Fuzzy logic and neural network system identification for high alpha delta wing maneuvers with deployable control surfaces

Fuzzy logic and neural network system-identification and control techniques are employed in highalpha delta-wing unsteady aerodynamics. A delta wing, equipped with cavity flaps or an apex flap, is executing pitch-up maneuvers while the flaps are dynamically employed, aiming to modify and control the behavior of the two leading-edge vortical structures and thus their effect on the pressure distribution and aerodynamic loading of the wing. First a fuzzy identifier is constructed to predict the temporal evolution of the leeward pressure distribution and the aerodynamic loads for given time histories of pitching, a(f), a(t) and flap deployment (t), (t). Introduction The aerodynamics of supermaneuver-perfbrming aircraft has been a great challenge to aerodynamicists but still many questions in this area are unanswered. This is partly due to shortage of wind-tunnel hardware able to simulate complex maneuvers of sensorinstrumented models and allow the measurement of the properties of the model flowfield interaction. Moreover, when the control of these interactions is desired, the task becomes understandably overwhelming: different flow-control devices have to be tested, each one at several different dynamic deployment schedules and rates, as well as testing of combinations of flow-control devices. While a sufficiently large data bank of these ** Research Associate t Asst. Professor, Member AIAA * Research Assistant ft Professor, Associate Fellow AIAA Copyright © 1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. test data has been generated, then the daunting question emerges: How is all this information efficiently implemented into the next generation super-agile aircraft? Since the rapid rates of motion during a supermaneuver are beyond the pilot's response limits, an active controller between the pilot and the aircraft is necessary. To reinforce the gravity of the problem, along comes the inadequacy of the conventional adaptive control schemes: the high rates and large motion amplitudes involved in a supermaneuver preclude the local linearization of the strongly nonlinear governing, equations. Schreck et al demonstrated application in unsteady aerodynamics of system-identification and modern control methods based on the use of artificial neural networks (ANN). There', ANNs were shown to successfully model vortex dynamics principles. Further attempts were also reported later'. Fuzzy logic systems (FLS) appear to be equally capable system identifiers. Comparisons of the two techniques', i.e., ANN versus FLS in different applications seem to favor the latter. However, we believe that neural networks and fuzzy logic have complementary strengths and a symbiotic relationship between the two holds the secret to effective system identification and control. In this paper we first demonstrate that FLS and ANN can successfully identify non-linear aerodynamic systems. Our system consists of a pitching delta wing with dynamically deployed flaps during the maneuver. We identify the effect this system has on the temporal evolution of the leeward-side pressure distribution as well as the aerodynamic loads. Once a system model has been generated a fuzzy controller will be constructed with the objective to control the cavityflap deployment schedule during pitch-up, so that a certain optimization criterion is satisfied, for example, the maximizing of the ratio L/D (lift over drag) for all times during the maneuver. Facilities and Instrumentation FUZZY Logic Systems (FLS) The present research was conducted in the VPI & SU Stability Wind Tunnel and the ESM Wind Tunnel. The first has a 6' x 6' test section and an excellent quality of flow. This tunnel has been recently equipped with a dynamic strut which was given the acronym DyPPiR for "Dynamic-Plunge-Pitch-RolP mechanism. The design, construction and calibration of this facility involved many faculty at VPI&SU, under the direction of Dr. Roger Simpson and five years of intensive work. A discussion of the main elements of the design can be found in Ref. 6 and the accompanying instrumentation La Ref. 7. The DyPPiR can provide simultaneous plunging, pitching and rolling of models on the order of 100 Ib in weight, at a frequency of up to 10 Hz, depending on the amplitude of the motion. These motions can be independently controlled by software. Any combination of arbitrary motions is possible. In this case, pitch up motions are executed. Such motions have been tested earlier in two much smaller facilities', a wind tunnel and a water tunnel and at Reynold numbers of the order of 10. Simultaneous plunging of the DyPPiR carriage and pitching of the pitch actuator induces pitching of the model about its quarter-chord axis. The aim here is to control the leading edge vortices and delay breakdown, while pitching up to high angles of attack. This is pursued by deploying cavity flaps. In the present experiments we employ a 2' x 3' delta wing model (Fig. 1) which has been tested extensively in this facility in steady flow. The model is hollow to provide space for instrumentation. The top surface of the model is equipped with three rows of pressure taps. Pressure transducers are positioned beneath the instrumented surface to provide unsteady pressures with a high frequency response. Fifteen pressure ports were aligned with a normal to the leading edge, at a distance of x/c = 0.61 from the apex. A 32-transducer Electronic Pressure Scanner (ESP) from PSI, Inc. with a pressure full scale of ± 20 in H^O was employed. The ESM Pressure Scanner was interfaced with a laboratory computer and was on-line calibrated through instrumentation by AEROPROBE Corp. The system consists of an ESP interface/dataacquisition board PDA-3101 (31 KHz max sampling rate) and an ACCUPRES computer-controlled, online pressure calibrator. Figures 2(a) and 2(b) present the coordinate system used and the pressure port distribution, respectively. A recently developed field in mathematics, the theory of fuzzy sets and the logic stemming from it has been gaining ground as a system identifier, sometimes at the expense of ANN popularity. In fact, in the semiconductor industry, microcontroller pundits predict that semiconductor-based fuzzy technology will be as prevalent in products by the end of the decade as microprocessor technology is today. Although traditionally, fuzzy logic has been viewed as a technique for representing imprecise, ambiguous and vague information, nothing prevents it from successfully dealing with concrete, quantitative and precise data. In fact, the Universal Approximation Theorem stated below proves that fuzzy logic systems are capable of uniformly approximating any nonlinear function to any degree of accuracy. Figure 3 presents a schematic of the basic configuration of the fuzzy logic systems proposed hi this work. The fuzzy rule base consists of a collection of fuzzy if-then rules in the following form: flW : If an is F£ and ...and xn is F^.THEN y is G*v. where F/ and G are fuzzy sets, x. =(zi,...,xn) , y are the input and output linguistics variables, respectively, and I = l,...,Af with M being the numbers of rules. However, in engineering systems, inputs and outputs are real-valued variables in crisp sets and not linguistic variables hi fuzzy sets. The conversion from the former to the latter and vice-versa is achieved through the fuzzifier and defuzzifier respectively. The fuzzy inference engine is the heart of the system and maps the fuzzy inputs to the fuzzy outputs, properly employing the rules from the fuzzy rule base. In one of our approaches we use center average defuzzifier, productinference rule, singleton fuzzifier and Gaussian membership function. Then the fuzzy system reduces to: where x_ = (xi...,xn) eU (U is the universe of discourse) is the input vector, n is the number of antecedents (inputs) and M is the number of rules. +xj>&i,i a* th parameters of the Gaussian membership functions and j^ are the centers of the output fuzzy sets. Although our techniques are capable of identifying multi-input, multi-output systems, here to facilitate the reader's understanding, a multi-input, single-output system is presented. We state here the following University Approximation Theorem: For any given real and continuous function g on a compact set ufR and arbitrary e > 0 there exists a fuzzy logic system / in the form of (A) such that