A hybrid fuzzy logic proportional- integral-derivative and conventional on-off controller for morphing wing actuation using shape memory alloy Part 1: Morphing system mechanisms and controller architecture design

The present paper describes the design of a hybrid actuation control concept, a fuzzy logic proportional-integral-derivative plus a conventional on-off controller, for a new morphing mechanism using smart materials as actuators, which were made from shape memory alloys (SMA). The research work described here was developed for the open loop phase of a morphing wing system, whose primary goal was to reduce the wing drag by delaying the transition (from laminar to fully turbulent flows) position toward the wing trailing edge. The designed controller drives the actuation system equipped with SMA actuators to modify the flexible upper wing skin surface. The designed controller was also included, as an internal loop, in the closed loop architecture of the morphing wing system, based on the pressure information received from the flexible skin mounted pressure sensors and on the estimation of the transition location. The controller’s purposes were established following a comprehensive presentation of the morphing wing system architecture and requirements. The strong nonlinearities of the SMA actuators’ characteristics and the system requirements led to the choice of a hybrid controller THE AERONAUTICAL JOURNAL MAY 2012 VOLUME 116 NO 1179 433 A hybrid fuzzy logic proportionalintegral-derivative and conventional on-off controller for morphing wing actuation using shape memory alloy Part 1: Morphing system mechanisms and controller architecture design T. L. Grigorie, R. M. Botez and A. V. Popov École de Technologie Supérieure Montréal, Québec, Canada M. Mamou and Y. Mébarki National Research Council Ottawa, Ontario, Canada Paper No. 3699(i). Manuscript received 12 February 2011, revised version received 2 September 2011, accepted 13 October 2011. architecture as a combination of a bi-positional on-off controller and a fuzzy logic controller (FLC). In the chosen architecture, the controller would behave as a switch between the SMA cooling and heating phases, situations where the output current is 0A or is controlled by the FLC. In the design phase, a proportional-integral-derivative scheme was chosen for the FLC. The input-output mapping of the fuzzy model was designed, taking account of the system’s error and its change in error, and a final architecture for the hybrid controller was obtained. The shapes chosen for the inputs’ membership functions were s-function, π-function, and z-function, and product fuzzy inference and the center average defuzzifier were applied (Sugeno). NOMENCLATURE A fuzzy set in the antecedent associated individual antecedent fuzzy sets of each input variable B fuzzy set in the antecedent scalar offset dY1, dY2 displacements of the two control points of the flexible skin dY1opt optimal vertical displacement of actuator 1 dY2opt optimal vertical displacement of actuator 2 dY1real real vertical displacement of actuator 1 dY2real real vertical displacement of actuator 2 e actuation loop error FLC fuzzy logic controller FP fuzzy proportional controller Faero aerodynamic force Fskin elastic force produced by the flexible skin Fspring elastic force of the gas spring f a crisp function in the consequent (a polynomial function) i(t) command variable (electrical current in the present case) KD derivative gain KI integral gain KO change in output gain KP proportional gain k discrete step M Mach number mf membership function N number of rules q number of inputs Re Reynolds number TD derivative time constant Ts sample period t time w(x) degree of fulfillment of the antecedent, i.e., the level of firing of the ith rule x independent variable on the universe of discourse xleft left breakpoint xq individual input variables xright right breakpoint x input vector 434 THE AERONAUTICAL JOURNAL MAY 2012