ADAPTIVE MODEL INVERSION FLIGHT CONTROL FOR TILTROTOR ...

Presented at the AIAA Guidance, Navigation and Control Conference, Aug. 1997, Paper No. 97-3758

ADAPTIVE MODEL INVERSION FLIGHT CONTROL FOR TILTROTOR AIRCRAFT Dr. Anthony J. Calise* and Rolf T. Rysdyk✝ Georgia Institute of Technology Atlanta, GA 30332

Abstract Neural network augmented model inversion control is used to provide a civilian tiltrotor aircraft with consistent response characteristics throughout its operating envelope, including conversion flight. The implemented response type is Attitude Command Attitude Hold in the longitudinal channel. Similar strategies can be applied to provide for Rate Command Attitude Hold in the roll channel, and Heading Hold and Turn Coordination for the yaw motion. Conventional methods require extensive gain scheduling with tiltrotor nacelle angle and speed. A control architecture is developed that can alleviate this requirement and thus has the potential to reduce development time, facilitate the implementation of handling qualities, and compensate for partial failures. One of the key aspects of the controller architecture is the accommodation of modeling error. It includes an online, i.e. learningwhile-controlling, neural network with guaranteed stability. The performance of the controller is demonstrated using the nonlinear Generic Tiltrotor Simulation code developed for the Vertical Motion Simulator at the NASA Ames Research Center.

1. Introduction The focus of this paper is on the development of adaptive nonlinear flight control algorithms that provide desired handling qualities as applied to a tiltrotor over a wide range of configurations. This includes, conversion from fixed wing to helicopter flight, mixing of the various forms of control, deployment and retraction of flaps and switching between flight augmentation modes. Developments in combining neural networks (NNW) and model inversion are exploited. Similar control strategies have been successfully applied to comprehensive simulations

of an F/A-18 airplane1 and an AH-64 helicopter2. The use of adaptive NNWs in this paper represents a unique application in the aerospace field in the sense that they are online, adapting while controlling, with guaranteed stability properties. This work also shows that the Stability and Control Augmentation System (SCAS) for a tiltrotor aircraft, with its ability to convert from airplane and large velocities to helicopter operation at low speeds, is an ideal candidate to benefit from a control architecture as presented here. Section 2 contains a description of desired handling characteristics and associated terminology. Section 3 outlines the implementation of the neural network augmented model inversion control architecture. The neural network structure is provided in section 4. Numerical results and evaluative remarks are included in the final sections.

2. Flight Control Augmentation for a Civilian Tiltrotor Two common types of control augmentation for aircraft are referred to as Rate Command Attitude Hold (RCAH) and Attitude Command Attitude Hold (ACAH). A good overview of various types of augmentation for the different control channels as used in the V22 are provided in Ref. (3). Ref. (4) represents an example of the considerations involved in an approach procedure, including; 1. a schedule for conversion of mast angle with speed, from airplane to helicopter in the regular approach and vice versa for a missed approach procedure, 2. deployment or retraction of flaps depending on nacelle angle, speed, and glide slope, 3. switching between augmentation types, and 4. desired altitude and speed trajectories. The tiltrotor provides a unique challenge since its control responses change as it converts from forward

*

Professor, School of Aerospace, Fellow AIAA. Phone: (404) 894-7145, E-mail: [email protected] Graduate Research Assistant, Student Member AIAA Copyright  1997 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. ✝

1 American Institute of Aeronautics and Astronautics


flight in aircraft configuration to slow flight as helicopter. Starting in airplane configuration, the throttle is used for speed and the longitudinal control (“cyclic” or “stick”) is used to initiate climb and descend. As the aircraft decelerates and converts into a helicopter configuration these controls trade roles. The throttle now represents the “collective”, controlling climb and descend, the longitudinal control results in changes in speed. In all flight conditions, the primary effect of longitudinal control is a change in pitch attitude. The attitude response to a longitudinal control input is therefore of considerable interest. The biggest challenge for augmentation is consequently offered by the longitudinal channel. A detailed report is provided in Ref. (5). ADS-33D6 prescribes Attitude Hold as the pitch attitude angle returning to ±10% of the peak excursion in less than 10 seconds following a pulse input. Similarly, Attitude Command implies that a step pitch command shall produce a proportional pitch attitude change within 6 seconds.

3. Neural Network Augmented Model Inversion This section contains the highlights of the neural network augmented model inversion as applied to the tiltrotor aircraft. It is based on the applications as described in Ref.(1) and Ref.(2). Fig.(1) contains the architecture used for implementation of ACAH control in the pitch channel. The pitch channel augmentation is the most challenging one and it has shown very good results. Preliminary results in the lateral channels have shown similar performance.

p

command filter

.. θp

K ac

Notation:

.

T

Θ = [θ, θ]

T

X=[u, w, q, θ ] Kpd=[Kd, Kp]

linear model of the rotational dynamics of the XV-15.

 u   p&   p δ LAT   v           + A2 ⋅  q  + B ⋅ δ LON   q&  = A1 ⋅   w   r&  r  δ       PED  δ COL 

~

Θ

K pd

U φ  U PDφ   φ&&C   0          U = U θ  = U PDθ  +  θ&&C  − U ADθ  U  U       ψ   PDψ  ψ&& C   0 

Θ

^

Uθ

U pdθ

^ -1

f

lon

XV-15

-

Here

neural net

(2)

X

Uad θ X Uθ

(1)

The states of interest for the augmentation are the Euler angular attitudes, and in particular the longitudinal pitch attitude θ and its primary control δLON. In order to implement an ACAH system in the longitudinal channel we consider inversion control using Eqn. (1). This involves replacing the left hand side of the equation with commanded angular accelerations and solving for the control perturbations. From the control architecture in Fig. (1) the pseudo control for the three rotational degrees of freedom is designed in terms of Euler angles as:

X

θc

Θc

nonlinear model for the XV-15. The model inversion is based on the linearized dynamics at 30 knots, level flight in helicopter configuration, with the rotor dynamics residualized. The purpose of this paper is to demonstrate that the pitch channel neural network is capable of adapting to errors caused by the linearized inverted model. Unmodeled dynamics originate from this linearization used in the derivation of the nominal inverting controller. Furthermore, any cross-coupling between fast rotational states and slow translational states is neglected in the inversion. The approximate inversion ( f$ −1 ) is based on a

scaling

bias

Figure 1: NNW Augmented Model Inversion Architecture. Model Inversion The simulation results presented here are from the extensive Generic Tiltrotor Simulation (GTRS)

U ADθ is an adaptive signal which represents the

neural network augmentation in the pitch channel. The proportional-derivative dynamics for the longitudinal channel are designed as:

U PDθ = K D ⋅ (θ&C − θ&) + K P ⋅ (θ C − θ )

(3)

The gains K P and K D are used to define the error dynamics. These dynamics are designed significantly faster than the command filter so as not to interfere with the handling qualities. These handling qualities are implemented through the design of the command filter. The quantities

θC

and


θ&C

are outputs of the command


filter. Thus the command filter serves both to limit the input rate, and as a model for desired response. Similar construction applies to the lateral channels. To use the pseudo control in Eqn. (1) it needs to be transformed from the Euler frame to the body axes. In terms of the individual components, the equivalent body angular acceleration commands are computed as: p&C = Uφ −Uψ ⋅ sθ −ψ& ⋅θ& ⋅ cθ q&C = Uθ ⋅ cφ −θ& ⋅φ& ⋅ sφ +Uψ ⋅ sφ ⋅ cθ +ψ& ⋅φ& ⋅ cφ ⋅ cθ −ψ& ⋅θ& ⋅ sφ ⋅ sθ r&C = −Uθ sφ −θ& ⋅φ& ⋅ cφ +Uψ cφcθ −ψ& ⋅φ& ⋅ sφcθ −ψ& ⋅θ& ⋅ cφ sθ

where

(4)

sφ is shorthand for sin(φ ) , etc. Replacing the

left hand side of Eqn.(1) with

{p&

C

q& C

r&C } and T

inverting gives:

 u   p δ LAT   p& C   v          −1  − A2 ⋅ q } δ LON  = B ⋅ {q&C  − A1 ⋅  w r    δ   r&     PED   C δCOL 

(5)

where

~ θ = θ C − θ , and ε θ

the inversion error when represented in the Euler frame. Eqn. (9) represents the error dynamics with the network compensation error as the forcing function. In the ideal case, the neural network output cancels ε θ .

4. Neural Network Architecture The neural network can consist of any linearly parameterized feedforward structure which is capable of approximately reconstructing the inversion error. For this demonstration a two layer sigma-pi network was used. The inputs to the network consist of the longitudinal state variables, the pseudo control and a bias term. Fig. (2) shows a general depiction of a sigma-pi network. The values vi represent the weights associated with a nested kronecker product of input signals, Eqn. (14), and therefore they are (binary) constants. The values wi are the variable network weights.

A1 , A2 , and B are not represented exactly we actually obtain δ$ .  u  δ$LAT   p& C   p    $  $ −1   $  v  $   & A B q A δ = ⋅ − ⋅ { − ⋅  LON   C  1  2  q } δ$   r&   w  r   C    PED  δ COL 

v1

V

C1

(6)

C2

V

^ W

V

1

Because in practice

is the pitch component of

π

2

1 u w q θ Uθ

v

1

vM

i

π

^ w1 ^ w2

^

Σ

UAD

^ wN

The inversion error in this case is defined as:

 u  δ$ LAT   p&   p  v          ε ≡  q&  − { A$1 ⋅   + A$ 2 ⋅  q  + B$ ⋅ δ$ LON } w δ$    r&   r       PED  δ COL  We may equivalently represent the effect of pitch attitude dynamics as:

θ&& = U θ + ε θ

ε

C3 (7)

Input Layer

π Output Layer

Figure 2: Neural Network Structure

in the

(8)

The input/output map of the neural network for the longitudinal channel may be represented as,

U ADθ = W T ⋅ β ( X , U θ )

(10)

where W is a vector of variable network weights, and β

Combining Eqn. (2), (3), and (8) we have:

~ ~& ~ && θ + K D ⋅ θ + K P ⋅ θ = U ADθ − ε θ

θ

(9)

is a vector of network basis functions, X represents the normalized states. The basis functions are chosen from a sufficiently rich set of functions so that the inversion error function, ε θ , can be accurately reconstructed at



the network output. The basis functions were constructed by grouping normalized inputs into three categories. The first category consists of,

5. Numerical Results

C1 = {1, V , V } 2

(11)

where V is the normalized airspeed. This is used to model inversion error due to changes in airspeed, since the stability and control derivatives are strongly airspeed dependent. The second category consists of normalized longitudinal state variables and the pseudo control.

C2 = {1, u, w, q, θ , U θ }

(12)

The third category is used to approximate higher order effects due to changes in pitch attitude. These are mainly due to the transformation between the body frame and the inertial frame.

C3 = {1, θ }

(13)

The vector of basis functions is composed of possible products of the elements of C1 , C2 , and C3 , by means of the kronecker product.

all

(

β = kron kron(C1 , C2 ), C3

that the network can not exactly reconstruct the functional form of inversion error.

)

(14)

where,

The XV-15 itself is represented by the comprehensive nonlinear Generic Tiltrotor Simulation code. This code includes complete augmentation, here referred to as ‘original SCAS’. This SCAS is gain scheduled with speed and with mast-angle (though not with altitude). In the longitudinal channel it provides ACAH and RCAH, depending on the mode selected by the pilot. The ACAH setting was used for the comparison in the following results. Model inversion control, as given by Eqn. (6), was applied to the XV-15 with the aerodynamics linearized about the 30 Kts level flight helicopter configuration. The linear model used for inversion is based on the assumption that the rotor was in a quasi steady state. A third order command filter is used so that θ&&C is continuous for a step in θ P , see Fig. (1). The dominant complex poles of the filter provide minimal overshoot ( ζ =.8 ) and a 5% settling time of

1.5 seconds ( ω n = 2.5 rad sec ), which provides Level 1 handling characteristics in the pitch channel5. The gains KP and KD were chosen so that the error dynamics settle in 0.5 second ( ζ = 10 . ,

ω n = 6.0 rad sec ).

Comparison at Nominal Operating Point

kron(x, y) = [x1 y1

x1 y2 L xm yn ]

T

(15)

Figure 3 shows the response to a commanded square wave pitch input, shaped by the command filter.

The network weights are adapted on-line according to the following equation,

γ >0 s=

is the adaptation gain and,

actual attitude commanded attitude 0

−5 Original SCAS −10 0

1 1 ~ ~& ⋅θ + ⋅θ K 2 ⋅ KP 2 ⋅ D (1 + K ) ⋅ K P P

(17)

The adaptation law was designed based on a Lyapunov stability analysis of the error signals1. It relies on the use of a deadzone in which the adaptation law is turned off when a weighted norm of the error signals is small. The purpose of the deadzone is to account for the fact

Mod.Inv.SCAS

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(16)

Pitch Attitude [deg]

W& = −γ ⋅ s ⋅ β

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Figure 3: Comparison near the nominal operating point.



Pitch [deg]

The aircraft is trimmed at the 30 Kts level flight helicopter configuration. During the first thirty seconds it responds using the original gain scheduled SCAS design, the aircraft remains within 10 Kts and within 250 ft of its altitude. At t = 30 sec. the model inversion SCAS is activated as evidenced by the NNW weight histories. The improvement in pitch response is clearly visible in Fig. (3).

7 6 5 0

Actuator [in] NNW Weights

Fig. (4) shows the results of engaging the model inversion SCAS near one of the boundaries of the operating envelope. The XV-15 is flying in airplane configuration, with 300 Kts, at 35,000 ft. Two remarks are important here. First, the original SCAS is not scheduled with altitude and merely serves to show the effects of operating at 35,000 ft. Second, the NNW is now suddenly engaged which is not likely to be a normal operating procedure. However, it shows the essential effects of the adaptation of the weights. Fig. (5) shows a detail of this process.

Pitch [deg] Elevator [deg]

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ADS-33D6, states as one of the so called Level 1 (most stringent) flying quality requirements: “…The pitch attitude shall return to ± 10 % of the peak excursion, following a pulse input, in less than 10 seconds for UCE > 1. … …The attitude [.] shall remain within the specified 10 % for at least 30 seconds… ”

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Figure 5: Detail of step response in Fig. 4.

Mod.Inv.SCAS Original SCAS

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Operation near the Boundary of the Envelope

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Fig. (6) shows the results for the longitudinal channel at the nominal operating point, in helicopter configuration. The model inversion SCAS provides a Level 1 response whereas the original SCAS does not.

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Mod.Inv.SCAS Original SCAS Open Loop

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Figure 4: Step response at 300 Kts, 35,000 ft, aircraft configuration. The first second the aircraft is flying open loop, in approximate trim flight at 35,000 ft. At t = 1 sec. the model inversion SCAS is suddenly activated. The model inversion is based on the 30 Kts trim values and this instantaneously causes an actuator deflection that reflects this discrepancy. However, in the next 0.5 sec. the NNW, with the initial weights all zero, is able to adjusts for the error caused by the model inversion. (Actuator dynamics are not modeled in GTRS, but similar applications with actuator dynamics modeled have not shown significant differences.)

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Figure 6: Attitude hold demonstration at nominal operating point, helicopter configuration.


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Figure 7: Attitude hold demonstration at a boundary of the flight envelope. To further evaluate the performance of the neural network adaptive control a pilot model was developed. This model is able to perform such tasks as, 1. follow desired altitude profiles, 2. follow desired speed profiles, 3. operate on both sides of powercurve, 4. convert, including flaps as well as nacelle angle changes, 5. operate with different SCAS modes. The pilot model can provide lead, lag, or act as a P+I controller if necessary. Root locus methods were used to select desirable closed loop characteristics. Ref. (4) details the development of the longitudinal pilot model, which includes the mixing of control strategies mentioned above. The neural network augmented control is evaluated in a nonlinear simulation of transition from forward flight in airplane mode to landing in helicopter mode. In addition, an indication of the performance and the pilot workload under turbulent conditions is possible. An example is provided in Fig.’s (8) and (9). The figures show a comparison between the original SCAS and the model inversion SCAS. The data for the model inversion was recorded every .1 sec, the original SCAS was recorded every second. (For both cases GTRS uses an integration step size of .01 sec.)

Altitude profile [ft]

Mod.Inv.SCAS Original SCAS Open Loop

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1000

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Pitch [deg]

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The maneuver shown is a simulated approach to minimum descend altitude, starting at 1,000 ft, from the nominal operating configuration, i.e. 30 Kts in helicopter configuration. The desired descend rate is 1,000 fpm. The primary control for establishing the descend rate is the collective. However, the maneuver has an effect on the velocity which is subsequently controlled by the pilot model through pitch commands. The pitch histories show that the model inversion SCAS provides some improvement in this benign maneuver. The model inversion control is based on the nominal operating point and this is reflected in the first 5 sec. of the NNW weight histories. At t = 0.5 sec the descend is initiated and a new trim point is established. After approximately 50 sec. the desired altitude is reached and maintained. Subsequently, the aircraft is once more established close to the nominal operating conditions but this time at 200 ft. This is visible in the NNW weights as they are again reduced.

NNW Weights

With zero commanded input, the architecture in Fig. (1) provides the ‘hold-part’ or ‘stabilization-part’ of ACAH by the dynamics determined by KP and KD, i.e. the error dynamics as represented by Eqn.(9). With reference to the two remarks made for Fig. (4) above, Fig. (7) shows the Attitude Hold performance at the 35,000 ft condition in aircraft configuration.

0 −1 −2 0 0

−0.1 −0.2 0

Figure 8: Approach to landing. Fig. (9) shows the same approach but now in turbulent conditions. The flight progresses through Dryden turbulence with a spatial turbulence intensity σ = 5 ft sec and a turbulence scale length of

LW = 1750 ft . The results suggest that the model inversion SCAS might provide for a reduction in pilot workload under these circumstances and perhaps increased passenger comfort. Perturbations in pitch also occur when converting from aircraft to helicopter, due to the changing angle of the rotor systems, i.e. the nacelle angle. The nacelle angle is 0 deg. in aircraft configuration, and converts to 90 deg. for helicopter flight. Fig. (10) contains the results of a − 01 . G decelerating conversion. The nacelle angles and flap



settings were scheduled with airspeed. The results show a similar suppression of the pitch excursions as in the turbulence situation in the case of the model inversion SCAS. The neural network weights follow the changes in configuration as the aircraft converts.

4.

Similar strategies as applied to the pitch channel should provide for good performance in the lateral channels. An extension of the architecture as outlined in section 3 should lead to fully automated trajectory following.

Vert.turb. [ft/s]

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References

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[1]

Kim, B.S., and Calise, A.J., “Nonlinear Flight Control Using Neural Networks,” AIAA Journal of Guidance, Navigation and Control, Vol. 20, No. 1, 1997.

[2]

Leitner, J., Calise, A., and Prasad, J. V. R., “Analysis of Adaptive Neural Networks for Helicopter Flight Controls,” Proceedings of the AIAA Guidance, Navigation, and Control Conference, Baltimore, MD, 1995, pp. 871-879.

[3]

Goldstein, K.W., and Dooley, L.W., “V-22 Control Law Development,” AHS 42nd Annual Forum, Washington, D.C., June 1986.

[4]

Decker, W.A., “Piloted Simulator Investigations of a Civil Tiltrotor Aircraft on Steep Instrument Approaches,” AHS 48th Annual Forum, Washington, D.C., June 1992.

[5]

Calise, A.J., and Rysdyk, R.T., “Research in Nonlinear Flight Control for Tiltrotor Aircraft Operating in the Terminal Area,” NASA NCC†2-922, November 1996.

[6]

Aeronautical Design Standard, “Handling Qualities Requirements for Military Rotorcraft”, ADS-33D, U.S.Army, St. Louis, MO, July 1994.

[7]

Churchill, G.B., and Gerdes, R.M., “Advanced AFCS Developments on the XV-15 Tiltrotor Research Aircraft,” AHS 40th Annual Forum, Arlington, VA, May, 1984.

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Figure 9: Approach to landing with turbulence. Mod.Inv.SCAS Original SCAS

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Conclusions and Further Work The following conclusions can be drawn from this research: 1. The neural network augmented model inversion control is a valuable method for providing augmentation throughout conversion of a tiltrotor aircraft. 2. Tracking error and network parameters converge fast. 3. A relatively simple neural network is sufficient to provide stability for the operations considered.
