Trajectory Tracking of Small Helicopters Using Explicit Nonlinear MPC

Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Trajectory tracking of small helicopters using explicit nonlinear MPC and DOBC Cunjia Liu ∗ Wen-Hua Chen ∗ John Andrews ∗∗ Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK. (e-mail: {c.liu5, w.chen}@lboro.ac.uk) ∗∗ Nottingham Transportation Engineering Centre, University of Nottingham, Nottingham NG7 2RD, UK. (e-mail: [email protected]) ∗

Abstract: Small-scale helicopters are very attractive for a wide range of applications due to their unique features. However, autonomous flight of a small helicopter is quite challenging because it is naturally unstable, has strong nonlinearities and couplings, and are very susceptible to wind and small variation of helicopter structures. A robust nonlinear control scheme is proposed to address these issues. It consists of a nonlinear model predictive controller and a nonlinear disturbance observer. First, an analytic solution for the nonlinear MPC is developed based on the nominal model and under the assumption that all disturbances are measurable. Then a nonlinear disturbance observer is designed to estimate the influence of external force/torque inducted by wind turbulence, unmodelled dynamics and variations of the helicopter structure. Simulations and flight tests including hovering under wind gust have been carried out to demonstrate the performance of the proposed control scheme. Keywords: Model predictive control, nonlinear disturbance observer, helicopter, flight control. 1. INTRODUCTION Autonomous helicopters are versatile flying machines capable of vertical take-off and landing, hovering, flying in very low altitudes, and performing complicated manoeuvres. These properties make them suitable for a board range of applications like surveillance, board patrol, search and rescue, etc. On the other hand, their nonlinearities and dynamic couplings pose a challenge for the controller design and attract considerable interests from academia. Thereby, many control techniques have been applied to address the autonomous flight of helicopters. Recently, model predictive control (MPC) has been recognised a promising method in the unmanned aerial vehicle (UAV) community (Ollero and Merino, 2004). The “foresee” feature of MPC makes it as a suitable control strategy for UAV applications, especially in trajectory tracking where MPC can take into account the future value of the reference to improve the performance. The essential procedure in the implementation of MPC algorithms is to solve the formulated optimisation problem. For nonlinear system, MPC technique generally requires solving an optimisation problem numerically at every sampling instant, which poses obstacles on the real-time implementation due to the heavy computational burden. The associated low bandwidth and computational delay make it very difficult to meet the control requirement for systems with fast dynamics like helicopters. Only few applications on helicopter flight control have been reported in (Shim et al., 2003), where the authors adopt a high-level MPC to solve the tracking problem and rely on a local linear feedback controller to compensate the high-level MPC. Moreover, Copyright by the International Federation of Automatic Control (IFAC)

the formulated nonlinear optimisation problem has to be solved by a secondary flight computer. The extra payload and power consumption are quite luxury for a small-scale helicopter. To avoid online optimisation, this paper introduces an explicit nonlinear MPC (ENMPC) for trajectory tracking of autonomous helicopters. By approximating the tracking error and control efforts in the receding horizon using their Taylor expansion to a specified order, an analytic solution to nonlinear MPC can be found and consequently the closed form controller can be formulated without online optimisation (Chen et al., 2003). The benefits of using this MPC algorithm are not only the elimination of the online optimisation and the associated resource, but also a higher control bandwidth, which is very important for helicopters in aggressive flight scenarios. There are practical issues in controlling autonomous helicopters from an engineering point of view. It is known that the control performance of MPC or the other model based control technologies heavily relies on the quality of the model. However, the model of high accuracy for a helicopter is difficult to obtain due to the complicated aerodynamic nature of the rotor system. On the other hand, due to the light-weighted structure, small-scale helicopters are more likely to be affected by wind gusts and other disturbances than their full size counterpart, and the physical parameters such as mass and inertia of moments can be easily altered by changing a payload and even its location. All these factors compromises the actual performance of the controller designed based on the nominal model.

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Robust control techniques, like the H∞ technique, have been used to handle the parametric uncertainty and ummodelled dynamics (Marconi and Naldi, 2007; Gadewadikar et al., 2008). Although satisfactory performances have been demonstrated, robust control is known to result in conservative solutions and presents trade-offs between performance and robustness. Adaptive control also shows promising results of controlling helicopters in the presence of uncertainties (Johnson and Kannan, 2005). However, the controllers usually have complicated structures and very high order. Other methods to compensate the wind disturbances can be found in (Cheviron et al., 2009; Martini et al., 2009). To enhance the performance of ENMPC in complex operation environment, this paper advocates a disturbance observer based control (DOBC) approach. Disturbance observers have been applied to estimate unknown disturbances in the control process (Chen, 2004). As the estimation of disturbances is provided, the control system can explicitly take them into account and compensate them. The advantage of the DOBC is that it preserves the tracking and other properties of the original baseline control while being able to compensate disturbances rather than resorting to a different control strategy. To design an ENMPC with DOBC for trajectory tracking of autonomous helicopters, two problems need to be addressed, namely, designing the nonlinear disturbance observer to estimate the disturbances acting on the helicopter, and integrating the disturbance information into ENMPC to compensate their influences. To this end, another contribution of this paper lies in the synthesis of the ENMPC and DOBC by exploiting the helicopter model structure. The disturbances are assumed to exist in the form of forces and torques, so that coupling terms can also be lumped into disturbance terms. In this way an ENMPC is derived under the assumption that all the disturbances are measurable and then these disturbances are replaced by their estimation provided by the proposed disturbance observer. On the other hand, the lumped disturbance terms simplify the model structure allowing the derivation of ENMPC for helicopters becoming possible. The composite control framework provides a promising solution to autonomous helicopter trajectory tracking in the presence of uncertainties and disturbances. The performance of the proposed control system is tested through simulations and verified in our indoor flight testbed. 2. HELICOPTER MODELLING A helicopter is a highly nonlinear system with multiple inputs multiple outputs (MIMO) and complicated internal couplings. The complete model taking into account the flexibility of the rotors and fuselage usually results in a model of high degrees-of-freedom. The complexity of such a model would make the following system identification much more difficult. A practical way to deal with this issue is to capture the primary dynamics by a simplified model and treat the other trivial factors that affect dynamics as uncertainties or disturbances. The general dynamics of a small-scale helicopter can be captured by a sixdegrees-of-freedom rigid-body model augmented with a simplified rotor dynamic model (Mettler et al., 2002). In

this way, kinematics of a helicopter, i.e. the position and the orientation represented by Z-Y-X Euler angles, can be expressed as: [ x˙ y˙ z˙ ]T = Rib (φ, θ, ψ)[ u v w ]T T  T φ˙ θ˙ ψ˙ = Φ(φ, θ, ψ) [p q r]

(1) (2)

where (x, y, z) describe the helicopter inertial position, (u, v, w) are velocities along three body axes, (p, q, r) are angular rates, and (φ, θ, ψ) are attitude angles. Rib is the transformation matrix from body to inertial coordinates and Φ(φ, θ, ψ) is the Euler matrix. The model of translational dynamics of helicopters used in this paper is modified by keeping the thrust of main rotor as a dominating force and considering other force contributions as disturbances, such that u˙ = vr − wq − g sin θ + dx v˙ = wp − ur + g cos θ sin φ + dy w˙ = uq − vp + g cos θ cos φ + T + dz

(3)

where, T is the normalised main rotor thrust controlled by collective pitch δcol and (dx , dy , dz ) are normalised force disturbances that include external wind gusts, internal couplings and unmodelled dynamics. This modification on one hand increases the valid range of the model comparing to simplified helicopter models for control design that neglects all other forces other than the main thrust (Marconi and Naldi, 2007; Raptis et al., 2010). On the other hand it reduces the workload of deriving the ENMPC for helicopters as different disturbances are lumped into one term . The model of angular dynamics follows the same principle in (Mettler et al., 2002), which is driven by the flapping angles of main rotor (a, b) and the collective pitch of tail rotor δped , respectively. The flapping angles are originally controlled by lateral and longitudinal cyclic δlat and δlon . Their relationship can be approximated by steady state dynamics of the main rotor: a = −τ q + Alat (δlat + dlat ) + Alon (δlon + dlon ) b = −τ p + Blat (δlat + dlat ) + Blon (δlon + dlon )

(4)

where dlat and dlon account for the trim errors in the real helicopter. These trim errors may arise from structural uncertainties and physical alterations like payload change, which usually are ignored in the control design but will degrade the control performance in real life operations. Similarly, we consider the trim error dped in the yaw channel. The full helicopter model can be expressed by a general affine form: x˙ = f (x) + g1 (x)u + g2 (x)d y = h(x)

(5)

where x = [ x y z u v w p q r φ θ ψ ]T is the helicopter state, u = [δlat δlon δcol δped ] is the control input, y is the output of the helicopter, and d = T [dx dy dz dlat dlon dped ] is the lumped disturbance acting on the helicopter. In the trajectory tracking control of an autonomous helicopter, the interested outputs are the position and heading angle. Thus, y = [ x y z ψ ]T .

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3. ENMPC WITH DISTURBANCES ˆ (t + τ ) = y To achieve trajectory tracking function for an autonomous helicopter, we need to design a controller such that the output y(t) of the helicopter (5) tracks the prescribed reference w(t). In the MPC strategy, tracking control can be achieved by minimising a receding horizon performance index Z 1 T J= (ˆ y(t + τ ) − w(t + τ ))T Q(ˆ y(t + τ ) − w(t + τ ))dτ 2 0 (6) where weighting matrix Q = diag{q1 , q2 , q3 , q4 }, qi > 0, i = 1, 2, 3, 4. Note that the hatted variables belong to the prediction time frame. Conventional MPC algorithm requires solving of an optimisation problem at each sampling instant to obtain control signals. To avoid the computationally intensive online optimisation, we adopt an explicit solution for the nonlinear MPC problem based on the approximation of the tracking error in the receding prediction horizon (Chen et al., 2003). 3.1 Output approximation For a nonlinear MIMO system like the helicopter, it is well known that after differentiating the outputs for a specific number of times, the control inputs appear in the expressions. The number of times of differentiation is defined as relative degree. For the helicopter with out′ put y = [ x y z ψ ] and the corresponding input u = [ δlon δlat δcol δped ], the relative degree is a vector, ρ = [ ρ1 ρ2 ρ3 ρ4 ]. If continuously differentiating the output after the control input appears, the derivatives of control input appear, where the number of the input derivatives r is defined as the control order. Since the helicopter model has different relative degrees, the control order r is first specified in the controller design. The ith output of the helicopter in the receding horizon can be approximated by its Taylor series expansion up to order ρi + r: r+ρi

[r+ρ ]

i τ yˆi (t + τ ) ≈ yi (t) + τ y˙ i (t) + · · · + (r+ρ y (t) i )! i h i h iT [r+ρi ] τ r+ρi = 1 τ · · · (r+ρ y (t) y ˙ (t) · · · y (t) i i )! i i (7)

where 0 ≤ τ ≤ T and i = 1, 2, 3, 4. In this way, the approximation of the overall output of the helicopter can be cast in a matrix form:   τ r+ρ1 1, τ, · · · , (r+ρ · · · 0 1×(r+ρ +1) 4 )! 1   ··· ··· ··· ˆ (t + τ ) =  y  r+ρ4 τ 01×(r+ρ1 +1) · · · 1, τ, · · · , (r+ρ 4 )! h iT [r+ρ ] [r+ρ ] y1 (t) · · · y1 1 (t) · · · y4 (t) · · · y4 4 (t) (8) For each channel in the output matrix, the control orders r are the same and can be decided during the control design, whereas the relative degrees ρi are different but determined by the helicopter model structure. Manipulating the output matrix (8) gives the following partition:

"

τ¯1 ···

· · · 01×ρ4 | · · · · · · | τ˜1 · · · τ˜r+1 · · · τ¯4 |

#

01×ρ1  T Y¯1 (t)T · · · Y¯4 (t)T |Y˜1 (t)T · · · Y˜r (t)T

where

iT h Y¯i = yi (t) y˙ i (t) · · · yi[ρi −1] , i = 1, 2, 3, 4

(9)

(10)

h iT Y˜i = y1[ρ1 +i−1] y2[ρ2 +i−1] · · · y4[ρ4 +i−1] , i = 1, . . . , r + 1 (11) i h ρi −1 (12) τ¯i = 1 τ · · · (ρτ i −1)! , i = 1, 2, 3, 4

and

τ˜i = diag

n

τ ρ1 +i−1 (ρ1 +i−1)!

···

τ ρ4 +i−1 (ρ4 +i−1)!

o

, i = 1, . . . , r+1 (13)

It can be observed from Eq(9) that the prediction of ˆ (t + τ ), 0 ≤ τ ≤ T , in the the helicopter output y receding horizon needs the derivatives of each output of the helicopter up to r + ρi order at time instant t. Except for the output y(t) itself that can be directly measured, the other derivatives have to be derived according to the helicopter model (5). A considerable effort is required during this process. However, due to the limited space of this paper we represent these derivatives using Lie notation, such that: [j]

yi = Ljf hi (x, d)

(14)

where i = 1, 2, 3, 4, corresponds to four helicopter outputs, and j = 1, . . . , ρi . The control inputs will appear in the expression of ρi th derivatives. In order to make sure that all the related control inputs appear in the differentiation, we introduce δ¨col as the new control input in the third output, whereas δcol and δ˙col are treated as the states which can be obtained by adding integrators. This procedure is known as achieving relative degree through dynamics extension (Isidori, 1995). As a result, the vector relative degree for the helicopter is ρ = [ 4 4 4 2 ]. By invoking Eq.(14), we can construct matrix Y¯i , i = 1, 2, 3, 4. However, in order to find the elements in Y˜i , i = 1, 2, . . . , r + 1, further manipulation is required such that:  [ρ ]     ρ1  y1 1 Lf h1 (x, d) x[4]  [ρ2 ]   [4]  Lρ2 h (x, d) y   f 2 y   + A(x, d)˜ = Y˜1 =  2[ρ3 ]  =  u (15) ρ3 y3   z [4]  Lf h3 (x, d) ρ 4 [ρ ] Lf h4 (x, d) ψ [2] y4 4 ˜ = [ δlat + dlat δlon + dlon δ¨col δped + dped ]; nonwhere u linear terms Lρfi hi (x, d), i = 1, 2, 3, 4, can be found in the previous derivation, and   Lg4 Lfρ1 −1 h1 Lg1 Lfρ1 −1 h1 · · ·    Lg Lρ1 −1 h2 · · · Lg4 Lfρ1 −1 h2  1   (16) f A(x, d) =   ··· ··· ···   ρ1 −1 ρ1 −1 Lg1 Lf h4 (x) · · · Lg4 Lf h4 (x)

Differentiating (15) with respect to time together with substituation of the system’s dynamics gives

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  [ρ +1]   ρ1 +1 Lf h1 (x) y1 1  [ρ2 +1]  Lρ2 +1 h (x)  y   2 ˜) u[1] + p1 (x, u Y˜2 =  2[ρ3 +1]  =  ρf3 +1  + A(x, d)˜ y3  Lf h3 (x) [ρ +1] Lρf4 +1 h4 (x) y4 4 (17) ˜ ) is a nonlinear vector function of x and u ˜. where p1 (x, u By repeating this procedure, the higher derivatives of the output and Y˜i , i = 1, 2, . . . , r, can be calculated. So far by exploiting the helicopter model, the elements to construct Y¯ and Y˜ in Eq.(9) are available. Therefore, the output of the helicopter in the future horizon y(t + τ ) can be expressed by its Taylor expansion in a generalized linear form with respect to the prediction time τ and current states as shown in Eq.(9). In the same fashion as in Eq.(9), the reference in the receding horizon w(t + τ ), 0 ≤ τ ≤ T can also be approximated by: # " τ¯1 · · · 01×ρ4 | w(t + τ ) = · · · · · · · · · | τ˜1 · · · τ˜r+1 01×ρ1 · · · τ¯4 |   ˜ r+1 (t)T T ˜ 1 (t)T · · · W ¯ 4 (t)T |W ¯ W1 (t)T · · · W (18) ¯ i (t), i = 1, 2, 3, 4, and W ˜ i, where the construction of W i = 1, . . . , r + 1, can refer to the structure of Y¯i (t) and Y˜i , respectively. 3.2 Explicit nonlinear MPC solution The conventional MPC needs to solve a formulated optimisation problem to generate the control signal, where the control performance index is minimised with respect to the future control input over the prediction horizon. In this paper, after the output is approximated by its Taylor expansion, the control profile can be defined as τ r [r] ˜ (t+τ ) = u ˜ (t)+τ u ˜ [1] (t)+· · ·+ u ˜ (t), 0 ≤ τ ≤ T (19) u r! Thereby, the helicopter outputs depend on the control ¯ = {u variables u ˜, u ˜ [1] , . . . , u ˜ [r] }. Recalling the performance index (6) and the output and reference approximation (9) and (18), we have:   1 ¯ T1 T2 ¯ T ¯ (t)) ¯ (Y (t) − W (20) J = (Y (t) − W (t)) T2T T3 2 where T  Y¯ (t) = Y¯1 (t)T · · · Y¯4 (t)T |Y˜1 (t)T · · · Y˜r (t)T , (21)   ¯ (t) = W ¯ 1 (t)T · · · W ¯ 4 (t)T |W ˜ 1 (t)T · · · W ˜ r+1 (t)T T W (22) T1 , T2 and T3 can be calculated by using the first matrix in Eq(9) or (18). Therefore, instead of minimising the performance index (6) with respect to control profile u(t + τ ), 0 < τ < T directly, we can minimise the approximated ¯ , where the necessary condition index (20) with respect to u for the optimality is given by ¯=0 ∂J/∂ u (23) After solving the nonlinear equation (23), we can obtain ¯ ∗ to construct the optimal the optimal control variables u control profile defined by Eq.(19). As in MPC only the

current control in the control profile is implemented, the ˜∗ = u ˜ (t + τ ), for τ = 0. The resulting explicit solution is u controller is given by ˜ ∗ = −A(x, d)−1 (KMρ + M1 ) u (24) where K ∈ R4×(ρ1 +···+ρ4 ) is the first 4 row of the matrix T3−1 T2T ∈ R4(r+1)×(ρ1 +···+ρ4 ) where the ijth block of T2 is of ρi × 4 matrix, and all its elements are zeros except the ith column is given by h iT T ρi +j T 2ρi +j−1 (25) qi (ρi +j−1)!(ρ · · · q i (ρi +j−1)!(ρi −1)!(2ρi +j−1) i +j)

for i = 1, 2, 3, 4 and j = 1, 2, . . . , r + 1, and ijth block of T3 is given by 2ρ1 +i+j−1

diag{q1 (ρ1 +i−1)!(ρT1 +j−1)!(2ρ1 +i+j−1) , · · · , 2ρ4 +i+j−1

q4 (ρ4 +i−1)!(ρT4 +j−1)!(2ρ4 +i+j−1) }

(26)

for i, j = 1, 2, . . . , r + 1; the matrix Mρ ∈ Rρ1 +···+ρ4 and matrix Mi ∈ R4 are defined as:     ¯ 1 (t)T W Y¯1 (t)T     (27) Mρ =  ...  −  ...  T T ¯ ¯ W4 (t) Y4 (t) and

  ρ1 +i−1 Lf h1 (t)   .. ˜ i (t)T , i = 1, 2, . . . , r + 1. (28) Mi =  −W . Lfρ4 +i−1 h4 (t)

The detailed derivation and closed-loop stability of control law (24) can refer to (Chen et al., 2003). The overall controller structure is shown in Fig.1. Note that the system has a trivial zero dynamics as ρ1 + ρ2 + ρ3 + ρ4 = 14, which is the order of the helicopter dynamics plus the dynamic extension. In order to implement the above control strategy, the disturbances must be available, which is unrealistic for helicopter flight. Next section will introduce a nonlinear disturbance observer to estimate these unknown disturbances.

Fig. 1. ENMPC structure 4. DISTURBANCE OBSERVER BASED CONTROL 4.1 Disturbance observer For a system like a small-scale helicopter, precisely modelling its dynamics or directly measuring the disturbances acting on it are very difficult. However, the disturbance observer technique provides an alternative way to estimate them. Therefore, we introduce a nonlinear disturbance observer to estimate the lumped unknown disturbances d in the helicopter model (5). The disturbance observer

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(Chen, 2004) is as follows (scalar variables are used instead of vectors for the sake of simplicity): dˆ = z + p(x) (29) z˙ = −l(x)g2 (x)z − l(x)(g2 (x)p(x) + f (x) + g1 (x)u) T  is the estimation where dˆ = dˆx dˆy dˆz dˆlat dˆlon dˆped of disturbances; z is the internal state of the nonlinear observer, p(x) is a nonlinear function to be designed, and l(x) is the nonlinear observer gain given by l(x) = ∂p(x) (30) ∂x In this observer, the estimation error is defined as ed = d− ˆ Under the assumption that disturbance is slowly varying d. comparing to the observer dynamics, i.e. d˙ ≈ 0, and by combining Eq.(29)-Eq.(30) and Eq.(5), it can be shown that the estimation error has the following property: ˙ (31) e˙ d = d˙ − dˆ = −z˙ − ∂p(x) x˙ = −l(x)g2 (x)ed ∂x

ˆ Therefore, d(t) approaches d(t) exponentially if p(x) is chosen such that Eq.(31) is globally exponentially stable for all x ∈ Rn . The design of a disturbance observer is essentially to chose an appropriate gain l(x) and associated p(x) such that the convergence of estimation error is guaranteed. Hence, there exist a considerable degree of freedom. Since the disturbance input matrix g2 (x) in the helicopter model is constant, we can chose l(x) as a constant matrix such that the matrix −l(x)g2 (x) is Hurwitz. Next, integrating l(x) with respect to the helicopter state x yields p(x) = l(x)x. The observer gain matrix l(x) corresponding to g2 is designed in the form: (32) l(x) = [06×3 L 06×3 ] where matrix L = diag{l1 , . . . , l6 }, li > 0, i = 1, . . . , 6. Form the above analysis, it can be seen that the convergence of the disturbance observer is guaranteed regardless of the helicopter state x.

Fig. 2. Composite controller structure DOBC can be established, which is beyond the scope of this paper. 5. SIMULATION AND EXPERIMENT Simulations and experiments are based on a Trex-250 miniature helicopter. The parameters in the mathematical model are obtained through system identification. Flight experiments are carried out in our indoor testbed consisted of the Vicon motion tracking system and the ground station. Numerical simulations are first carried out to investigate the proposed control framework. In the simulation, it is assumed that there are 20% uncertainties on the model parameters. Furthermore, there is a constant wind disturbance with the speed of 5m/s acting on the helicopter. The helicopter is required to track an eight-shape trajectory with and without the compensation of DOBC. The tracking results are shown in Fig. 3. 2.5 Reference

ENMPC+DOBC

ENMPC

2 1.5 1

4.2 Composite controller

Start point

Disturbances no matter from external turbulences or internal uncertainties may significantly degrade the helicopter tracking performance, and may even cause instability unless their influence has been properly taken into account in the system design. It can be noted that in the previous derivation of ENMPC, the lumped disturbances appear in the control law. Therefore, once the disturbance observer provides the estimation of disturbances, ENMPC controller takes into account the disturbances by replacing the disturbance by their estimation and achieves desired tracking performance. The composite controller law using the estimated disturbances is given in ˆ −1 (K M ˆρ + M ˆ 1) ˜ = −A(x, d) u (33) where, the hatted variables denote the estimated values. If we consider trim errors in the helicopter dynamics, the overall control is ˜ −u ˆ0 u=u (34) T ˆ ˆ ˆ ˆ 0 = [dlat dlon 0 dped ] is the control trim error where u estimated by the disturbance observer. The composite controller structure is illustrated in Fig.2. The global asymptotic stability of the helicopter under the proposed composite controller consisting of ENMPC and

y (m)

0.5 0

End point

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Fig. 3. Eight-shape tracking It can be seen from the simulation that the ENMPC is able to deal with uncertainties and achieve satisfactory tracking, but it cannot compensate the steady state error mainly caused by the wind disturbance. In contrast, the action of DOBC taking into account the disturbances from both external and internal sources is able to eliminate the tracking error and achieve a better performance. Various flight tests, including aerobatic maneouvers, have been conducted to investigate the performance of the proposed control scheme on a real helicopter. One test presented here is a hovering and perturbation test. The

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helicopter was required to take-off and hovering on the origin at the height of 0.5m. A wind perturbation was then applied on the helicopter by posing a fan in front of the helicopter. The test results are given in Fig.4 and 5. In the test, the helicopter was first under the control of ENMPC to perform take-off and hovering. It can be seen that the ENMPC stabilised the helicopter but with a steady state error due to the mismatch between the model used for ENMPC design and the real helicopter dynamics. At 25 second of the test, the disturbance observer switched on and the composite controller took action to bring the helicopter to the setpoint. About 60 second, the fan was turned on to generate the wind gust. The average wind speed is about 3m/s, which is significant strong for our test helicopter with a small dimension. However, the composite controller exhibited an excellent performance under the wind gust and maintained the helicopter position very well.

solves the difficulties of applying model based control technique into practical environment. The design of ENMPC provides a seamless way of integrating the disturbance information. On the other hand the robustness and disturbance attenuation of the controller are enhanced by the nonlinear disturbance observer. Simulation and experiment results show promising performance of the combination of ENMPC and DOBC. Apart from the reliable tracking that the proposed controller guarantees, it also has the ability of estimating the helicopter trim condition during the flight which helps controller to deal with the variation of the helicopter status like payload changing and component upgrades. ACKNOWLEDGEMENTS The authors would like to thank financial support from Higher Education Council, EPSRC and BAE Systems. Cunjia Liu would like to thank Chinese Scholarship Council for supporting his study in UK.

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REFERENCES

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time (s)

Fig. 5. Control signals 6. CONCLUSION This paper describes a composite control framework for trajectory tracking of autonomous helicopters. The nonlinear tracking control is achieved by an explicit MPC algorithm, which eliminates the computational intensive online optimisation in the traditional MPC. On the implementation side, the introducing of disturbance observer

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