A NEURAL CONTROLLER FOR ON BOARD TRACKING PLATFORM

A NEURAL CONTROLLER FOR ON BOARD TRACKING PLATFORM OCTAVIAN GRIGORE- MÜLER 1 Key words: Airborne warning and control systems (AWACS), Incremental motion controller, DC servomotors with low inertia induce, Electro-hydrostatic actuators (EHA), Electro backup hydrostatic actuators (EBHA). The changing of classical actuators of an automatic control system of the position in a digital one implied to develop a new philosophy to control them. Thus for these automatic control systems was developed a full digital control. The existing of this type of control can be possible to apply a neural controller. In this paper a platform-tracking neural controller on board of an AWACS aircraft is designed. 1. INTRODUCTION It is well known that the actually forced actuators on board of aircraft are made both hydraulically and electrically with so-called EHA and EBHA actuators. But in the last years with the appearance of the idea of an all electric aircraft the forced actuators must be made electrically. These significant actuators which was specially developed to be compatible with the digital data processing are the stepping motors, the low-inertia DC servomotors, the DC brushless servomotors, the electromagnetic clutches and some hybrid motors. A block scheme of a digital position automatic control system with such type of actuators is shown in Fig. 1. In this case the command of the actuators was made with a digital controller. To decrease the time of response and increasing the reliability of the digital command system, especially for military applications, the command of such digital actuator can be made by intelligent techniques, respectively with aide of a neural controller (Fig. 2). 1 Politehnica University of Bucharest, Faculty of Aerospace Engineering, Veteranilor 27, Bl. D4, Apt. 18, Sect. 6, Bucharest, E-mail: octavian.grigore@gmail.com,octavian grigore@avionics.pub.ro Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 54, 2, p. 213 222, Bucarest, 2009

214 Octavian Grigore-Müler 2 Fig. 1 The complete digital position automatic control system. Fig. 2 The digital position automatic control system made with neural controller. 2. THE CLASSICAL DIGITAL MOTOR CONTROLLER DESIGN The classical digital motor controller is made with the DC-DC converters. From literature is known that this type of converter may operate in either continuous or discontinuous mode. In the discontinuous mode, the nonlinear external family characteristics affect the gain characteristics of the current control loop [5]. If, for example, the loop gain is optimized for discontinuous mode at a certain operating point, the loop will tend to be unstable at continuous conduction. The normalized armature circuit equation in the conduction mode for a DC- DC converter can be given as follows [8]: 1. for the discontinuous mode: where: I 2 is the average load current; 2 D N =, if I 2n < I 2n,B 2 1 D + I2 4 n

3 A neural controller for on board tracking platform 215 I I 2n 2n = is the normalized average load current; I2B,max ton D = is the duty cycle of the switch; T U N = 2 is the equivalent transformer ration of the DC-DC U1 converter, U 1 is the input converter tension and U 2 is the output converter tension. 2. for the boundary between discontinuous and continuous mode: N=D if I 2n = I 2n,B, I 2 B where: I 2 n,b = = 4D( 1 D) is the normalized average load current in I 2 B,max boundary mode; I 2B the average load current in boundary mode, U1 I2B,max = the maximum of I 2B. 8 fl 3. for the continuous mode: N =D if I 2n > I 2n, B, 1 where: f = is the switching frequency. T From the equations above, it seen that the family of external characteristics of a DC-DC converter for N = U 2 /U 1 as a function of I 2n and with D as parameter in all modes of operation for a constant U 1, is nonlinear. To linearize these converter external characteristics at discontinuous conduction mode the look-up table method of Ohmae is suggested [9]. 3. NEURAL CONTROLLER DESIGN FOR COMMAND THE DC MOTOR From [5] and [11] can be seen that in practical DC motors applications with neural controllers one obtains better results for rise time, overshot, speed drop and recovery time than in case of classical controller. The advantage of using the first controller is that of an implemented hardware or software possibility. Hardware, the relation F(D) = f (D, I 2N ) representing the rule base, can be stored in the form of a look-up table in microcomputer s memory. Software, a single subroutine can be accessed by all the neural converters in the control loop, with different data basis. In this paper is presented a method based on learning by example in order to design the neural controller based on competitive learning network with feedforward connections.

216 Octavian Grigore-Müler 4 In the simplest form of competitive learning, the neural network has a single layer of output neurons, each of which is fully connected to the input nodes [5]. The network may include feedback connections among the neurons, as indicated in Fig. 3. In the network architecture the feedback connections perform lateral inhibition, with each neuron tending to inhibit the neuron to which it is laterally connected. In contrast the feedforward synaptic connections in the network are all excitatory. Fig. 3 Weights initialization architectural graph of a competitive learning network with feedforward connections and lateral connections. For a neuron k to be the winning neuron, its induced local fields v k for a specified input pattern x must be the largest among all the neuron in the network. The output signal y k of winning neuron k is set equal to one; the output signal of all the neurons that lose the competition are set equal to zero. We thus it ca write: 1 if vk > v j for all j, j k yk =, 0 otherwise where the induced local field v k represents the combined action of all the forward and feedback inputs to neuron k. Let w kj denote the synaptic weight connecting input node j to neuron k. Suppose that each neuron is allotted a fixed amount of synaptic weight which is distributed among its input nodes, that is: wkj = 1, for all k. j

5 A neural controller for on board tracking platform 217 A neuron then learns by shifting synaptic weights from its inactive to active input nodes. If a neuron does not respond to a particular input pattern, no learning takes place in that neuron. If a particular neuron wins the competition, each input node of neuron relinquishes some proportion of synaptic weight, and the weight relinquished is then distributed equally among the active input nodes. According to the standard competitive learning rule, the change w kj of synaptic weight w kj is defined by: w kj ( xj wkj) if the neuron k wins the competition η = 0 if the neuron k loses the competition. where η is the learning rate parameter. The rule has the overall effect of moving the synaptic weight vector w k of winning neuron k toward the input pattern x. Fig. 4 The on board tracking platform on a AWACS. 4. NEURAL CONTROLLER FOR COMMAND THE DIRECTLY ON BOARD PLATFORM To design the neural controller that commands the on board platform of an AWACS aircraft let s consider in the DC-DC external converter characteristic D = 0.7 [5].

218 Octavian Grigore-Müler 6 Fig. 5 The kinematics system and the parameters needed in a tracking scenario. To determine the input for neural controller that command the DC motor which drive the directly platform it must be designed first an automatic flight control system that tracks mobile target. The tracking scenario is illustrated in [3] and [4] and in Fig. 5. From these we assumed that the AWACS airplane flies at approximately 40,000 ft with a 0.8 Mach number. In this case the linear equations of motion of the airplane in vertical plane are: u 0.006868 0.01395 0 32.2 u w 0.09055 0.3151 773.98 0 w = + q 0.0001187 0.001026 0.4285 0 q θ 0 0 1 0 θ 0.00187 9.66 17.85 0 δe + 1.158 0 δ t 0 0

7 A neural controller for on board tracking platform 219 and, respectively, in horizontal plane are: v 0.0558 0 235.9 32.2 v p 0.003865 0.4342 0.4136 0 p = + r 0.001086 0.006112 0.1458 0 r Φ 0 0 1 0 Φ 0 5.642 0.1434 0.1144 δr +, 0.003741 0.4859 δ a 0 0 where: u is the x component of airspeed vector of airplane mass center V; w the z component of airspeed vector of airplane mass center V; q the y component of angular velocity vector of the airplane ω; θ the y component of attitude angles pitch angle; v the y component of airspeed vector of airplane mass center V; p the x component of angular velocity vector of the airplane ω; r the z component of angular velocity vector of the airplane ω; φ the x component of attitude angles bank angle; δ e is the elevator command of airplane; δ t is the throttle command; δ r is the ruder command of airplane; δ a is the aileron command. Applying commands on the airplane the kinematics parameters Φ, which is the line of sight angle in longitudinal plane, Γ, which is the line of sight angle in vertical plane, and R, the distance between airplane and satellite, will be changed. The kinematics angles with aide of two taho-generators, that has the constant k TG = = 2 /V s, are transformed in the command tension u c of the characteristics of a DC servomotor: 100 100 100 2 100 2 6 1 0.0003 6 1 1 + + 1 + 6 6 θm ( s ) = c( ) c( ) 820 6 u s = 820 6 u s = s 1 s + s 1+ s ( 1+ 0.0003) 6 + 100 2 6 + 100 2 1 0.48 1 0.02 0.5 0.5 = uc( s) = uc( s) = uc( s). s1+ 23.88s s s+ 0.04 s s+ 0.04 Practically θ m is the output of the two DC servomotors, one in the horizontal plane and other in the vertical plane. With these functions one train the neural controller which command those two DC servomotors. Then because the output of automatic flight control system is continuous and the output of the DC motor must be also continue, those are also the values which

220 Octavian Grigore-Müler 8 are training the network, it must applied a clustering method to assign these in a finite classes. Fig. 6 The trajectory of aircraft and missile and tracking system parameters for R 0 =1000 km, Φ 0 = 45 and Γ= 0. For example the values command of on board platform in lateral plane of the aircraft are between 180 and 180. Dividing this domain in 18 subclasses corresponding to a number of 18 output winning neurons (a neuron cover a class of 20 dimension). Like input it was choose one neuron represented the output of speed transducer block (Fig. 2). Also from optimizing the learning algorithm results two hidden layers with 4 and respectively 5 neurons. In Figs. 6 and 7 is represented the aircraft trajectory, the line of sight angle Φ in longitudinal plane and line of sight angle Γ in lateral plane, angles which command the DC motor of directly platform in longitudinal plane, respectively in the lateral plane for R 0 =1000 km, Φ 0 = 45 o, Γ 0 = 0 o and R 0 = 315 km, Φ 0 = 30 o, Γ 0 = 45 o.

9 A neural controller for on board tracking platform 221 Fig. 7 The trajectory of aircraft and missile and tracking system parameters for R 0 =315 km, Φ 0 = 30 and Γ= 45. Also in those Figs. is represented the output of DC motor (an angle of motion, one in horizontal plane θ l,neural and another in the vertical plane θ neural ), that is in fact the integration of the neural network output. 5. CONCLUSIONS Speaking from the quality point for view it can see from Fig.s above that the neural controller that command the DC motors tracking well the line of sight angle, that means the missile target. Speaking from the quantity point for view a neural controller is more cheaper and more lighter than a classical one (characteristics more important for an airplane) and also is elementary to connect them to the airplane s digital bus (in accordance with ARINC 429) Received on June 16, 2008

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