted response

3) Optimise the cost function to obtain the best futurecontrol sequence (over the control horizon)

4) Apply the first control input from the estimated controlsequence to servo channel.

The MPC optimisation problem is solved as a constraintoptimisation problem thereby putting a bound on the futurecontrol moves. Upper and lower bounds on the calculatedcontrol input provide the desired damping to the systemthereby eliminating the abrupt changes in the dynamics of thesystem [6].

Consider the discrete time linear dynamics of the helicopter

x(k +1) =Ax(k)+Bu(k− τd)y(k) =Cx(k)

(1)

subject to constraints in the control input

Umin ≤ u(k) ≤Umax

where, Umax and Umin are the maximum and minimum per-missible servo deflections respectively. In (1), x ∈ ℜn is thestate vector, y ∈ ℜp is the output vector, u ∈ ℜm is the inputvector, τd is the pure delay in the control loop, A,B and C aresystem matrices corresponding to the state, input and outputparameters. For any state x at time step k, it is required to find aset of control input u(k),u(k+1), · · · ,u(k+N2) in a predictionhorizon time frame N2, such that the objective function

J(k) =N2

∑j=1

[yre f (k + j)− y(k + j)]2

+Nu

∑j=1

ρ( j)[Δu(k + j−1)]2(2)

is minimised. In (2), J(k) is the cost function, yre f (k + j)is the reference trajectory at jth step ahead, y(k + j) is thejth step ahead model response, ρ is the penalty factor usedto penalize the changes in control input, u(k) is the control

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input calculated at time k, N2 and Nu are the prediction andcontrol horizon respectively. The change in control input Δu(k)is defined as Δu(k) = u(k)−u(k−1).

The above objective function is minimised subject to fol-lowing input-output constraints;

umin ≤ u(k + j|k) ≤ umax, j = 0, · · · ,Nu −1, ∀k

Δumin ≤ Δu(k + j|t) ≤ Δumax, j = 0, · · · ,Nu −1,∀k

ymin ≤ y(k + j|k) ≤ ymax, j = 1, · · · ,N2 ∀k

(3)

where

u =

⎡⎢⎢⎢⎣

u(k)u(k +1)

...u(k +Nu −1)

⎤⎥⎥⎥⎦ , y =

⎡⎢⎢⎢⎣

y(k)y(k +1)

...y(k +N2 −1)

⎤⎥⎥⎥⎦ .

The computational time required for optimisation processdepends upon the initial guess values for the decision vari-ables. For faster convergence of the optimisation routine,a good initial guess of decision variable u0(k + i) for i =1, · · · ,Nc is required at every sample time. A good initialguess is the solution computed at the previous time step, i.e.,u0(k + i) = u(k + i) for i = 1, · · · ,Nc. Since the next operatingpoint always lies close to the current one due to a smallsampling time of 20ms, this initial guess improves the speedof convergence of the optimisation process.

The input constraint defined in (3) arises due to the actuatorrate limit. In addition to the rate limitation, the actuatortime delay deteriorates the performance of the controllersignificantly. To improve the controller performance, the servodynamics and the associated time delay should be consideredin the MPC design.

A. Servo dynamics included in the prediction model

Digital servos are used in the Vario helicopter for actuatingthe control surfaces. The dynamics of these servos are modeledas a simple first order model

Gs =1

τss+1(4)

with servo time constant, τs = 30ms. The governing actuatordynamics in the discrete time state space form is given as;

xact(k +1) =Aactxact(k)+Bactucmd(k)u(k) =Cactxact(k)

(5)

where, xact(k),ucmd(k) and u(k) are the actuator state, com-manded surface deflection input and the control surface de-flection respectively. The actuator dynamics given in (5) isaugmented to the plant model to make the prediction more re-alistic. In the proposed MPC algorithm, the computed controldeflection input from the MPC optimiser is passed through theservo dynamics and the output from the servo model (controlsurface deflection) is then used for model prediction. Thisalgorithm actively accounts for the actuator dynamics duringthe MPC optimisation process and hence takes into account theactuator limitations. Hard constraints of actuators are realised

as soft constraints in the MPC algorithm as shown in Algo 1.The time delay arising in the system due to sensors, actuatorsand process are considered as pure delay in this work. In thecontroller design, a pure input delay of 2 sample time (40ms) isconsidered in the prediction model. In order to include a pureinput delay of 40ms, the control input used in the predictionmodel at the current time step corresponds to the control inputequal to the value of the input at the current time minus adelay time of 2 sample. A more detailed description of theproposed algorithm where the servo dynamics is consideredin the model prediction is given in Algo 1.

Algorithm 1 MPC with augmented actuator and helicopterdynamicsRequire: Stopping Criteria, itermax, UL, LL, N2, Nc

1: Initialize UL, LL, iter = 1, t = 1.2: while 1 do3: yre f = Re f Data(t +1 : N2) and yp = ySensorData(t −1)

uold = uSensorData(t −1)uopt = uold

x0servo = uold

and x0 = xmeasured

4: while (not Stopping Criteria and iter < itermax) do5: uservo = ServoDynamics(x0servo,uopt)6: y(t + 1 : N2) = ModelPredict(yp,xmeasuold , System

matrices A,B,C, uservo)7: J = CostFunctionCalculation(y,yre f ,Δuopt)8: Minimise J such that unew(1 : Nu) = minimize(J)9: if unew ≤ LL then

10: unew = LL11: else if unew ≥UL then12: unew = UL13: end if14: uopt = unew

15: iter = iter +116: end while17: uvec(1 : Nu) = uopt(1 : Nu)18: Accept u = uopt(1)19: t = t +120: end while

As discussed above, MPC explicitly uses the process modelto predict the future response of the helicopter. Hence theperformance of the controller depends on the accuracy of theprediction model. In the next section, the linear state spacemodel used in the MPC design is discussed.

IV. VARIO HELICOPTER MODEL

The nonlinear dynamics of RUAV can be expressed bydiscrete time difference equation given by:

x(k +1) = f (x(k),u(k− τd))y(k) = g(x(k),u(k))

(6)

where x(k) ∈ ℜn is the state vector, y(k) ∈ ℜp is the outputvector and u(k)∈ℜm is the input vector at discrete time step k,

572

f and g are nonlinear functions. With suitable assumptions, theabove nonlinear dynamics can be linearised about an operatingpoint and the resulting continuous time state space model ofthe system can be formulated as (1).

With suitable assumptions [7], the 6-DOF system can bebroken down to two 3-DOF systems. These are represented aslongitudinal dynamics and lateral dynamics. In the longitudinaldynamics, the modeling of forward velocity (Vx), pitch rate (q)and pitching angle (θ) as a function of elevator input (δlon)is undertaken in the presented work. Similarly, in the lateraldynamics, roll angle (φ), yaw angle (ψ) and the side-wardvelocity (Vy) are modeled as a function of aileron (δlat) input.

The longitudinal dynamics of the Vario helicopter in thecontinious time state space form can be expressed as;

⎡⎢⎢⎣

Vx

qθa

⎤⎥⎥⎦ =

⎡⎢⎢⎣

Xu 0 −g Xa

Mu 0 0 Ma

0 1 0 0Auτ f

−1 0 −1τ f

⎤⎥⎥⎦

⎡⎢⎣

Vx

qθa

⎤⎥⎦+

⎡⎢⎢⎣

000

Alonτ f

⎤⎥⎥⎦δlon, (7)

where Vx,q,θ and a are the body velocity in X-axis, pitchrate, pitch angle and flapping angle respectively. δlon is thelongitudinal cyclic input applied to the helicopter. Similarly,the lateral dynamics of the helicopter in the continuous timestate space form can be expressed as;

⎡⎢⎢⎣

Vy

pφb

⎤⎥⎥⎦ =

⎡⎢⎢⎣

Yv 0 g Yb

Lv 0 0 Lb

0 1 0 0Bvτ f

−1 0 −1τ f

⎤⎥⎥⎦

⎡⎢⎣

Vy

pθb

⎤⎥⎦+

⎡⎢⎢⎣

000

Blatτ f

⎤⎥⎥⎦δlat , (8)

where Vy, p,φ and b are the body velocity in Y -axis, roll rate,roll angle and flapping angle respectively. δlat is the lateralcyclic input applied to the helicopter. The stability and controlderivatives in (7) and (8) are calculated from the informationavailable for the Vario helicopter.

Current states of the system are required in the state spacemodel as the initial state to propagate the states and predict thefuture response of the helicopter. A suitable state observer isneeded if all the states in (7) and (8) are not measurable. It isdifficult to measure flapping angle in our helicopter. Flappingangle dynamics is assumed to be fast and thus not considered.This leads to a reduced order model for the longitudinaland lateral dynamics of the helicopter, given in (9) and (11)respectively. With this reduced order model, all the statesrequired for the design of MPC are measurable and henceno observer is employed.

The reduced order state space model for longitudinal dy-namics is given as

⎡⎢⎢⎣

xVx

qθ

⎤⎥⎥⎦ =

⎡⎢⎣

0 1 0 00 −gAu gτ f −g0 MaAu −Maτ f 00 0 1 0

⎤⎥⎦

⎡⎢⎣

xVx

qθ

⎤⎥⎦+

⎡⎢⎣

0−gAlon

MaAlon

0

⎤⎥⎦δlon.

(9)

⎡⎢⎢⎣

xVx

qθ

⎤⎥⎥⎦ =

⎡⎢⎣

0 1 0 00 −0.02 0.25 −9.80 0.51 −6.4 00 0 1 0

⎤⎥⎦

⎡⎢⎣

xVx

qθ

⎤⎥⎦+

⎡⎢⎣

0−9.82530

⎤⎥⎦δlon. (10)

The reduced order state space model for lateral dynamics

is given as⎡⎢⎣

yVy

pφ

⎤⎥⎦ =

⎡⎢⎣

0 1 0 00 −gBv −gτ f g0 LbBv −Lbτ f 00 0 1 0

⎤⎥⎦

⎡⎢⎣

yVy

pφ

⎤⎥⎦+

⎡⎢⎣

0gBlat

LbBlat

0

⎤⎥⎦δlat .

(11)

⎡⎢⎣

yVy

pφ

⎤⎥⎦ =

⎡⎢⎣

0 1 0 00 −0.02 −0.25 9.80 −1.66 −20.9 00 0 1 0

⎤⎥⎦

⎡⎢⎣

yVy

pφ

⎤⎥⎦+

⎡⎢⎣

09.8

828.70

⎤⎥⎦δlat . (12)

For the controller design purpose, above continuous timemodel is discretised with 20ms sampling time. In the nextsection, the controller architecture is presented.

V. RESULTS AND DISCUSSION

A. Controller architecture

A behaviour based control architecture as mentioned in [8]and [9], where the complete helicopter control problem ispartitioned into several subproblems to achieve autonomouslanding of the helicopter, is used in this work. In this hi-erarchy based controller design, the helicopter is controlledby two nested loops. The outer-loop controller is designedby a proportional-integral-derivative (PID) controller whichprovides pitch and roll commands to the inner-loop controllerby taking lateral and longitudinal velocities into consideration.The decoupled lateral and longitudinal dynamics are controlledby separate SISO MPC controllers for attitude stabilisation.A schematic diagram of controller architecture is shown inFig. 3. The helicopter response for hover and forward flightconditions with the proposed controller strategy are providednext.

B. Controller result for hover flight condition

The reduced order state space model is used in Algo 1 topredict the future responses of the helicopter. The propagationof state space model of the helicopter for N2 predictionhorizon requires initial state vector x0. Since all the statesof the longitudinal and lateral dynamics are measurable, thecurrent measured states are used as the initial state vector.For designing the controller for lateral cyclic channel, theprediction horizon, N2 = 10 and control horizon, Nu = 6 werechosen by trial and error. Similarly, N2 = 14 and Nu = 8 wasselected for longitudinal cyclic channel.

To simulate a real flight condition, a transport delay of 40mswas introduced in the control loop. The helicopter is requiredto hover at an altitude of 3m while maintaining a commandedX and Y location. The close-loop performance of the controllerin presence of time delay in longitudinal and lateral cyclicchannels are shown in Figures 4 and 5. The pitch and rollresponse of the helicopter are plotted against the desired pitchand roll angle in Fig. 4. It can be seen from the figure thatthe helicopter tracks and maintains the commanded attitudeduring the flight. It can also be seen from the Fig. 4 that thecontroller stabilises delayed system.

573

Lateral_Cyc

Pedal

Long_Cyc

Collective

Transport Delay

Transport Delay

Out1

[theta]

[phi]

[r]

[q]

[p]

[Zref]

[Yaw_ref]

[Xref]

[Vx]

[Vy]

[Vz]

[Y]

[X]

[psi]

[Z]

[Yref]

Tail PitchController

PIDzYaw

Wrap

euler_discrete

OuterLoop_longitudinal

In1

In2

In3

Out1

OuterLoop_lateral

In1

In2

In3

Out1

Longitudinal MPC

MPC_linear_sfunction_long

Lateral MPC

MPC_linear_sfunction_lat

−1

[Z]

[psi]

[r]

[Zref]

theta]

[q]

[Vx]

[X]

[Yaw_ref]

[theta]

[Vx]

[Xref]

[X]

[Y]

[phi]

[p]

[Vy]

[Vy]

[Yref]

[Y]

[phi]

[Vz]

m

m

m

D2R

Collective PitchController

PIDz

Desired States2

State Estimate1

Qobs

q3

q2

q1

q0

Vz

Z

ax

ay

az

X

Y

Vx

Vy

Fig. 3. Controller Simulation Block Diagram

0 1 2 3 4 5−3

−2

−1

0

1

2

Pitc

h an

gle

(θ)

in D

eg

0 1 2 3 4 5−10

−5

0

5

Time in Sec

Rol

l ang

le (

φ) in

Deg

φ in Degφ

d in Deg

θ in Degθ

d in Deg

Fig. 4. Comparison of pitch and roll response of the helicopter with thedesired response

C. Controller result for forward flight condition

To study the performance of the controller at a low speedforward flight condition, a simulation was carried out suchthat the helicopter tracks a circular trajectory (x = 0.5sin(ωt)mand y = 0.5cos(ωt)m, ω = 0.5rad/sec) while hovering at analtitude of 2m. Similar to the hover flight, a time delay of40ms was also introduced in the control loop. The closed loopresponse of the helicopter are plotted in Fig. 6 and Fig. 7.The servo inputs used to drive the helicopter are presentedin Fig. 8. It can be seen from the figures that the helicoptertracks the desired circular trajectory while maintaining thecommanded altitude. The simulation result show that the

0 1 2 3 4 5−1

−0.5

0

0.5

δ lat in

Deg

0 1 2 3 4 5−1.5

−1

−0.5

0

0.5

1

δ lon in

Deg

Time in Sec

Fig. 5. Servo inputs for lateral and longitudinal channels

controller stabilises the delayed system and tracks the desiredsystem response.

D. Comparison of MPC design with and without the servodynamics

To show the qualitative improvement in the performance ofthe closed-loop system when the servo dynamics is consideredin the MPC design, a simulation test is carried out and thecontroller response is plotted in Fig.9. It can be noticed that asmoother control input and pitch response is achieved with theproposed MPC design compared to the one without includingthe servo dynamics in the design.

574

0 2.5 5 7.5 10 12.5 15 17.5 20−3

−2

−1

0

1P

itch

angl

e (θ

) in

Deg

0 2.5 5 7.5 10 12.5 15 17.5 20−20

−10

0

10

20

Time in Sec

Rol

l ang

le (

φ) in

Deg

θ in Degθ

d in Deg

φ in Degφ

d in Deg

Fig. 6. Forward flight Comparison of pitch and roll response of the helicopterwith the desired response with 40ms time delay

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

X position in m

Y p

ositi

on in

m

Measure positionDesired position

Fig. 7. XY position plot

VI. CONCLUSION

Model predictive control scheme for attitude stabilisation ofVario helicopter is presented in this paper. In this work, weproposed a MPC scheme which considers actuator dynamicsand time delay during controller design process. The proposedalgorithm was implemented on a nonlinear simulation modelof the unmanned helicopter. By considering servo dynamicsand time delay during the model prediction phase, a smootherresponse from the controller is achieved.

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0 2.5 5 7.5 10 12.5 15 17.5 20−2

−1

0

1

2

δ lat in

Deg

0 2.5 5 7.5 10 12.5 15 17.5 20−0.4

−0.2

0

0.2

0.4

Time in Sec

δ lon in

Deg

Fig. 8. Forward flight: Servo inputs for lateral and longitudinal channels

0 0.5 1 1.5 2 2.5 3 3.5 4

−1

−0.5

0

0.5

1

Time in Sec

δ lon in

Deg

0 0.5 1 1.5 2 2.5 3 3.5 4−4

−3

−2

−1

0

1

2

θ in

Deg

δlon

: Considering servo model in MPC

δlon

: Without considering servo model in MPC

θ: Considering servo model in MPCθ: Without considering servo model in MPC

Fig. 9. Comparison of system response with and without considering servodynamics

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