design of autopilots for tactical aerospace vehicles - Science Direct

Third International Conference on Advances in Control and Optimization of Dynamical Systems March 13-15, 2014. Kanpur, India

DESIGN OF AUTOPILOTS FOR TACTICAL AEROSPACE VEHICLES: A COMPARITIVE STUDY Narayanan, Vignesh*. Swarup, Akhilesh* Halder, Pulak** 

* National Institute of Technology, Kurukshetra, Department of Electrical engineering, India (email:[email protected]) **National Institute of Technology, Kurukshetra, Department of Electrical engineering, India (e-mail:[email protected]) ***Research Centre Imarat, Hyderabad, India(e-mail: [email protected]) Abstract: The objective of this paper is to provide an analysis of some of the control techniques for autopilot design for tactical aerospace vehicles (TAV). The major contribution of this paper is to bring together few control techniques used for the design of autopilot for TAVs and assessment of the performance of the autopilots with the same airframe dynamics as comparative study. A comparative account of control methods has been presented on the basis of system performance, which will be helpful in selection of proper control. The control design and analysis has been illustrated through simulation exercise. Keywords: Non-minimum phase system, optimal control, PID control, Pole assignment 

and pitch acceleration/attitude while keeping side-slip angle and lateral acceleration zero. In STT type of tactical aerospace vehicle roll angle/rate is kept zero and tracking in pitch and yaw planes are required.

1. INTRODUCTION The operation of controllers for a tactical aerospace vehicle can be explained in three layers, the guidance system, the autopilot system and the actuator system. These three subsystems are present in all the tactical aerospace vehicles. The guidance system does the job of path correction, i.e. it finds the relative distance/direction of the vehicle with its target with the help of on-board or off-board sensor systems and gives command to the autopilot subsystem in the form of desired acceleration/orientation required to keep the vehicle in the desired trajectory which will eventually lead to successful interception of the target. The autopilot system is the inner feedback control system which detects and reduces the difference between the commanded and actual acceleration/orientation by giving commands to the actuator system. The actuator system produces the desired deflection in the control effectors such that sufficient force/moment is produced to steer the vehicle along the desired trajectory. The block diagram of the three layered control scheme is shown in Fig. 1 given in Kadam, N.V. (2006).

The dynamics of the autopilot system of TAV is non-linear, time varying and also subject to uncertainty. Additional challenges in the design of autopilots for such system are the disturbances due to wind gusts, atmospheric pressure, and temperature, interaction between guidance and actuator loops and coupling between the three channels(roll, pitch and yaw). In practice, few assumptions are made to simplify the system dynamics and controllers are designed for a simplified linear time invariant model of the air-frame of the vehicle. The assumption made for design of autopilot is time-slice approach where for a short time interval, few parameters are assumed to be constant. In addition to this, for BTT configuration adiabatic approximation is made i.e., roll rate is assumed to be constant and for STT configuration it is assumed that the TAV is roll stabilized. (Garnell, P., East, D.J.(1977)., Siouris, G.M(2004))

Based on the method of steering, the TAVs are classified as bank-to-turn (BTT) and skid-to-turn (STT). The BTT type vehicle use polar co-ordinates and follow ‘rotate (bank) and accelerate’ type of steering. The STT type use Cartesian coordinates and follow ‘up-down and left-right’ type of steering. The BTT vehicles usually have asymmetric structure, less structural weight, high lateral acceleration (latax) capability and they provide easier accommodation to air-breathing engines as compared to STT vehicles. But, in the STT configuration the effects of coupling in the rollpitch-yaw channels is less as compared to the BTT configuration where couplings are very high. The general design goal for a BTT system is tracking of roll angle/rate

978-3-902823-60-1 © 2014 IFAC

Fig. 1: Three layered control architecture for tactical aerospace systems

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2014 ACODS March 13-15, 2014. Kanpur, India

In this paper, the main focus is on design of autopilot for a tail controlled STT tactical aerospace vehicle. The paper is organised as follows: in the next section review of autopilot design and current trends are discussed. In section - 3, PID and pole placement techniques are used to design the autopilots. In the section - 4, linear quadratic function based control technique is used for designing the autopilot. In the section - 5, all the controller performances are tabulated and a qualitative analysis is done. Conclusions follow in section 6.

the robustness of the controllers modal synthesis was proposed by Chung, J.C., Shapiro, E.Y. (1982). Using output feedback, Eigenstructure assignment was done and it was shown that the robustness of the controller improved at the expense of performance. To obtain robust co-ordinated autopilots for BTT vehicle, an optimal control technique was proposed by Lin and Yeuh (1985). Similarly H-infinity control, structured singular value technique were proposed and µ- synthesis techniques (Reichart, R.T., (1990)) with Hinfinity technique (Wise, K.A., et al. (1990)), disturbance rejection using projective controls, generalized singular robust control design were all applied to the autopilot design for a TAV and their effectiveness are well documented in the literature.

2. REVIEW OF AUTOPILOT DESIGN TECHNIQUES AND CURRENT TRENDS The autopilots were designed and implemented using microprocessors in early 1970. Despite the extra dynamics introduced due to sample and hold circuits because of analog to digital conversion/digital to analog conversion, the computational delays and quantization errors, the digital autopilots proved to be an effective method to design and implement autopilots which is evident from the work done by Albanes, W.V., Bosley, J.T.(1979)., Butler et al.(1982).

Similarly for performance improvement, several control techniques were proposed such as linear quadratic Gaussian control, LQR technique, LQG with loop transfer recovery and many variants. As the theory of non-linear control developed non-linear dynamics of the TAV airframe was considered and control design was done. Optimal control using polynomial feedback was proposed, feedback linearization techniques (Jin-Young Choi, et al(2000)), robust feedback linearization techniques, functional inversion (Jae Hyk Oh., In-Joong Ha.(1997)), sliding mode control, singular perturbation techniques (Ju-Il Lee, In-Joong Ha (1999)) etc., were also applied for design of autopilot for tactical aerospace vehicle as the performance requirements of the system greatly increased. Some adaptive techniques such as robust adaptive back-stepping (Kim, S.H., et al. (2004)), hybrid neural network based control (McFarland, M.B., Calise, A.J.(2000)., McDowell, D.M., Irwin, J.W.(1997)), fuzzy based self-tuning control were proposed and their applicability for autopilots were proven. Despite enormous research efforts the autopilot design still provides lot of challenges and still many TAVs prefer classical design approach which can be attributed due to the implementation problems associated with adaptive control laws or may be due to the effectiveness of the classical control techniques. Due the requirements of the modern day tactical aerospace vehicles the physical system configurations are also changing, TAVs employ reactive thrusters to change their orientation instantly. It is highly essential to provide effective control methodologies to accommodate the changing scenario in the autopilot design for a TAV. In this paper, few control techniques which are available and practically used in the autopilot design for a TAV have been used to design autopilot systems and their performance are analysed.

The control parameters commonly used in the autopilots of TAV are attitude, lateral acceleration, and angle of attack. The attitude autopilot is less efficient as compared to the latax autopilot (Kadam, N.V. (2006)). But the disadvantage of the latax autopilot is that sufficient latax can be produced only after the TAV has gained a minimum velocity. One other complication in the latax autopilot is that for tail controlled configuration the dynamics obtained for the airframe plant model is of non-minimum phase type. The angle of attack based autopilot is shown to be better than the latax autopilot (Garnell, P., East, D.J.(1977)., Siouris, G.M(2004)). But the disadvantage is that angle of attack should be estimated and cannot be measured directly which requires a robust observer. The basic design of an autopilot for a TAV is done by linearizing the dynamics of the vehicle for a number of operating points and controllers at each of these operating points are designed. The control gains are available in look-up table which are then scheduled as a function of altitude or atmospheric pressure or Mach number or roll angle/rate or angle of attack or some suitable function. Although the design procedure is tedious and time consuming they provide an excellent control of the vehicle over the complete flight path, (Garnell, P., East, D.J.(1977)). So to improve the performance of the system controlled by gain scheduling interpolation techniques were introduced (Stilwell, D.J., Rugh, W.J.(1999), Nichols, et al. (1993)). But due to growing requirements of high manoeuvrability, and minimum miss distance, the design requirements have become more demanding and solutions for highly swift, light weight air-to-air TAV autopilots are being investigated.

3. AUTOPILOT DESIGN USING PID CONTROLLER AND POLE-PLACEMENT TECHNIQUE The airframe dynamics used in this paper are derived for a STT, tail-controlled vehicle. The data of aerodynamic coefficients are obtained from (Kadam, N.V. (2006)). Actuator dynamics are taken as second order with damping factor 0.6 and 180 rad/sec. In this section, PID controller and controllers based on pole-placement technique for the wellknown 2-loop configuration, 3-loop configurations are

A number of control techniques have been proposed and tried out for the autopilot design for a TAV. The entire flight path of the aerospace vehicle is not known in advance. It depends on their target and the autopilots should take care of all the uncertainties and stabilize the airframe during the entire flight. So a number of control techniques were proposed to improve the robustness of the autopilots and stabilize the airframe in the face of uncertainties. For the improvement of 272


designed for the pitch plane autopilot. The rigid body angular rate dynamics of the airframe in pitch plane is given by,

The oscillations in the PID based latax autopilot, where noise is assumed to be zero, is not desired. If the values of kp, ki, kd are tuned further, the response of the system can be obtained which is devoid of oscillations but the bandwidth of the system reduces greatly and the response of the system becomes very slow. For a tactical aerospace vehicle speed of response and stability are two main performance requirements. Though they are inversely related the trade-off that is achieved with PID control is not satisfactory. The performance plots for the PID control with no oscillations is given in Fig. 4.

(1) And the acceleration dynamics is given by, (2) Where, = normal moment component per unit control deflection angle about body Y axis

In the step response plots, the time in x-axis is in seconds and y-axis is output (latax in m/s2).

= normal force component per unit angle of attack along body Z axis = normal moment component per unit angle of attack about body Y axis = normal force component per unit control deflection angle along body Z axis. q = Rigid body rotation rate az = Acceleration achieved perpendicular to TAV body = Control surface deflection angle Classical PID controller is designed for the lateral acceleration control of the airframe in pitch plane. The block diagram is shown in Fig. 2. The classical PID is tuned initially using Zieglar-Nichols technique and fine tuned later to obtain the best performance in terms of speed of response which can be obtained with the control gains Kp, Ki, Kd are 0.0004,-0.029,-0.0491e-5 respectively.

Fig. 4: Performance plots for the PID controlled autopilot with gains Kp = 0.0001, Ki = -0.005, Kd = -0.0491e-5

Fig. 2: Classical PID based autopilot block diagram

If the sensor noise is added in the feedback path, the following step response is obtained. The measurement noise (white noise) in the feedback path is considered to be in the range of 0.03 m/s2 at the accelerometer input and in the rate gyro it is considered to be in the range of 0.1 degrees per second.

Fig. 5: Step response for PID controller with measurement noise

Fig. 3: Performance plots for the system given in Fig. 2 273


As second method, classical pole-placement technique with output feedback is used to design the autopilot for the same airframe dynamics. The block diagram of the two-loop configuration is given by Fig. 6. In the two-loop configuration an additional constraint on the bandwidth is laid to preserve the stability of the overall closed loop structure. The ratio of the rate loop and acceleration loop bandwidth should be greater than 4 (Kadam, N.V.(2006), Garnell, P., East, D.J.(1977)). By using pole placement technique, control gains are obtained. The step response and the bode plot of the configuration yielding best performance for the give airframe dynamics is given in Fig. 7. The control gains Ks, Ka, Kr are -0.019, 0.3555,-51.1837 respectively.

Fig. 8: Step response for the two-loop latax configuration with sensor noise The third approach is to apply pole-placement technique for three loop configuration. The advantage of three loop configuration over the two-loop configuration is that it gives direct control over the maximum vehicle body rate, which can be controlled by suitably changing the control gain. In homing vehicles, such control over maximum body rate is essential as high body rates affect the seeker system and could lead to high bore sight error (Kadam, N.V. (2006)). The block diagram of the three-loop latax autopilot configuration is given in Fig. 9 and the corresponding step response and frequency plot with the control gains Ks, Ki, Kr, Ka are -0.0133, 27.4519, 0.3323, 0.8794 respectively is in Fig. 10 and Fig. 11 shows the response with measurement noise.

Fig. 6: Two-Loop configuration block diagram The performance of the two-loop, lateral autopilot when the sensor noises are considered were simulated and the step response for the same is given in Fig. 8.

Fig. 9: Three-loop latax autopilot block diagram

Fig. 7: Performance plots for the system given in Fig. 6

Fig. 10: Performance plots for the system given in Fig. 9

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Fig. 11: Step response for the three-loop latax configuration with sensor noise

Fig. 12b: Performance plots of LQR controller For a cost function which includes the output terms instead of the states, a control law was derived with the MATLAB tool, which gave zero over-shoot.

For the design of controllers by the above three methods, the controller gains can be obtained from standard tuning techniques like parameter plane method. 4. LINEAR QUADRATIC FUNCTION CONTROLLERS FOR AUTOPILOTS

∫

BASED

Where, Y is the output vector with lateral acceleration and pitch rate as its entries. The step response and the Bode plot for the system designed with the objective to minimise cost function for the following weighting functions is given in (4) is given in Fig. 13.

LQR based controller is designed for the same airframe dynamics of the TAV autopilot to achieve tracking and meet the performance requirements. For the design of LQR, standard cost function is used which is given by (3). ∫

(4)

(3)

R=(

) and Q = (

)

Where, J is the cost function. X is the state vector, u is the control input and Q and R are the weighting matrices. The performance plots of the latax autopilot using LQR technique is given in Fig. 12. The velocity of the vehicle along the body z-axis, pitch rate, control surface deflection angle and control surface deflection rate are the states of the system. The weighting matrices are chosen to get the best performance for this control configuration. The simulation results are given for

R=(

) and Q = (

)

Fig. 13: Performance plots of LQ controller with cost function in (4) A control law was obtained for reducing the cost function which includes an integral of the error, whose controller configuration is given in Fig. 14, using the tool available in MATLAB. The performance of the autopilot designed by the above method is given in Fig. 15.

Fig. 12a: Step response of LQR controller

Fig. 14: Linear quadratic integral error control autopilot block diagram (Young, P.C., Willems, J.C.(1972))

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The configuration in Fig. 13 is used to design a tracking controller to improve the tracking of the command signal by the system.

5. COMPARITIVE RESULTS The performance of the control schemes which are designed using standard control techniques in the last two sections are tabulated in Table 1. The table provides a quick overview of the performance of different controllers for autopilot design of a TAV. The tactical vehicles whose objective is to intercept a fast moving target needs a good speed of response. The TAV whose targets are not manoeuvring rapidly can settle for a moderate speed of response and hence it will have robustness. The stability margins can also be interpreted in the following way. If the stability margins are high, the number of gain scheduling points may reduce. The measure of high stability margin is relative to the physical system and the designed flight path, altitude and velocity. Table - 1

Fig. 15a: Performance plots for the configuration in Fig. 13

Fig. 15b: Performance plots for the configuration in Fig. 13

SPECIFICATION

2loop

3loop

PID

LQR

LQG

LQI

LQRY

Under-Shoot %

21

15.9

8

17.5

10

52

11.8

Over-Shoot

8.78

0

49

6

0

20

7

Rise time in s

0.07

0.12

0.16

0.11

3.2

0.05

0.09

Settling time in s

0.2

0.18

2.13

0.23

5.5

0.12

0.13

Gain Margin in dB

15.6

10

2.03

21

5

16

Inf

Phase Margin in deg

Inf

75

26.4

72.3

41

50

82.6

%

The 2-loop and 3-loop mentioned in the table are the two configurations which are used where pole placement technique is used to obtain the controller gains.

A controller was obtained for the control of the same airframe dynamics using the LQG synthesis tool in the MATLAB software considering minimum noise at the sensor inputs. The performance of the obtained controller is provided in Fig. 16.

From the simulation results obtained for the different control schemes, the following inferences have been made. (a) PID control produces the least undershoot which implies, less actuator effort is required to produce the lateral acceleration as compared to other controllers. But the stability margins are very poor and bandwidth is so low and hence the system response is very slow. (b) The pole placement using two-loop configurations and three-loop configurations differ in the bandwidth ratio of inner loop and outer loop, which is good for three loop configuration as compared to two loop configuration. The stability margins are reduced a bit in three loop configurations but are satisfactory. And the major advantage of the three loop configuration is the direct control over the maximum angular rate which was already mentioned. (c) In the presence of measurement noise, PID controller based autopilot, two-loop latax autopilot and three-loop latax autopilot shows jitters in their step response. PID and three-loop configurations based autopilot show more fluctuations in their response as compared to the two-loop latax autopilot. In all the cases, the acceleration loop noise

Fig. 16: Performance plots of LQ controller with noise in the system

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has little effect on the overall response of the system. This is because the bandwidth of the acceleration loop is less. But the noise picked up by the rate gyros is having higher impact on the system response. The bandwidth of the rate loop is the reason behind the variations in the response of twoloop configuration, three-loop configuration and PID based autopilot.

Garnell, P., East, D.J.(1977). Guided weapon systems. Pergamon press. Siouris, G.M. (2004). Missile guidance and control systems, Springer-verlog, New York. Nichols, A.R., Reichart, R.T., Rugh, W.J.(1993). Gain scheduling for H – infinity controllers: A flight control example. IEEE transactions on control systems technology, Vol – 1, 69-79.

(d) The optimal control laws obtained by minimizing three different cost functions are provided here. The standard LQR based control law gives an excellent response. If the output term is added to the cost function instead of states, the performance improves further. But the addition of integral of the error in the cost function degrades the performance of the autopilot. The major disadvantage in this case was the undershoot.

Stilwell, D.J., Rugh, W.J. (1999). Interpolation of observer state feedback controllers for gain scheduling. IEEE transactions on automatic control, Vol – 44, 1225-1229. Albanes, W.V., Bosley, J.T. (1979). Digital autopilot design for a microprocessor controlled small tactical terminal homing missile. IEEE transactions on aerospace and electronics systems, Volume: AES-15, 908-911. Butler, Marlon .L., Pastrick, Harold.L. (1983). Digital autopilot design and evaluation for FAMMS American control conference, San fransico, 1062-1067.

(e) The control law obtained by taking into account the measurement noise to give a control law which minimizes the standard linear quadratic cost function yields a controller of fifth order and the response curves are highly damped.

Chung, J.C., Shapiro, E.Y. (1982). Modal synthesis of missile autopilot control law, American control conference, Arlington, 1166-1171.

(f) The major disadvantage with LQ based control law is that the state estimates are required for applying the control law.

Ching-Fang Lin., William, R. Yueh. (1985). Coordinated bank-to-turn autopilot design, American control conference, Boston, 922-926.

(g) The controller designed by using LQG synthesis tool in MATLAB with minimum noise has a response which is very robust making the system slow and immune to noise. Such controller can be used when the target of the TAV is stationary or moving very slowly.

Riechert, R.T.(1990). Robust autopilot design using µsynthesis. American control conference, San diego, 23682373. Wise, K.A., Mears, B.C., Poolia, K. (1990). Missile autopilot design using H – infinity optimal control with µ- synthesis. American control conference, San Diego, 2362-2367.

6. CONCLUSIONS

McFarland, M.B., Calise, A.J.(2000). Adaptive nonlinear control of agile antiair missiles using neural networks. IEEE transactions on control systems technology, Volume:8, 749756.

The dynamics of tactical aerospace vehicle autopilot is controlled using PID controller, Pole-placement technique for two configurations and optimal control laws were obtained for three different cost functions. Also, one control law for considering the measurement noise has been analysed for control performance. The performance of the PID and Pole placement based control configurations in the presence of noise has also been presented for comparison with the LQG based controller. The performance of all the controllers is obtained from simulations done in MATLAB software. The comparative results obtained and presented in this paper provide a good understanding of suitability of the controllers for specific applications. Such study was not available in the literature directly. Further, efforts will be made to understand the effects of noise in the LQ based control laws and design compensators to improve the performance of the controllers in the presence of noise.

Jin-Young Choi., Dongkyoung Chwa., Min-soon Kim. (2000). Adaptive control of feedback linearized missiles with uncertainities, IEEE transactions on aerospace and electronics, Vol – 36, 467-481. Ju-Il Lee., In-Joong Ha. (1999). Autopilot design for highly maneuvering STT missiles via singular perturbation like technique, IEEE transactions on control systems technology, Vol – 7, 527-541. McDowell, D.M., Irwin, J.W., Lightbody, G., McConnell, G. (1997). Hybrid neural adaptive control for bank-to-turn missiles. IEEE transactions on control systems technology, Vol – 5, 297-308. Jae-Hyuk Oh., In-Joong Ha. (1997). Missile autopilot design via functional inversion and time scaled transformation. IEEE transactions on aerospace and electronic systems, Vol – 33, 64-76.

REFERENCES Kadam, N.V. (2009). A practical design of flight control systems, Allied publishers Pvt. Ltd.

Seung-Hwan Kim, Yoon-Sik Kim, Chanho Song. (2004). A robust adaptive nonlinear control approach to missile 277


autopilot design. Control engineering practice, Elsevier, Vol – 12, 149-154 Nesline F, Jr., Nesline, L. Mark. (1985). Phase vs gain stabilization of structural feedback oscillations in homing missile autopilots. American control conference, Boston, 323-329. Young, P.C., Willems, J.C. (1972). An approach to linear multivariable servomechanism problem. International journal of control, Vol – 15, 961-979.

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